Institute for Mathematics and its Applications University of Minnesota 114 Lind Hall 207 Church Street SE Minneapolis, MN 55455 
20102011 Program
See http://www.ima.umn.edu/20102011/ for a full description of the 20102011 program on Simulating Our Complex World: Modeling, Computation and Analysis.
20102011 IMA Participating Institutions Conferences
All Day  Morning Chair: Richard S. Falk (Rutgers University) Afternoon Chair: Jan S. Hesthaven (Brown University)  W11.15.10  
8:30am9:00am  Coffee  Keller Hall 3176  W11.15.10  
9:00am9:45am  Two grids approximation of non linear eigenvalue problems  Yvon Jean Maday (Université de Paris VI (Pierre et Marie Curie))  Keller Hall 3180  W11.15.10 
9:45am10:30am  Exterior calculus and the finite element approximation of Maxwell's eigenvalue problem  Daniele Boffi (Università di Pavia)  Keller Hall 3180  W11.15.10 
10:30am11:00am  Coffee break  W11.15.10  
11:00am11:45am  Trefftzdiscontinuous Galerkin methods for timeharmonic wave problems  Ilaria Perugia (Università di Pavia)  Keller Hall 3180  W11.15.10 
11:45am2:00pm  Lunch  W11.15.10  
2:00pm2:45pm  New algorithms for high frequency wave propagation  Bjorn Engquist (University of Texas at Austin)  Keller Hall 3180  W11.15.10 
2:45pm3:30pm  A new class of adaptive discontinuous PetrovGalerkin (DPG) finite element (FE) methods with application to singularly perturbed problems  Leszek Feliks Demkowicz (University of Texas at Austin)  Keller Hall 3180  W11.15.10 
3:30pm4:00pm  Coffee break  Keller Hall 3176  W11.15.10  
4:00pm4:45pm  Absolutely stable IPDG and LDG methods for high frequency wave equations  Xiaobing Henry Feng (University of Tennessee)  Keller Hall 3180  W11.15.10 
All Day  Morning Chair: Ronald H.W. Hoppe (University of Houston) Afternoon Chair: Ricardo H. Nochetto (University of Maryland)  W11.15.10  
8:30am9:00am  Coffee  Keller Hall 3176  W11.15.10  
9:00am9:45am  Sparse tensor Galerkin discretizations for first order transport problems  Christoph Schwab (ETH Zürich)  Keller Hall 3180  W11.15.10 
9:45am10:30am  New efficient spectral methods for highdimensional PDEs and for FokkerPlanck equation of FENE dumbbell model  Jie Shen (Purdue University)  Keller Hall 3180  W11.15.10 
10:30am11:00am  Coffee break  W11.15.10  
11:00am11:45am  Stable enrichment and treatment of complex domains in the particle–partition of unity method  Marc Alexander Schweitzer (Rheinische FriedrichWilhelmsUniversität Bonn)  Keller Hall 3180  W11.15.10 
11:45am2:00pm  Lunch  W11.15.10  
2:00pm2:45pm  Adaptive tensor product wavelet methods for solving wellposed operator equations  Rob Stevenson (Universiteit van Amsterdam)  Keller Hall 3180  W11.15.10 
2:45pm3:30pm  Variational consistent discretization schemes and numerical algorithms for contact problems  Barbara Wohlmuth (Technical University of Munich )  Keller Hall 3180  W11.15.10 
5:00pm6:30pm  Social "hour" Stub and Herbs 227 Oak St Minneapolis, MN 55414  Stub and Herbs 227 Oak St Minneapolis, MN 55414 (612) 3790555 
W11.15.10 
All Day  Morning Chair: Lucia Gastaldi (Università di Brescia) Afternoon Chair: Ragnar Winther (University of Oslo)  W11.15.10  
8:30am9:00am  Coffee  Keller Hall 3176  W11.15.10  
9:00am9:45am  A different look at transport problems  Wolfgang Dahmen (RWTH Aachen)  Keller Hall 3180  W11.15.10 
9:45am10:30am  Spacetime adaptive wavelet methods for control problems constrained by parabolic PDEs  Angela Kunoth (Universität Paderborn)  Keller Hall 3180  W11.15.10 
10:30am11:00am  Coffee break  W11.15.10  
11:00am11:45am  Isogeometric Analysis of Fluids, Structures and FluidStructure Interaction  Yuri Bazilevs (University of California, San Diego)  Keller Hall 3180  W11.15.10 
11:45am2:00pm  Lunch  W11.15.10  
2:00pm2:45pm  Adaptive data analysis via nonlinear compressed sensing  Thomas Yizhao Hou (California Institute of Technology)  Keller Hall 3180  W11.15.10 
2:45pm3:30pm  The adaptive Anisotropic PML method for timeharmonic acoustic and electromagnetic scattering problems  Zhiming Chen (Chinese Academy of Sciences)  Keller Hall 3180  W11.15.10 
3:30pm4:00pm  Coffee break  Keller Hall 3176  W11.15.10  
4:00pm5:00pm  Roundtable/Discussion Panel Moderator: ChiWang Shu (Brown University)  Keller Hall 3180  W11.15.10 
All Day  Chair: Claudio Canuto (Politecnico di Torino)  W11.15.10  
8:30am9:00am  Coffee  Keller Hall 3176  W11.15.10  
9:00am9:45am  Optimizationbased computational modeling, or how to achieve better predictiveness with less complexity  Pavel B. Bochev (Sandia National Laboratories)  Keller Hall 3180  W11.15.10 
9:45am10:30am  Finite element discretizations of the contact between two membranes  Christine Bernardi (Université de Paris VI (Pierre et Marie Curie))  Keller Hall 3180  W11.15.10 
10:30am11:00am  Coffee break  W11.15.10  
11:00am11:45am  HDG methods for secondorder elliptic problems  Bernardo Cockburn (University of Minnesota)  Keller Hall 3180  W11.15.10 
11:45am11:50am  Closing remarks  Keller Hall 3180  W11.15.10  
12:30pm1:30pm  Registration and coffee  Keller Hall 3176  SW11.56.10  
1:30pm1:45pm  Welcome to the IMA  Fadil Santosa (University of Minnesota)  Keller Hall 3180  SW11.56.10 
1:45pm3:15pm  Contributed talks  Keller Hall 3180  SW11.56.10  
3:15pm3:45pm  Group photo/coffee break  Keller Hall 3176  SW11.56.10  
3:45pm4:45pm  Contributed talks  Keller Hall 3180  SW11.56.10  
4:45pm5:30pm  Plenary talk: On the lumped mass finite element method for parabolic problems  Vidar Thomée (Chalmers University of Technology)  Keller Hall 3180  SW11.56.10 
6:00pm8:00pm  Conference banquet at Campus Club  Campus Club 4th Floor Coffman Memorial Union 
SW11.56.10 
8:30am9:00am  Coffee  Keller Hall 3176  SW11.56.10  
9:00am9:45am  Plenary talk: Analysis of a Cartesian PML approximation to an acoustic scattering problem  James H. Bramble (Texas A & M University)  Keller Hall 3180  SW11.56.10 
9:45am10:30am  Contributed talks  Keller Hall 3180  SW11.56.10  
10:30am11:00am  Coffee break  Keller Hall 3176  SW11.56.10  
11:00am12:00pm  Contributed talks  Keller Hall 3180  SW11.56.10  
12:00pm1:30pm  Lunch  Study areas, Keller Hall Atrium  SW11.56.10  
1:30pm2:45pm  Contributed talks  Keller Hall 3180  SW11.56.10  
2:45pm3:15pm  Coffee break  Keller Hall 3176  SW11.56.10  
3:15pm4:15pm  Contributed talks  EE/CS 3180  SW11.56.10  
4:15pm5:00pm  Plenary talk: Canonical families of finite elements  Douglas N. Arnold (University of Minnesota)  Keller Hall 3180  SW11.56.10 
10:45am11:15am  Coffee break  Lind Hall 400 
10:45am11:15am  Coffee break  Lind Hall 400  
11:15am12:15pm  Robust numerical solution of singularly perturbed problems  Niall Madden (National University of Ireland, Galway)  Lind Hall 305  PS 
7:00pm8:00pm  Arnold family lecture: Burst, cascades, and hot spots: A glimpse of some online social phenomena at global scales  Jon Kleinberg (Cornell University)  Willey Hall 175  PUB11.9.10 
10:45am11:15am  Coffee break  Lind Hall 400  
11:15am12:15pm  The generalized finite element method  Uday Banerjee (Syracuse University)  Lind Hall 305 
10:45am11:15am  Coffee break  Lind Hall 400  
11:15am12:15pm  Special course: Finite element exterior calculus  Douglas N. Arnold (University of Minnesota)  Lind Hall 305 
10:45am11:15am  Coffee break  Lind Hall 400  
11:15am12:15pm  The generalized finite element method  Uday Banerjee (Syracuse University)  Lind Hall 305  
1:25pm2:25pm  A perspective on the use of mathematics in industry  Jeffrey Abell (General Motors)  Vincent Hall 16  IPS 
10:45am11:15am  Coffee break  Lind Hall 400  
2:00pm3:30pm  An introduction to the a posteriori error analysis of elliptic optimal control problems  Ronald H.W. Hoppe (University of Houston)  Lind Hall 305 
10:45am11:15am  Coffee break  Lind Hall 400  
11:15am12:15pm  Discontinuous Galerkin approximation for the VlasovPoisson system  Blanca Ayuso de Dios (Centre de Recerca Matemàtica )  Lind Hall 305  PS 
10:45am11:15am  Coffee break  Lind Hall 400  
2:00pm3:30pm  An introduction to the a posteriori error analysis of elliptic optimal control problems  Ronald H.W. Hoppe (University of Houston)  Lind Hall 305 
10:45am11:15am  Coffee break  Lind Hall 400  
11:15am12:15pm  Special course: Finite element exterior calculus  Douglas N. Arnold (University of Minnesota)  Lind Hall 305 
10:45am11:15am  Coffee break  Lind Hall 400 
10:45am11:15am  Coffee break  Lind Hall 400 
10:45am11:15am  Coffee break  Lind Hall 400  
11:15am12:15pm  TBA  Sylvain Nintcheu Fata (Oak Ridge National Laboratory)  PS 
10:45am11:15am  Coffee break  Lind Hall 400 
All Day  Thanksgiving holiday. The IMA is closed. 
All Day  Floating holiday. The IMA is closed. 
All Day  Morning Chair: Liyeng Sung (Louisiana State University)
Afternoon Chair: Susanne C. Brenner(Louisiana State University)  T11.2829.10  
8:30am9:00am  Registration and coffee  Keller Hall 3176  T11.2829.10  
9:00am10:30am  Geometric Multigrid Methods  Susanne C. Brenner (Louisiana State University)  Keller Hall 3180  T11.2829.10 
10:30am11:00am  Break  Keller Hall 3176  T11.2829.10  
11:00am12:30pm  An algebraic multigrid tutorial  Robert Falgout (Lawrence Livermore National Laboratory)  Keller Hall 3180  T11.2829.10 
12:30pm2:00pm  Lunch  T11.2829.10  
2:00pm3:30pm  Domain decomposition methods for partial differential equations  David Keyes King Abdullah University of Science & Technology, Columbia University  Keller Hall 3180  T11.2829.10 
3:30pm4:00pm  Break  Keller Hall 3176  T11.2829.10  
4:00pm5:30pm  An introduction to domain decomposition algorithms  Olof B. Widlund (New York University)  Keller Hall 3180  T11.2829.10 
All Day  Chair: Robert Falgout (Lawrence Livermore National Laboratory)  T11.2829.10  
All Day  Chair: Ulrich Rüde (FriedrichAlexanderUniversität ErlangenNürnberg) General announcements during the week: Susanne C. Brenner (Louisiana State University)  W11.2912.3.10  
8:15am8:45am  Coffee  Keller Hall 3176  T11.2829.10  
8:45am10:15am  Adaptive finite element methods  Ricardo H. Nochetto (University of Maryland)  Keller Hall 3180  T11.2829.10 
10:15am10:45am  Break  Keller Hall 3176  T11.2829.10  
10:45am12:15pm  A parallel computing tutorial  Ulrike Meier Yang (Lawrence Livermore National Laboratory)  Keller Hall 3180  T11.2829.10 
1:15pm2:00pm  Registration and coffee  Keller Hall 3176  W11.2912.3.10  
2:00pm2:15pm  Welcome to the IMA  Fadil Santosa (University of Minnesota)  Keller Hall 3180  W11.2912.3.10 
2:15pm3:00pm  Some algorithmic aspects of hpadaptive finite elements  Randolph E. Bank (University of California, San Diego)  Keller Hall 3180  W11.2912.3.10 
3:00pm3:45pm  Why it is so difficult to solve Helmholtz problems with iterative methods  Martin J. Gander (Universite de Geneve)  Keller Hall 3180  W11.2912.3.10 
3:45pm4:00pm  Group photo  W11.2912.3.10  
4:00pm5:30pm  Reception and Poster Session Poster submissions welcome from all participants Instructions  Lind Hall 400  W11.2912.3.10  
Domain decomposition preconditioning for the hpversion of the discontinuous Galerkin method  Paola Francesca Antonietti (Politecnico di Milano)  
Twolevel additive Schwarz preconditioners for the local discontinuous Galerkin method  Andrew T. Barker (Louisiana State University)  
Multigrid methods for twodimensional Maxwell's equations on graded meshes  Jintao Cui (University of Minnesota)  
Fast adaptive collocation by radial basis functions  Tobin A. Driscoll (University of Delaware)  
Adaptive solution of parametric eigenvalue problems for partial differential equations  Joscha Gedicke (HumboldtUniversität)  
Adaptivity for the Hodge decomposition of Maxwell's equations  Joscha Gedicke (HumboldtUniversität)  
An efficient rearrangement algorithm for shape optimization on eigenvalue problems  ChiuYen Kao (Ohio State University)  
Scalable electromagnetic simulations with the Auxiliaryspace Maxwell Solver (AMS)  Tzanio V Kolev (Lawrence Livermore National Laboratory)  
Convergence and optimality of adaptive finite element methods  Christian Kreuzer (Universität DuisburgEssen)  
HLU factorization of stabilized saddle point problems  Sabine Le Borne (Tennessee Technological University)  
A comparison of two domain decomposition methods for a linearized contact problem  Jungho Lee (Argonne National Laboratory)  
3D boundary integral analysis by a precorrected fast Fourier transform algorithm  Sylvain Nintcheu Fata (Oak Ridge National Laboratory)  
Twolevel additive Schwarz preconditioners for a weakly overpenalized symmetric interior penalty method  EunHee Park (Louisiana State University)  
Energy minimization algebraic multigrid: Robustness and flexibility in multilevel software  Ray S. Tuminaro (Sandia National Laboratories)  
Finite element analysis and a fast solver approach to a nonlocal dielectric continuum model  Dexuan Xie (University of Wisconsin)  
Hypre: A scalable linear solver library  Ulrike Meier Yang (Lawrence Livermore National Laboratory)  
A jumping multigrid method via finite element extrapolation  Shangyou Zhang (University of Delaware) 
All Day  Morning Chair: Ronald H.W. Hoppe (University of Houston) Afternoon Chair: Ulrike Meier Yang (Lawrence Livermore National Laboratory)  W11.2912.3.10  
8:30am9:00am  Coffee  Keller Hall 3176  W11.2912.3.10  
9:00am9:45am  Fast Solvers for Higher Order Problems  Susanne C. Brenner (Louisiana State University)  Keller Hall 3180  W11.2912.3.10 
9:45am10:30am  Nonsmooth Schur Newton Methods and Applications  Ralf Kornhuber (Freie Universität Berlin)  Keller Hall 3180  W11.2912.3.10 
10:30am11:00am  Coffee break  Keller Hall 3176  W11.2912.3.10  
11:00am11:45am  Nonlinear Multigrid Revisited  Irad Yavneh (TechnionIsrael Institute of Technology)  Keller Hall 3180  W11.2912.3.10 
11:45am2:00pm  Lunch  W11.2912.3.10  
2:00pm2:45pm  Multilevel iterative methods for PDEs based on one or no grid  Jinchao Xu (Pennsylvania State University)  Keller Hall 3180  W11.2912.3.10 
2:45pm3:30pm  Domain Decomposition Solvers for PDEs: Some Basics, Practical Tools, and New Developments  Clark R. Dohrmann (Sandia National Laboratories)  Keller Hall 3180  W11.2912.3.10 
All Day  Morning Chair: Guido Kanschat (Texas A & M University) Afternoon Chair: Ludmil Zikatanov (Pennsylvania State University)  W11.2912.3.10  
8:30am9:00am  Coffee  Keller Hall 3176  W11.2912.3.10  
9:00am9:45am  Towards Exascale Computing: Multilevel Methods and Flow Solvers for Millions of Cores  Ulrich Rüde (FriedrichAlexanderUniversität ErlangenNürnberg)  Keller Hall 3180  W11.2912.3.10 
9:45am10:30am  Preconditioning Interior Penalty Discontinuous Galerkin Methods  Blanca Ayuso de Dios (Centre de Recerca Matemàtica )  Keller Hall 3180  W11.2912.3.10 
10:30am11:00am  Coffee break  Keller Hall 3176  W11.2912.3.10  
11:00am11:45am  Preconditioners for interface problems in Eulerian formulations  David Keyes King Abdullah University of Science & Technology, Columbia University  Keller Hall 3180  W11.2912.3.10 
11:45am2:00pm  Lunch  W11.2912.3.10  
2:00pm2:45pm  Compatible Relaxation in Algebraic Multigrid  Robert Falgout (Lawrence Livermore National Laboratory)  Keller Hall 3180  W11.2912.3.10 
2:45pm3:30pm  New Domain Decomposition Algorithms from Old  Olof B. Widlund (New York University)  Keller Hall 3180  W11.2912.3.10 
5:00pm6:30pm  Social "hour" Stub and Herbs 227 Oak St Minneapolis, MN 55414  Stub and Herbs 227 Oak St Minneapolis, MN 55414 (612) 3790555 
W11.2912.3.10 
All Day  Morning Chair: Xiaobing Henry Feng (University of Tennessee) Afternoon Chair: Uday Banerjee (Syracuse University)  W11.2912.3.10  
8:30am9:00am  Coffee  Keller Hall 3176  W11.2912.3.10  
9:00am9:45am  Optimally Blended SpectralFinite Element Scheme for Wave Propagation, and NonStandard Reduced Integration  Mark Ainsworth (University of Strathclyde)  Keller Hall 3180  W11.2912.3.10 
9:45am10:30am  Local and global approximation of gradients with piecewise polynomials  Andreas Michael Veeser (Università di Milano)  Keller Hall 3180  W11.2912.3.10 
10:30am11:00am  Coffee break  Keller Hall 3176  W11.2912.3.10  
11:00am11:45am  A Parallel, Adaptive, FirstOrder System LeastSquares (FOSLS) Algorithm for Incompressible, Resistive Magnetohydrodynamics  Thomas A. Manteuffel (University of Colorado)  Keller Hall 3180  W11.2912.3.10 
11:45am2:00pm  Lunch  W11.2912.3.10  
2:00pm2:45pm  Implicit Solution Approaches: Why We Care and How We Solve the Systems  Carol S. Woodward (Lawrence Livermore National Laboratory)  Keller Hall 3180  W11.2912.3.10 
2:45pm3:30pm  Coupled atmosphere  wildland fire numerical simulation by WRFFire  Jan Mandel (University of Colorado)  Keller Hall 3180  W11.2912.3.10 
3:30pm4:00pm  Coffee break  Keller Hall 3176  W11.2912.3.10  
4:00pm5:00pm  Roundtable/discussion Moderator: Robert Falgout (Lawrence Livermore National Laboratory)  Keller Hall 3180  W11.2912.3.10 
All Day  Morning Chair: Axel Klawonn (Universität DuisburgEssen) Afternoon Chair: Susanne C. Brenner (Louisiana State University)  W11.2912.3.10  
8:30am9:00am  Coffee  Keller Hall 3176  W11.2912.3.10  
9:00am9:45am  Developing fast and scalable implicit methods for shallow water equations on cubedsphere  XiaoChuan Cai (University of Colorado)  Keller Hall 3180  W11.2912.3.10 
9:45am10:30am  Domain Decomposition for the Wilson Dirac Operator  Andreas Frommer (Bergische UniversitätGesamthochschule Wuppertal (BUGH))  Keller Hall 3180  W11.2912.3.10 
10:30am11:00am  Coffee break  Keller Hall 3176  W11.2912.3.10  
11:00am11:45am  A posteriori error estimator competition for 2ndorder partial differential equations^{*}  Carsten Carstensen (Yonsei University)  Keller Hall 3180  W11.2912.3.10 
11:45am2:00pm  Lunch  W11.2912.3.10  
2:00pm2:45pm  Projection based model reduction for shape optimization of the Stokes system  Ronald H.W. Hoppe (University of Houston)  Keller Hall 3180  W11.2912.3.10 
2:45pm3:30pm  Convergence rates of AFEM with H ^{1} Data  Ricardo H. Nochetto (University of Maryland)  Keller Hall 3180  W11.2912.3.10 
Event Legend: 

IPS  Industrial Problems Seminar 
PS  IMA Postdoc Seminar 
PUB11.9.10  Arnold Family Lecture  Jon Kleinberg: Burst, Cascades, and Hot Spots: A Glimpse of Some OnLine Social Phenomena at Global Scales 
SW11.56.10  Finite Element Circus featuring a Scientific Celebration of Falk, Pasciak, and Wahlbin 
T11.2829.10  Fast Solution Techniques 
W11.15.10  Numerical Solutions of Partial Differential Equations: Novel Discretization Techniques 
W11.2912.3.10  Numerical Solutions of Partial Differential Equations: Fast Solution Techniques 
Jeffrey Abell (General Motors)  A perspective on the use of mathematics in industry 
Abstract: A (possibly personal) perspective on how research that has a significant theoretical component should be constructed and organized. Questions regarding "what" and "why" will be explored with the group, along with a discussion of topics that are being investigated currently. Anyone interested in an interactive discussion is welcome to attend.  
Mark Ainsworth (University of Strathclyde)  Optimally Blended SpectralFinite Element Scheme for Wave Propagation, and NonStandard Reduced Integration 
Abstract: In an influential article, Marfurt suggested that the best scheme for computational wave propagation would involve an averaging of the consistent and lumped finite element approximations. Many authors have considered how this might be accomplished for first order approximation, but the case of higher orders remained unsolved. We describe recent work on the dispersive and dissipative properties of a novel scheme for computational wave propagation obtained by averaging the consistent (finite element) mass matrix and lumped (spectral element) mass matrix. The objective is to obtain a hybrid scheme whose dispersive accuracy is superior to both of the schemes. We present the optimal value of the averaging constant for all orders of finite elements and proved that for this value the scheme is two orders more accurate compared with finite and spectral element schemes, and, in addition, the absolute accuracy is of this scheme is better than that of finite and spectral element methods.
Joint work with Hafiz Wajid, COMSATS Institute of Technology, Pakistan. 

Roman Andreev (ETH Zürich)  Spacetime sparse wavelet FEM for parabolic equations 
Abstract: For the model linear parabolic equation we propose a nonadaptive wavelet finite element spacetime sparse discretization. The problem is reduced to a finite, overdetermined linear system of equations. We prove stability, i.e., that the finite section normal equations are wellconditioned if appropriate Riesz bases are employed, and that the Galerkin solution converges quasioptimally in the natural solution space to the original equation. Numerical examples confirm the theory. This work is part of a PhD thesis under the supervision of Prof. Christoph Schwab, supported by Swiss National Science Foundation grant No. PDFMP2127034/1.  
Paola Francesca Antonietti (Politecnico di Milano)  Domain decomposition preconditioning for the hpversion of the discontinuous Galerkin method 
Abstract: We address the problem of efficiently solving the algebraic
linear systems of equations arising from
the discretization of a symmetric, elliptic boundary value
problem using hp discontinuous Galerkin finite element methods.
We introduce a class of domain decomposition preconditioners based
on the Schwarz framework, and prove bounds on the condition
number of the resulting iteration operators. Numerical results
confirming the theoretical estimates are also presented. Joint work with Paul Houston, University of Nottingham, UK. 

Todd Arbogast (University of Texas at Austin)  Properties of the volume corrected characteristic mixed method 
Abstract: Our goal is to accurately simulate transport of a miscible component in a bulk fluid over long times, i.e., locally conservatively and with little numerical diffusion. Characteristic methods have the potential to do this, since they have no CFL timestep constraints. The volume corrected characteristic mixed method was developed to conserve mass of both the component and the bulk fluid. We have proved that it has the important properties of monotonicity and stability, and therefore exhibits no overshoots nor undershoots. Moreover, the method converges optimally with or without physical diffusion. We show its performance through example simulations of pure curl flow and a nuclear waste repository. 

Douglas N. Arnold (University of Minnesota)  Hilbert complexes and the finite element exterior calculus 
Abstract: The finite element exterior calculus, FEEC, has provided a viewpoint from which to understand and develop stable finite element methods for a variety of problems. It has enabled us to unify, clarify, and refine many of the classical mixed finite element methods, and has enabled the development of previously elusive stable mixed finite elements for elasticity. Just as an abstract Hilbert space framework helps clarify the theory of finite elements for model elliptic problems, abstract Hilbert complexes provides a natural framework for FEEC. In this talk we will survey the basic theory of Hilbert complexes and their discretization, discuss their applications to finite element methods. In particular, we will emphasize the role of two key properties, the subcomplex property and the bounded cochain projection property, in insuring stability of discretizations by transferring to the discrete level the structures that insure wellposedness of the PDE problem at the continuous level.  
Douglas N. Arnold (University of Minnesota)  Plenary talk: Canonical families of finite elements 
Abstract: The most familiar family of finite elements is the Lagrange family, which provide the canonical finite element approximation of H1 on simplicial meshes in any dimension. In this talk we discuss families of simplicial and cubical finite elements—some previously known and some new—which are natural extensions of the Lagrange family in various ways. Even for some of the long known elements, a modern viewpoint based on the finite element exterior calculus provides new properties and insights.  
Gerard Michel Awanou (Northern Illinois University)  Pseudotime continuation and time marching methods for MongeAmpère type equations 
Abstract: We discuss the performance of three numerical methods for the fully nonlinear MongeAmpère equation. The first two are pseudotime continuation methods while the third is a pure pseudotime marching algorithm. The pseudotime continuation methods are shown to converge for smooth data on a uniformly convex domain. We give numerical evidence that they perform well for the nondegenerate MongeAmpère equation. The pseudotime marching method applies in principle to any nonlinear equation. Numerical results with this approach for the degenerate MongeAmpère equation are given as well as for the Pucci and Gausscurvature equations.  
Blanca Ayuso de Dios (Centre de Recerca Matemàtica )  Preconditioning Interior Penalty Discontinuous Galerkin Methods 
Abstract: We propose iterative methods for the solution of the linear systems resulting from Interior Penalty (IP) discontinuous Galerkin (DG) approximations of elliptic problems. The precoonditioners are derived from a natural decomposition of the DG finite element spaces. We present the convergence analysis of the solvers for both symmetric and nonsymmetric IP schemes. Extension to problems with jumps in the coefficients and linear elasticity will also be discussed. We describe in detail the preconditioning techniques for low order (piecewise linear ) IP methods and we indicate how to proceed in the case of high order (odd degree) approximations. The talk is based on joint works with Ludmil T. Zikatanov from Penn State University (USA). 

Blanca Ayuso de Dios (Centre de Recerca Matemàtica )  Discontinuous Galerkin approximation for the VlasovPoisson system 
Abstract: One of the simplest model problems in the kinetic theory of plasmaphysics is the VlasovPoisson (VP) system with periodic boundary conditions. Such system describes the evolution of a plasma of charged particles (electrons and ions) under the effects of the transport and selfconsistent electric field. In this talk, we construct a new family of semidiscrete numerical schemes for the approximation of the VlasovPoisson system. The methods are based on the coupling of discontinuous Galerkin (DG) approximation to the Vlasov equation and several finite element (conforming, nonconforming and mixed) approximations for the Poisson problem. We present the error analysis in the case of smooth solutions. The issue of energy conservation is also analyzed for some of the methods. If time allows, I will also comment on the issue of approximating nonsmooth solutions of the VP system. The talk is based on joint works with J.A. Carrillo (Universidad Autonoma de Barcelona) and CW. Shu (Brown University).  
Uday Banerjee (Syracuse University)  The generalized finite element method 
Abstract: The Generalized Finite Element Method (GFEM) is class of fexible Galerkin methods to approximate the solutions of partial differential equations. It allows to incorporate the "features" of the unknown solution into the trial space. This is done locally based on the available information about the unknown solution, which is often incomplete and "fuzzy." GFEM (in its various forms) has been used extensively in the engineering community to address problems involving cracks, interfaces, and certain microstructures. In these talks, we will present a general survey of various aspects of the GFEM in the context of elliptic problems. We will discuss examples of trial spaces tailored to individual problems, together with their approximation properties. We will also address the condition number of the associated stiffness matrix, which can be a major issue in the GFEM. Some open problems in this area will also be highlighted in these lectures.  
Randolph E. Bank (University of California, San Diego)  Some algorithmic aspects of hpadaptive finite elements 
Abstract: We will discuss our ongoing investigation of hpadaptive finite elements. We will focus on a posteriori error estimates based on superconvergent derivative recovery. Besides providing both global error estimates and local error indicators, this family of error estimates also provides information that forms the basis of our hpadaptive refinement and coarsening strategies. In particular, these a posteriori error estimates address in a cost efficient and natural way the critical issue of deciding between h or p refinement/coarsening. Some numerical examples will be provided.  
Andrew T. Barker (Louisiana State University)  Twolevel additive Schwarz preconditioners for the local discontinuous Galerkin method 
Abstract: We propose and analyze twolevel overlapping additive Schwarz preconditioners for the local discontinuous Galerkin discretization. We prove a condition number estimate and show numerically that the method is scalable in terms of linear iterations. We also present numerical evidence that a parallel implementation of the method shows good scalability and speedup.  
Yuri Bazilevs (University of California, San Diego)  Isogeometric Analysis of Fluids, Structures and FluidStructure Interaction 
Abstract: Isogeometric Analysis [1] is a recently developed novel discratization technique that is based on the basis functions of computeraided design and computer graphics. Although the main motivation behind the development of Isogeometric Analysis was to establish a tighter link between geometry modeling and computational analysis procedures, the new technology demonstrated better perdegreeoffreedom performance than standard finite elements on a broad range of problems in computational mechanics. This better "efficiency" of isogeometric analysis was attributed to more accurate analysis geometry definition and higherorder smoothness of the underlying basis functions. In this presentation, I will give an overview of the early developments in isogeometric analysis of fluids and structures. I will aslo give a summary of approximation results for the function spaces employed in isogeometric analysis. In the main body of the presentation I will show our recent work on isogeometric shell structures, turbulence modeling and fluidstructure interaction (FSI). I will conclude by presenting our recent isogeometric FSI simulations of a wind turbine rotor operating under realistic wind conditions and at full spatial scale in 3D [2,3]. References [1] J.A. Cottrell, T.J.R. Hughes, and Y. Bazilevs, “Isogeometric Analysis. Toward Integration of CAD and FEA”, Wiley 2009. [2] Y. Bazilevs, M.C. Hsu, I. Akkerman, S. Wright, K. Takizawa, B. Henicke, T. Spielman, and T.E. Tezduyar, “3D Simulation of Wind Turbine Rotors at Full Scale. Part I: Geometry Modeling and Aerodynamics”, International Journal of Numerical Methods in Fluids, (2010). Published online. [3] Y. Bazilevs, M.C. Hsu, J. Kiendl, R. Wuechner and K.U. Bletzinger, “3D Simulation of Wind Turbine Rotors at Full Scale. Part II: FluidStructure Interaction”, International Journal of Numerical Methods in Fluids, (2010). Accepted for publcation.


Christine Bernardi (Université de Paris VI (Pierre et Marie Curie))  Finite element discretizations of the contact between two membranes 
Abstract: The contact between two membranes can be described by a system of variational inequalities, where the unknowns are the displacements of the membranes and the action of a membrane on the other one. We first propose a discretization of this system, where the displacements are approximated by standard finite elements and the action by a local postprocessing which admits an equivalent mixed reformulation. We perform the a posteriori analysis of this discretization and prove optimal error estimates. Numerical experiments confirm the efficiency of the error indicators.  
Pavel B. Bochev (Sandia National Laboratories)  Optimizationbased computational modeling, or how to achieve better predictiveness with less complexity 
Abstract: Discretization converts infinite dimensional mathematical models into finite dimensional algebraic equations that can be solved on a computer. This process is accompanied by unavoidable information losses which can degrade the predictiveness of the discrete equations.
Compatible and regularized discretizations control these losses directly by using suitable field representations and/or by modifications of the variational forms. Such methods excel in controlling "structural" information losses responsible for the stability and wellposedness of the discrete equations.
However, direct approaches become increasingly complex and restrictive for multiphysics problems comprising of fundamentally different mathematical models, and when used to control losses of "qualitative" properties such as maximum principles, positivity, monotonicity and local bounds preservation. In this talk we show how optimization ideas can be used to control externally, and with greater flexibility, information losses which are difficult (or impractical) to manage directly in the discretization process. This allows us to improve predictiveness of computational models, increase robustness and accuracy of solvers, and enable efficient reuse of code. Two examples will be presented: an optimizationbased framework for multiphysics coupling, and an optimizationbased algorithm for constrained interpolation (remap). In the first case, our approach allows to synthesize a robust and efficient solver for a coupled multiphysics problem from simpler solvers for its constituent components. To illustrate the scope of the approach we derive such a solver for nearly hyperbolic PDEs from standard, offtheshelf algebraic multigrid solvers, which by themselves cannot solve the original equations. The second example demonstrates how optimization ideas enable design of highorder conservative, monotone, bounds preserving remap and transport schemes which are linearity preserving on arbitrary unstructured grids, including grids with polyhedral and polygonal cells. This is a joint work with D. Ridzal , G. Scovazzi (SNL) and M. Shashkov (LANL). Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin company, for the U.S. Department of Energy's National Nuclear Security Administration under contract DEAC0494AL85000. 

Daniele Boffi (Università di Pavia)  Exterior calculus and the finite element approximation of Maxwell's eigenvalue problem 
Abstract: Maxwell's eigenvalue problem can be seen as a particular case of the
HodgeLaplace eigenvalue problem in the framework of exterior calculus.
In this context we present two mixed formulations that are equivalent
to the problem under consideration and their numerical approximation.
It turns out that the natural conditions for the good approximation of
the eigensolutions of the mixed formulations are equivalent to a
wellknown discrete compactness property that has been firstly used by
Kikuchi for the analysis of edge finite elements. The result can be applied to the convergence analysis of the pversion of edge finite elements for the approximation of Maxwell's eigenvalue problem. 

James H. Bramble (Texas A & M University)  Plenary talk: Analysis of a Cartesian PML approximation to an acoustic scattering problem 
Abstract: We consider a Cartesian PML approximation to solutions of acoustic scattering problems on an unbounded domain in ℝ^{2} and ℝ^{3}. The perfectly matched layer (PML) technique modifies the equations outside of a bounded domain containing the region of interest. This is done in such a way that the new problem (still on an unbounded domain) has a solution which agrees with the solution of the original problem. The new problem has a solution which decays much faster, thus suggesting replacing it by a problem on a bounded domain. The perfectly matched layer (PML) technique, in a curvilinear coordinate system and in Cartesian coordinates, has been studied for acoustic scattering applications both in theory and computation. Using a different approach we extend the results of Kim and Pasciak concerning the PML technique in Cartesian coordinates. The exponential convergence of approximate solutions as a function of domain size and/or the PML "strength" parameter, σ_{0} is also shown. We note that once the stability and convergence of the (continuous) truncated problem has been established, the analysis of the resulting finite element approximations is then classical. Finally, the results of numerical computations illustrating the theory, in terms of efficiency and parameter dependence of the Cartesian PML approach will be given.  
Susanne C. Brenner (Louisiana State University)  Geometric Multigrid Methods 
Abstract: Geometric multigrid methods solve an elliptic boundary value problem on a sequence of grids generated by a refinement procedure. They have optimal complexity in the sense that the computational cost is proportional to the number of unknowns. In this tutorial we will introduce various multigrid algorithms (Vcycle, Wcycle, Fcycle, etc.) and discuss their convergence analysis. 

Susanne C. Brenner (Louisiana State University)  Fast Solvers for Higher Order Problems 
Abstract: There are two main difficulties in solving higher order elliptic boundary value problems: the discretization schemes are more complicated and the discrete problems are very illconditioned. In this talk we will discuss an approach that can solve higher order problems with an efficiency similar to that for second order problems. It is based on discontinuous Galerkin methods, embedded multigrid algorithms and domain decomposition techniques. 

XiaoChuan Cai (University of Colorado)  Developing fast and scalable implicit methods for shallow water equations on cubedsphere 
Abstract: We are interested in solving coupled systems of partial
differential equations on computers with a large number of processors. With some combinations of domain decomposition and multigrid methods, one can easily
design algorithms that are highly scalable in terms of the
number of linear and nonlinear iterations. However, if the goal is to minimize the
total compute time and keep the near ideal scalability at the
same time,
then the task is more difficult. We discuss some recent
experience in
solving the shallow water equations on the sphere for the
modeling of
the
global climate. This is a joint work with C. Yang. 

Claudio Canuto (Politecnico di Torino)  Multiagent cooperative dynamical systems: Theory and numerical simulations 
Abstract: We are witnessing an increasing interest for cooperative
dynamical systems proposed in the recent literature as possible
models for
opinion dynamics in social and economic networks.
Mathematically,
they consist of a large number, N, of 'agents' evolving
according to
quite simple dynamical systems coupled in according to some
'locality'
constraint. Each agent i maintains a time function
x_{i}(t)
representing the 'opinion,' the 'belief' it has on something.
As time elapses, agent i interacts with neighbor agents
and modifies its opinion by averaging it with
the one of its neighbors. A critical issue is the way
'locality'
is modelled and interaction takes place. In Krause's model
each agent can see the opinion of all the others but
averages with only those which are within a threshold R from
its current opinion. The main interest for these models is for N quite large. Mathematically, this means that one takes the limit for N → + ∞. We adopt an Eulerian approach, moving focus from opinions of various agents to distributions of opinions. This leads to a sort of master equation which is a PDE in the space of probabily measures; it can be analyzed by the techniques of Transportation Theory, which extends in a very powerful way the Theory of Conservation Laws. Our Eulerian approach gives rise to a natural numerical algorithm based on the `push forward' of measures, which allows one to perform numerical simulations with complexity independent on the number of agents, and in a genuinely multidimensional manner. We prove the existence of a limit measure as t → ∞, which for the exact dynamics is purely atomic with atoms at least at distance R apart, whereas for the numerical dynamics it is 'almost purely atomic' (in a precise sense). Several representative examples will be discussed. This is a joint work with Fabio Fagnani and Paolo Tilli. 

Carsten Carstensen (Yonsei University)  A posteriori error estimator competition for 2ndorder partial differential equations^{*} 
Abstract: Five classes of up to 13 a posteriori error estimators compete in three secondorder model
cases, namely the conforming and nonconforming firstorder approximation of the PoissonProblem
plus some conforming obstacle problem.
Since it is the natural first step, the error is estimated in the energy norm exclusively
— hence the competition has limited relevance. The competition allows merely guaranteed
error control and excludes the question of the best error guess.
Even nonsmooth problems can be included. For a variational inequality,
Braess considers Lagrange multipliers and some resulting auxiliary equation to view
the a posteriori error control of the error in the obstacle problem
as computable terms plus errors and residuals in the auxiliary equation.
Hence all the former a posteriori error estimators apply to this nonlinear benchmark
example as well and lead to surprisingly accurate guaranteed upper error bounds.
This approach allows an extension to more general boundary conditions
and a discussion of efficiency for the affine benchmark examples.
The LuceWohlmuth and the leastsquare error estimators win the
competition in several computational benchmark problems.
Novel equilibration of nonconsistency residuals and novel conforming averaging
error estimators win the competition for CrouzeixRaviart
nonconforming finite element methods.
Our numerical results provide sufficient evidence that guaranteed error control in the
energy norm is indeed possible with efficiency indices between one and two. Furthermore,
accurate error control is slightly more expensive but pays off in all applications under
consideration while adaptive meshrefinement is sufficiently pleasant as accurate when
based on explicit residualbased error estimates.
Details of our theoretical and empirical ongoing investigations will be found in
the papers quoted below. References:
^{*} This work was supported by DFG Research Center MATHEON and by the World Class University (WCU) program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology R312008000100490. 

Feng Chen (Purdue University)  Spectral methods for systems of coupled equations and applications to CahnHilliard equations 
Abstract: I will present how our new developed spectral method solvers can be applied to highly nonlinear and highorder evolution equations such as strongly anisotropic CahnHilliard equations from materials science. In addition, we consider how to design schemes that are energy stable and easy to solve (avoid solving nonlinear equations implicitly). We use the LegendreGalerkin method to simulate the anisotropic CahnHilliard equation with the Willmore regularization. Excellent agreement between numerical simulations and theoretical results are observed.  
Yanlai Chen (University of Massachusetts, Dartmouth)  Reducedorder modelling for electromagnetics 
Abstract: The reduced basis method (RBM) is indispensable in scenarios where a large number of solutions to a parametrized partial differential equation are desired. These include simulationbased design, parameter optimization, optimal control, multimodel/scale simulation etc. Thanks to the recognition that the parameterinduced solution manifolds can be well approximated by finitedimentional spaces, RBM can improve efficiency reliably by several orders of magnitudes. This poster presents RBM for various electromagnetic problems including radar cross section computation of an object whose scattered field is highly sensitive to the geometry. We also propose a new reduced basis element method (RBEM) that simulate electromagnetic wave propagation in a pipe of varying shape. This is joint work with Jan Hesthaven and Yvon Maday.  
Zhiming Chen (Chinese Academy of Sciences)  The adaptive Anisotropic PML method for timeharmonic acoustic and electromagnetic scattering problems 
Abstract: We report our recent efforts in developing the adaptive perfectly matched layer (PML) method solving the timeharmonic electromagnetic and acoustic scattering problems. The PML parameters such as the thickness of the layer and the absorbing medium property are determined through sharp a posteriori error estimates. Combined with the adaptive ﬁnite element method, the adaptive PML method provides a complete numerical strategy to solve the scattering problem in the framework of FEM which produces automatically a coarse mesh size away from the ﬁxed domain and thus makes the total computational costs insensitive to the choice of the thickness of the PML layer. Numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method.  
Yingda Cheng (Brown University)  Positivitypreserving discontinuous Galerkin schemes for linear VlasovBoltzmann transport equations 
Abstract: We develop a highorder positivitypreserving discontinuous Galerkin
(DG) scheme for linear VlasovBoltzmann transport equations (BTE)
under the action of quadratically confined electrostatic potentials.
The solutions of the BTEs are positive probability distribution
functions. It is very challenging to have a massconservative,
highorder accurate scheme that preserves positivity of the
numerical solutions in high dimensions. Our work extends the
maximumprinciplesatisfying scheme for scalar conservation laws
to include the linear Boltzmann collision
term. The DG schemes we developed conserve mass and preserve the
positivity of the solution without sacrificing accuracy. A
discussion of the standard semidiscrete DG schemes for the BTE are
included as a foundation for the stability and error estimates for
this new scheme. Numerical results of the relaxation models are
provided to validate the method. 

Bernardo Cockburn (University of Minnesota)  HDG methods for secondorder elliptic problems 
Abstract: In this talk, we discuss a new class of discontinuous Galerkin methods called "hybridizable". Their distinctive feature is that the only globallycoupled degrees of freedom are those of the numerical trace of the scalar variable. This renders them efficiently implementable. Moreover, they are more precise than all other discontinuous Galerkin methods as thet share with mixed methods their superconvergence properties in the scalar variable and their optimal order of convergence for the vector variable. We are going to show how to devise these methods and comment on their implementation and convergence properties. 

Jintao Cui (University of Minnesota)  Hodge decomposition and Maxwell's equations 
Abstract: In this work we investigate the numerical solution for twodimensional Maxwell's equations on graded meshes. The approach is based on the Hodge decomposition for divergencefree vector fields. An approximate solution for Maxwell's equations is obtained by solving standard second order elliptic boundary value problems. We illustrate this new approach by a P1 finite element method.  
Jintao Cui (University of Minnesota)  Multigrid methods for twodimensional Maxwell's equations on graded meshes 
Abstract: In this work we investigate the numerical solution for twodimensional Maxwell's equations on graded meshes. The approach is based on the Hodge decomposition. The solution u of Maxwell's equations is approximated by solving standard second order elliptic problems. Quasioptimal error estimates for both u and curl of u in the L_{2} norm are obtained on graded meshes. We prove the uniform convergence of the Wcycle and full multigrid algorithms for the resulting discrete problem.  
Wolfgang Dahmen (RWTH Aachen)  A different look at transport problems 
Abstract: Joint work with Chunyan Huang, Christoph Schwab and Gerrit
Welper. The success of adaptive (wavelet) methods for operator equations relies on wellposedness of suitable variational formulations and on the availability of Riesz bases (or frames) for the corresponding energy space provided that the corresponding representation of the operator is in a certain sense quasi sparse. When dealing with transport dominated problems such favorable conditions are no longer met for the commonly used variational principles. Moreover, solutions typically exhibit strongly anisotropic features such as layers or shocks. Focussing for simplicity on the simplest model of linear transport we present alternative variational formulations that are, in particular, stable in L_{2} so that corresponding discrete solutions are best approximants in L_{2}. Moreover, this provides a theoretical platform for ultimately employing directional representation systems like shearlets, which are known to form L_{2}frames and offer much more economical sparse representations of anisotropic structures than classical wavelet systems. This is a central objective in an ongoing collaboration with G. Kutyniok's group within the Priority Research Programme (SPP) No. 1324 of the German Research Foundation. In principle, the approach can be understood as a PetrovGalerkin formulation in the infinite dimensional setting. We address several theoretical and (uncommon) numerical tasks arising in this context and indicate first steps towards rigorously founded adaptive solution concepts. These results are illustrated by preliminary numerical experiments first in a finite element setting. 

Leszek Feliks Demkowicz (University of Texas at Austin)  A new class of adaptive discontinuous PetrovGalerkin (DPG) finite element (FE) methods with application to singularly perturbed problems 
Abstract: Joint work with Jay Golapalakrishnan, U. Florida. Adaptive finite elements vary element size h or/and polynomial order p to deliver approximation properties superior to standard discretization methods. The best approximation error may converge even exponentially fast to zero as a function of problem size (CPU time, memory). The adaptive methods are thus a natural candidate for singularly perturbed problems like convectiondominated diffusion, compressible gas dynamics, nearly incompressible materials, elastic deformation of structures with thinwalled components, etc. Depending upon the problem, diffusion constant, Poisson ratio or beam (plate, shell) thickness, define the small parameter. This is the good news. The bad news is that only a small number of variational formulations is stable for adaptive meshes By the stability we mean a situation where the discretization error can be bounded by the best approximation error times a constant that is independent of the mesh. To this class belong classical elliptic problems (linear and nonlinear), and a large class of wave propagation problems whose discretization is based on hp spaces reproducing the classical exact gradcurldiv sequence. Examples include acoustics, Maxwell equations, elastodynamics, poroelasticity and various coupled and multiphysics problems. For singularly perturbed problems, the method should also be robust, i.e. the stability constant should be independent of the perturbation parameter. This is also the dream for wave propagation problems in the frequency domain where the (inverse of) frequency can be identified as the perturbation parameter. In this context, robustness implies a method whose stability properties do not deteriorate with the frequency (method free of pollution (phase) error). We will present a new paradigm for constructing discretization schemes for virtually arbitrary systems of linear PDE's that remain stable for arbitrary hp meshes, extending thus dramatically the applicability of hp approximations. The DPG methods build on two fundamental ideas:  a PetrovGalerkin method with optimal test functions for which continuous stability automatically implies discrete stability,  a discontinuous PetrovGalerkin formulation based on the socalled ultraweak variational hybrid formulation. We will use linear acoustics and convectiondominated diffusion as model problems to present the main concepts and then review a number of other applications for which we have collected some numerical experience including: 1D and 2D convectiondominated diffusion (boundary layers) 1D Burgers and compressible NavierStokes equations (shocks) Timoshenko beam and axisymmetric shells (locking, boundary layers) 2D linear elasticity (mixed formulation, singularities) 1D and 2D wave propagation (pollution error control) 2D convection and 2D compressible Euler equations (contact discontinuities and shocks) The presented methodology incorporates the following features: The problem of interest is formulated as a system of first order PDE's in the distributional (weak) form, i.e. all derivatives are moved to test functions. We use the DG setting, i.e. the integration by parts is done over individual elements. As a consequence, the unknowns include not only field variables within elements but also fluxes on interelement boundaries. We do not use the concept of a numerical flux but, instead, treat the fluxes as independent, additional unknowns (a hybrid method). For each trial function corresponding to either field or flux variable, we determine a corresponding optimal test function by solving an auxiliary local problem on one element. The use of optimal test functions guarantees attaining the supremum in the famous infsup condition from BabuskaBrezzi theory. The resulting stiffness matrix is always hermitian and positivedefinite. In fact, the method can be interpreted as a leastsquares applied to a preconditioned version of the problem. By selecting right norms for test functions, we can obtain stability properties uniform not only with respect to discretization parameters but also with respect to the perturbation parameter (diffusion constant, Reynolds number, beam or shell thickness, wave number) In other words, the resulting discretization is robust. For a detailed presentation on the subject, see [18]. [1] L. Demkowicz and J. Gopalakrishnan. A Class of Discontinuous PetrovGalerkin Methods. Part I: The Transport Equation. Comput. Methods Appl. Mech. Engrg., in print. see also ICES Report 200912. [2] L. Demkowicz and J. Gopalakrishnan. A Class of Discontinuous PetrovGalerkin Methods. Part II: Optimal Test Functions. Numer. Mth. Partt. D.E., accepted, ICES Report 200916. [3] L. Demkowicz, J. Gopalakrishnan and A. Niemi. A Class of Discontinuous PetrovGalerkin Methods. Part III: Adaptivity. ICES Report 20101, submitted to ApNumMath. [4] A. Niemi, J. Bramwell and L. Demkowicz, "Discontinuous PetrovGalerkin Method with Optimal Test Functions for ThinBody Problems in Solid Mechanics," ICES Report 201013, submitted to CMAME. [5] J. Zitelli, I. Muga, L, Demkowicz, J. Gopalakrishnan, D. Pardo and V. Calo, "A class of discontinuous PetrovGalerkin methods. IV: Wave propagation problems, ICES Report 201017, submitted to J.Comp. Phys. [6] J. Bramwell, L. Demkowicz and W. Qiu, "Solution of DualMixed Elasticity Equations Using AFW Element and DPG. A Comparison" ICES Report 201023. [7] J. Chan, L. Demkowicz, R. Moser and N Roberts, "A class of Discontinuous PetrovGalerkin methods. Part V: Solution of 1D Burgers and NavierStokes Equations" ICES Report 201025. [8] L Demkowicz and J. Gopalakrishnan, "A Class of Discontinuous PetrovGalerkin Methods. Part VI: Convergence Analysis for the Poisson Problem," ICES Report, in preparation. 

Leszek Feliks Demkowicz (University of Texas at Austin)  Solution of dualmixed elasticity equations using ArnoldFalkWinther element and discontinuous PetrovGalerkin method. A comparison 
Abstract: Joint work with J. Bramwell and W. Qiu. The presentation is devoted to a numerical comparison and illustration of the two methods using a couple of 2D numerical examples. We compare stability properties of both methods and their efficiency. 

Leszek Feliks Demkowicz (University of Texas at Austin)  Application of DPG method to wave propagation 
Abstract: Joint work with J. Zitelli, I. Muga, J. Gopalakrishnan,
D. Pardo, and V. M. Calo. The phase error, or the pollution effect in the finite element solution of wave propagation problems, is a well known phenomenon that must be confronted when solving problems in the highfrequency range. This paper presents a new method with no phase error. 1D proof and both 1D and 2D numerical experiments are presented. 

Leszek Feliks Demkowicz (University of Texas at Austin)  Application of DPG method to Stokes equations 
Abstract: Joint work with N.V. Roberts, D. Ridzal, P. Bochev, K.J.
Peterson, and Ch. M. Siefert. The DPG method of Demkowicz and Gopalakrishnan guarantees the optimality of the solution in what they call the energy norm. An important choice that must be made in the application of the method is the definition of the inner product on the test space. In te presentation we apply the DPG method to the Stokes problem in two dimensions, analyzing it to determine appropriate inner products, and perform a series of numerical experiments. 

Leszek Feliks Demkowicz (University of Texas at Austin)  Application of DPG method to hyperbolic problems 
Abstract: Joint work with J. Chan. We present an application of the DPG method to convection, linear systems of hyperbolic equations and the compressible Euler equations. 

Clark R. Dohrmann (Sandia National Laboratories)  Domain Decomposition Solvers for PDEs: Some Basics, Practical Tools, and New Developments 
Abstract: The first part of this talk provides a basic introduction to the building blocks of domain decomposition solvers. Specific details are given for both the classical overlapping Schwarz (OS) algorithm and a recent iterative substructuring (IS) approach called balancing domain decomposition by constraints (BDDC). A more recent hybrid OSIS approach is also described. The success of domain decomposition solvers depends critically on the coarse space. Similarities and differences between the coarse spaces for OS and BDDC approaches are discussed, along with how they can be obtained from discrete harmonic extensions. Connections are also made between coarse spaces and multiscale modeling approaches from computational mechanics. As a specific example, details are provided on constructing coarse spaces for incompressible fluid problems. The next part of the talk deals with a variety of implementation details for domain decomposition solvers. These include mesh partitioning options, local and global solver options, reducing the coarse space dimension, dealing with constraint equations, residual weighting to accelerate the convergence of OS methods, and recycling of Krylov spaces to efficiently solve problems with multiple right hand sides. Some potential bottlenecks and remedies for domain decomposition solvers are also discussed. The final part of the talk concerns some recent theoretical advances, new algorithms, and open questions in the analysis of domain decomposition solvers. The focus will be primarily on the work of the speaker and his colleagues on elasticity, fluid mechanics, problems in H(curl), and the analysis of subdomains with irregular boundaries. The speaker gratefully acknowledges contributions of Jan Mandel and Olof Widlund to many topics discussed in this talk. 

Tobin A. Driscoll (University of Delaware)  Fast adaptive collocation by radial basis functions 
Abstract: Radial basis functions provide flexible, meshfree approximations to functions and solutions of differential equations. Naive algorithms suffer from dense linear algebra and severe ill conditioning. Simple multiscale adaptive techniques for the nodes and shape parameters have previously proven very effective in controlling ill conditioning for small node sets. We present a new fast summation method suitable for adaptively generated basis functions with varying shape parameters. When coupled with an easily parallelized restricted additive Schwarz preconditioner, the method can find RBF coefficients in near O(N log N) time for N nodes.  
Bjorn Engquist (University of Texas at Austin)  New algorithms for high frequency wave propagation 
Abstract: We will give a brief overview of multiscale modeling for wave equation problems and then focus on two techniques. One is an energy conserving DG method for time domain and the other is a new a new sweeping preconditioner for frequency domain simulation. The latter is resulting in a computational procedure that essentially scales linearly even in the high frequency regime.  
Robert Falgout (Lawrence Livermore National Laboratory)  An algebraic multigrid tutorial 
Abstract: Multigrid methods are socalled optimal methods because they can solve a
system
of N unknowns with O(N) work. This optimality property is crucial for
scaling
up to huge highresolution simulations on parallel computers. To achieve
this,
the multigrid components must be designed with the underlying system in mind,
traditionally, the problem geometry. Algebraic multigrid, however, is a
method
for solving linear systems using multigrid principles, but requiring no
explicit
geometric information. Instead, AMG determines the essential multigrid
ingredients based solely on the matrix entries. Since the method's introduction in the mideighties, researchers have developed numerous AMG algorithms with different robustness and efficiency properties that target a variety of problem classes. In this tutorial, we will introduce the AMG method, beginning with a description of the classical algorithm of Achi Brandt, Steve McCormick, John Ruge, and Klaus Stüben, and then move on to more recent advances and theoretical developments. 

Robert Falgout (Lawrence Livermore National Laboratory)  Compatible Relaxation in Algebraic Multigrid 
Abstract: Algebraic multigrid (AMG) is an important method for solving the large sparse linear systems that arise in many PDEbased scientific simulation codes. A major component of algebraic multigrid methods is the selection of coarse grids and the construction of interpolation. The idea of compatible relaxation (CR) was introduced by Brandt as a cheap method for measuring the quality of a coarse grid. In this talk, we will review the theory behind CR, describe our CRbased coarsening algorithm, and discuss aspects of the method that require additional development such as coarsening for systems of PDEs. We will also discuss CR's ability to predict the convergence behavior of the AMG method and ideas for improving the accuracy of its predictions. Finally, we will talk about issues of parallelizing these methods to run on massively parallel computers. 

Xiaobing Henry Feng (University of Tennessee)  Absolutely stable IPDG and LDG methods for high frequency wave equations 
Abstract: In this talk I shall discuss some recent progresses in developing interior penalty discontinuous Galerkin (IPDG) methods and local discontinuous Galerkin (LDG) methods for high frequency scalar wave equation. The focus of the talk is to present some nonstandard (h and hp) IPDG and LDG methods which are proved to be absolutely stable (with respect to the wave number and the mesh size) and optimally convergent (with respect to the mesh size). The proposed IPDG and LDG methods are shown to be superior over standard finite element and finite difference methods, which are known only to be stable under some stringent mesh constraints. In particular, it is observed that these nonstandard IPDG and LDG methods are capable to correctly track the phases of the highly oscillatory waves even when the mesh violates the "ruleofthumb" condition. Numerical experiments will be presented to show the efficiency of the nonstandard IPDG and LDG methods. If time permits, latest generalizations of these DG methods to the high frequency Maxwell equations will also be discussed. This is a joint work with Haijun Wu of Nanjing University (China) and Yulong Xing of the University of Tennessee and Oak Ridge National Laboratory.  
Andreas Frommer (Bergische UniversitätGesamthochschule Wuppertal (BUGH))  Domain Decomposition for the Wilson Dirac Operator 
Abstract: In lattice QCD, a standard discretization of the Dirac operator is given by the WilsonDirac operator, representing a nearest neighbor coupling on a 4d torus with 3x4 variables per grid point. The operator is nonsymmetric but (usually) positive definite. Its small eigenmodes are nonsmooth due to the stochastic nature of the coupling coefficients. Solving systems with the WilsonDirac operator on stateoftheart lattices, typically in the range of 3264 grid points in each of the four dimensions, is one of the prominent supercomputer applications today.
In this talk we will describe our experience with the domain decomposition principle as one approach to solve the WilsonDirac equation in parallel. We will report results on scaling with respect to the size of the overlap, on deflation techniques that turned out to be very useful for implementations on QPACE, the no 1 top green 500 special purpose computer developed tiogethe with IBM by the SFBTR 55 in Regensburg and Wuppertal, and on first results on adaptive approaches for obtaining an appropriate coarse system. 

Martin J. Gander (Universite de Geneve)  Why it is so difficult to solve Helmholtz problems with iterative methods 
Abstract: In contrast to the positive definite Helmholtz equation, the 

Joscha Gedicke (HumboldtUniversität)  Adaptive solution of parametric eigenvalue problems for partial differential equations 
Abstract: Eigenvalue problems for partial differential equations (PDEs) arise in a large number of current technological applications, e.g., in the computation of the acoustic field inside vehicles (such as cars, trains or airplanes). Another current key application is the noise compensation in highly efficient motors and turbines. For the analysis of standard adaptive finite element methods an exact solution of the discretized algebraic eigenvalue problem is required, and the error and complexity of the algebraic eigenvalue problems are ignored. In the context of eigenvalue problems these costs often dominate the overall costs and because of that, the error estimates for the solution of the algebraic eigenvalue problem with an iterative method have to be included in the adaptation process. The goal of our work is to derive adaptive methods of optimal complexity for the solution of PDEeigenvalue problems including problems with parameter variations in the context of homotopy methods. In order to obtain low (or even optimal) complexity methods, we derive and analyse methods that adapt with respect to the computational grid, the accuracy of the iterative solver for the algebraic eigenvalue problem, and also with respect to the parameter variation. Such adaptive methods require the investigation of a priori and a posteriori error estimates in all three directions of adaptation. As a model problem we study eigenvalue problems that arise in convectiondiffusion problems. We developed robust a posteriori error estimators for the discretization as well as for the iterative solver errors, first for selfadjoint second order eigenvalue problems (undamped problem, diffusion problem), and then bring in the nonselfadjoint part (damping, convection) via a homotopy, where the stepsize control for the homotopy is included in the adaptation process.  
Joscha Gedicke (HumboldtUniversität)  Adaptive solution of parametric eigenvalue problems for partial differential equations 
Abstract: Eigenvalue problems for partial differential equations (PDEs) arise in a large number of current technological applications, e.g., in the computation of the acoustic field inside vehicles (such as cars, trains or airplanes). Another current key application is the noise compensation in highly efficient motors and turbines. For the analysis of standard adaptive finite element methods an exact solution of the discretized algebraic eigenvalue problem is required, and the error and complexity of the algebraic eigenvalue problems are ignored. In the context of eigenvalue problems these costs often dominate the overall costs and because of that, the error estimates for the solution of the algebraic eigenvalue problem with an iterative method have to be included in the adaptation process. The goal of our work is to derive adaptive methods of optimal complexity for the solution of PDEeigenvalue problems including problems with parameter variations in the context of homotopy methods. In order to obtain low (or even optimal) complexity methods, we derive and analyse methods that adapt with respect to the computational grid, the accuracy of the iterative solver for the algebraic eigenvalue problem, and also with respect to the parameter variation. Such adaptive methods require the investigation of a priori and a posteriori error estimates in all three directions of adaptation. As a model problem we study eigenvalue problems that arise in convectiondiffusion problems. We developed robust a posteriori error estimators for the discretization as well as for the iterative solver errors, first for selfadjoint second order eigenvalue problems (undamped problem, diffusion problem), and then bring in the nonselfadjoint part (damping, convection) via a homotopy, where the stepsize control for the homotopy is included in the adaptation process.  
Joscha Gedicke (HumboldtUniversität)  Adaptivity for the Hodge decomposition of Maxwell's equations 
Abstract: Recently a new numerical method for the twodimensional Maxwell's equation based on the Hodge decomposition for divergencefree vector fields has been introduced by Brenner, Cui, Nan and Sung. The advantage of this new approach is that an approximation of the vector field is obtained by solving several standard second order scalar elliptic boundary value problems instead of using more complicated methods. For the linear Courant finite elements standard energy residual type a posteriori error techniques can be applied to obtain guaranteed upper bounds for the L^{2}error. For smooth solutions a duality argument shows reliability of an L^{2} residual type a posteriori error estimator for the H(curl)error. A dual weighted residual error estimator is derived for singular solutions. Numerical experiments verify reliability and show empirically efficiency of the proposed error estimators. It is shown that adaptive meshrefinement numerically leads to optimal convergence rates for general domains that are nonconvex and may include holes.  
Marc Iwan Gerritsma (Technische Universiteit te Delft)  Cochain interpolation for spectral element methods 
Abstract: Cochains are the natural discrete analogues of the continuous
differential forms. The exterior derivative is replaced in the discrete
setting by the coboundary operator. In this way the vector operations
grad, curl and div are encoded. Since application of the coboundary
twice yields the zero operator, the vector identities div curl = 0 and
curl grad = 0 are identically satisfied on arbitrarily shaped grids,
since the coboundary operator acts on cochains in a purely topological
sense. For the application of cochains in numerical methods cochain interpolation is required which needs to satisfy two criteria: 1. When the interpolated kcochain is integrated over a kchain, the cochain should be retrieved. 2. The interpolated kcochain should be close the corresponding continuous kform in some norm. In this poster cochain interpolations will be presented which satisfy criterion 1. and which display exponential convergence with polynomial enrichment for suffiently smooth kforms. Several examples of the use of these interpolating functions will be presented, such as: 1. Discrete conservation laws naturally reduce to finite volume discretizations. 2. The condition number of the resulting system matrix grows much slower with polynomial enrichment than conventional spectral methods. 3. Low order finite volume methods are extremely good preconditioners. 4. The resonant cavity eigenvalue problem in a square box is resolved with exponential accuracy on orthogonal and highly deformed grids, whereas conventional spectral methods fail to do so. References: [1] Marc Gerritsma, Edge functions for spectral element methods, Proceedings of ICOSAHOM 2009, 2010. [2] Mick Bouman, Artur Palha, Jasper Kreeft and Marc Gerritsma, A conservative spectral element method for curvilinear domains, Proceedings of ICOSAHOM2009, 2010. [3] Bochev, P.B. and J.M. Hyman, Principles of mimetic discretizations of differential operators, IMA Volumes In Mathematics and its Applications, 142, 2006. 

Andrew Kruse Gillette (University of Texas at Austin)  Error estimates for generalized barycentric interpolation 
Abstract: We prove the optimal convergence estimate for first order interpolants used in finite element methods based on three major approaches for generalizing barycentric interpolation functions to convex planar polygonal domains. The Wachspress approach explicitly constructs rational functions, the Sibson approach uses Voronoi diagrams on the vertices of the polygon to define the functions, and the Harmonic approach defines the functions as the solution of a PDE. We show that given certain conditions on the geometry of the polygon, each of these constructions can obtain the optimal convergence estimate. In particular, we show that the wellknown maximum interior angle condition required for interpolants over triangles is still required for Wachspress functions but not for Sibson functions. This is joint work with Dr. Alexander Rand and Dr. Chandrajit Bajaj.  
Shiyuan Gu (Louisiana State University)  A C0 interior penalty method for a biharmonic problem with essential and natural boundary conditions of CahnHilliard type 
Abstract: We develop a C0 interior penalty method for a biharmonic problem with essential and natural boundary conditions of CahnHilliard type. Both a priori and a posteriori error estimates are derived. C0 interior penalty methods are much simpler than C1 finite element methods. Compared to mixed finite element methods, the stability of C0 interior penalty methods can be established in a straightforward manner and the symmetric positive definiteness of the continuous problems is preserved by C^{0} interior penalty methods. Furthermore, since the underlying finite element spaces are standard spaces for second order problems, multigrid solves for the Laplace operator can be used as natural preconditioners for C0 interior penalty methods.  
Ronald H.W. Hoppe (University of Houston)  Projection based model reduction for shape optimization of the Stokes system 
Abstract: The optimal design of structures and systems described by partial differential equations (PDEs) often gives rise to largescale optimization problems, in particular if the underlying system of PDEs represents a multiscale, multiphysics problem. Therefore, reduced order modeling techniques such as balanced truncation model reduction, proper orthogonal decomposition, or reduced basis methods are used to significantly decrease the computational complexity while maintaining the desired accuracy of the approximation. In particular, we are interested in such shape optimization problems where the design issue is restricted to a relatively small area of the computational domain. In this case, it appears to be natural to rely on a full order model only in that specific part of the domain and to use a reduced order model elsewhere. An appropriate methodology to realize this idea consists in a combination of domain decomposition techniques and balanced truncation model reduction. We will consider such an approach for shape optimization problems associated with the timedependent Stokes system and derive explicit error bounds for the modeling error. 

Ronald H.W. Hoppe (University of Houston)  An introduction to the a posteriori error analysis of elliptic optimal control problems 
Abstract: We give a survey on adaptive finite element methods for optimal control problems associated with second order elliptic boundary value problems. Both unconstrained and constrained problems will be considered, the latter in case of pointwise control and pointwise state constraints. Mesh adaptivity is realized in terms of a posteriori error estimators obtained by using residualtype error control and/or by weighted dual residuals within the goaloriented dual weighted approach. In order to make the exposition selfcontained, we provide the basic concepts of residualtype and goaloriented a posteriori error control for elliptic boundary value problems and then apply both concepts to unconstrained elliptic optimal control problems. Control constrained problems will be exemplarily treated within the residualtype a posteriori error analysis, whereas the case of pointwise state constraints will be dealt with by means of dual weighted residuals. The results are based on joint work with Michael Hintermueller (Humboldt Univ. at Berlin) and Michael Hinze (Univ. of Hamburg). 

Thomas Yizhao Hou (California Institute of Technology)  Adaptive data analysis via nonlinear compressed sensing 
Abstract: We introduce a new adaptive data analysis method to analyze multiscale nonlinear and nonstationary data. The purpose of this work is to find the sparsest representation of a multiscale signal using basis that is adapted to the data instead of being prescribed a priori. Using a variation approach base on nonlinear L1 optimization, our method defines trends and Instantaneous Frequency of amultiscale signal. One advantage of performing such decomposition is to preserve some intrinsic physical property of the signal without introducing artificial scales or harminics. For multiscale data that have a nonlinear sparse representation, we prove that our nonlinear optimization method converges to the exact signal with the sparse representation. Moreover, we will show that our method is insensitive to noise and robust enough to apply to realistic physical data. For general data that do not have a sparse representation, our method will give an approximate decomposition and the accuracy is controlled by the scale separation property of the original signal.  
ChiuYen Kao (Ohio State University)  An efficient rearrangement algorithm for shape optimization on eigenvalue problems 
Abstract: In this poster, an efficient rearrangement algorithm is proposed to find the optimal shape and topology for eigenvalue problems in an inhomogeneous media. The method is based on Rayleigh quotient formulation of eigenvalue and a monotone iteration process to achieve the optimality. The common numerical approach for these problems is to start with an initial guess for the shape and then gradually evolve it, until it morphs into the optimal shape. One of the difficulties is that the topology of the optimal shape is unknown. Developing numerical techniques which can automatically handle topology changes becomes essential for shape and topology optimization problems. The level set approach based on both shape derivatives and topological derivatives has been well known for its ability to handle topology changes. However, CFL constrain significantly slows down the algorithm when the mesh is further refined. Due to the efficient rearrangement, the new method not only has the ability of topological changes but also is exempt from CFL condition. We provides numerous numerical examples to demonstrate the robustness and efficiency of our approach.  
David Keyes (King Abdullah University of Science & Technology)  Domain decomposition methods for partial differential equations 
Abstract: Domain decomposition, a form of divideandconquer for mathematical problems posed over a physical domain is the most common paradigm for largescale simulation on massively parallel, distributed, hierarchical memory computers. In domain decomposition, a large problem is reduced to a collection of smaller problems, each of which is easier to solve computationally than the undecomposed problem, and most or all of which can be solved independently and concurrently. Domain decomposition has proved to be an ideal paradigm not only for execution on advanced architecture computers, but also for the development of reusable, portable software. The most complex operation in a typical domain decomposition method – the application of the preconditioner – carries out in each subdomain steps nearly identical to those required to apply a conventional preconditioner to the undecomposed domain. Hence software developed for the global problem can readily be adapted to the local problem, instantly presenting lots of legacy scientific code for to be harvested for parallel implementations. Finally, it should be noted that domain decomposition is often a natural paradigm for the modeling community. Physical systems are often decomposed into two or more contiguous subdomains based on phenomenological considerations, and the subdomains are discretized accordingly, as independent tasks. This physicallybased domain decomposition may be mirrored in the software engineering of the corresponding code, and leads to threads of execution that operate on contiguous subdomain blocks. This tutorial provides an overview of domain decomposition and focuses on the mathematical development of its two main paradigms: Schwarz and Schur preconditioning and their hybrids.  
David Keyes (King Abdullah University of Science & Technology)  Preconditioners for interface problems in Eulerian formulations 
Abstract: Eulerian formulations of problems with interfaces avoid the subtleties
of tracking and remeshing, but do they complicate solution of the
discrete equations, relative to domain decomposition methods that
respect the interface? We consider two different interface problems –
one involving cracking and one involving phase separation. Crack
problems can be formulated by extended finite element methods (XFEM),
in which discontinuous fields are represented via special degrees of
freedom. These DOFs are not properly handled in a typical AMG
coarsening process, which leads to slow convergence. We propose a
Schwarz approach that retains AMG advantages on the standard DOFs and
avoids coarsening the enriched DOFs. This strategy allows reasonably
meshindependent convergence rates, though the convergence degradation
of the (lower dimensional) set of crack DOFs remains to be addressed.
Phase separation problems can be formulated by the CahnHilliard
approach, in which the level set of a continuous Eulerian field
demarcates the phases. Here, scalable preconditioners follow
naturally, once the subtlety of the temporal discretization is sorted
out. The first project is joint with R. Tuminaro and H. Waisman and
the second with X.C. Cai and C. Yang. 

Jon Kleinberg (Cornell University)  Arnold family lecture: Burst, cascades, and hot spots: A glimpse of some online social phenomena at global scales 
Abstract: As an increasing amount of social interaction moves online, it becomes possible to study phenomena that were once essentially invisible: how our social networks are organized, how groups of people come together and attract new members, and how information spreads through society. With computational and mathematical ideas, we can begin to map the rich social landscape that emerges, filled with "hot spots" of collective attention, and behaviors that cascade through our networks of social connections.  
Tzanio V Kolev (Lawrence Livermore National Laboratory)  Scalable electromagnetic simulations with the Auxiliaryspace Maxwell Solver (AMS) 
Abstract: Secondorder definite Maxwell problems arise in many practical applications, such as the modeling of electromagnetic diffusion in ALEMHD simulations. Typically, these problems are discretized with Nedelec finite elements resulting in a large sparse linear system which is challenging for linear solvers due to the large nullspace of curloperator. In this poster we describe our work on the Auxiliaryspace Maxwell Solver (AMS) which is a provably efficient scalable code for solving definite Maxwell problems based on the recent HiptmairXu (HX) decomposition of the lowestorder Nedelec space. We demonstrate the scalability of the method and its robustness with respect to jumps in material coefficients. We also report some results from recent work on the algebraic extension of the AMS algorithm and theory to linear systems obtained by explicit element reduction.  
Ralf Kornhuber (Freie Universität Berlin)  Nonsmooth Schur Newton Methods and Applications 
Abstract: The numerical simulation of the coarsening of binary alloys based on the
CahnLarch`e equations requires fast, reliable and robust solvers for CahnHilliard equations with logarithmic potential. After semiimplicit time discretization (cf. Blowey and Elliott 92), the resulting spatial problem can be reformulated as a nonsmooth pdeconstrained
optimal control problem with cost functional induced by the Laplacian. The associated
KarushKuhnTucker conditions take the form of a nonsmooth saddle point problem
degenerating to a variational inclusion in the deep quench limit. Our considerations are based on recent work of Gr¨aser & Kornhuber 09 and the upcoming dissertation of Gr¨aser 10. The starting point is the elimination of the primal variable leading to a nonlinear Schur complement which turns out to be the Fr´ech`et derivative of a convex functional. Now socalled nonsmooth SchurNewton methods can be derived as gradientrelated descent methods applied to this functional. In the discrete case we can show global convergence for an exact and an inexact version independent of any regularization parameters. Local quadratic convergence or finite termination can be shown for piecewise smooth nonlinearities or in the deep quench limit respectively. The algorithm can be reinterpreted as a preconditioned Uzawa method and generalizes the wellknown primaldual active set strategy by Kunisch, Ito, and Hinterm¨uller 03. A (discrete) AllenCahntype problem and a linear saddle point problem have to be solved (approximately) in each iteration step. In numerical computations we observe meshindependent local convergence for initial iterates provided by nested iteration. In the deep quench limit, the numerical complexity of the (approximate) solution of the arising linear saddle point problem dominates the detection of the actual active set. 

Christian Kreuzer (Universität DuisburgEssen)  Convergence and optimality of adaptive finite element methods 
Abstract: We present convergence and optimality results for a standard AFEM


Angela Kunoth (Universität Paderborn)  Spacetime adaptive wavelet methods for control problems constrained by parabolic PDEs 
Abstract: Joint work with Max D. Gunzburger, School of Computational
Science, Florida State University. Optimization problems constrained by partial differential equations (PDEs) are particularly challenging from a computational point of view: the first order necessary conditions for optimality lead to a coupled system of PDEs. Specifically, for the solution of control problems constrained by a parabolic PDE, one needs to solve a system of PDEs coupled globally in time and space. For these, conventional timestepping methods quickly reach their limitations due to the enormous demand for storage. For such a coupled PDE system, adaptive methods which aim at distributing the available degrees of freedom in an aposteriorifashion to capture singularities in the data or domain, with respect to both space and time, appear to be most promising. Here I propose an adaptive method based on wavelets. It builds on a recent paper by Schwab and Stevenson where a single linear parabolic evolution problem is formulated in a weak spacetime form and where an adaptive wavelet method is designed for which convergence and optimal convergence rates (when compared to waveletbest N term approximation) can be shown. Our approach extends this paradigm to control problems constrained by evolutionary PDEs for which we can prove convergence and optimal rates for each of the involved unknowns (state, costate, and control). 

Angela Kunoth (Universität Paderborn)  Multiscale methods for complex systems 
Abstract: This poster presents different topics concerning the modelling and numerical solution of complex systems from my work group, all centering around multiscale methods for partial differential equations. Applications are from theoretical physics, geodesy, electrical engineering, and finance. Depending on the concrete application, we employ wavelet, adaptive wavelet or monotone multigrid methods.  
Sabine Le Borne (Tennessee Technological University)  HLU factorization of stabilized saddle point problems 
Abstract: The (mixed finite element) discretization of the linearized NavierStokes
equations leads to a linear system of equations of saddle point type.
The iterative solution of this linear system requires the construction
of suitable preconditioners, especially in the case of high Reynolds
numbers. In the past, a stabilizing approach has been suggested which
does not change the exact solution but influences the accuracy of
the discrete solution as well as the effectiveness of iterative solvers.
This stabilization technique can be performed on the continuous side before
the discretization,
where it is known as ``graddiv'' stabilization, as well as on the discrete
side where it is known as an ``augmented Lagrangian'' technique
(and does not change the discrete solution). We study the applicability of HLU factorizations to solve the arising subproblems in the different variants of stabilized saddle point systems. 

Jungho Lee (Argonne National Laboratory)  A comparison of two domain decomposition methods for a linearized contact problem 
Abstract: We compare two domain decomposition methods for a linearized contact problem. The first method we consider has been used in an engineering community; we provide theoretical and numerical evidence that this method is not scalable with respect to the number of subdomains (processors). We propose a scalable alternative and analyze its properties, both theoretically and numerically. We also solve a model problem using a combination of a primaldual active set method, viewed as a semismooth Newton method, and the scalable alternative.  
Dmitriy Leykekhman (University of Connecticut)  Local properties of finite element solutions for advectiondominated optimal control problems 
Abstract: We analyzes the local properties of several stabilized methods, namely symmetric interior penalty upwind discontinuous Galerkin method (SIPG) and Streamline diffusion method (SUPG) for the numerical solution of optimal control problems governed by linear reactionadvectiondiffusion equations with distributed controls. The theoretical and numerical results presented show that for advectiondominated problems the local convergence properties of the SIPG discretization can be superior to the convergence properties of stabilized finite element discretizations such as SUPG method. For example for a small diffusion parameter the SIPG method is optimal in the interior of the domain. This is in sharp contrast to SUPG discretizations, for which it is known that the existence of boundary layers can pollute the numerical solution of optimal control problems everywhere even into domains where the solution is smooth and, as a consequence, in general reduces the convergence rates to only first order. This favorable property of the SIPG method is due to the weak treatment of boundary conditions which is natural for discontinuous Galerkin methods, while for SUPG methods strong imposition of boundary conditions is more conventional. Our numerical results support this conclusion.  
Fengyan Li (Rensselaer Polytechnic Institute)  Central DG methods for HamiltonJacobi equations and ideal MHD equations 
Abstract: In this talk, I will present our recent work in developing high order
central discontinuous Galerkin (DG) methods for HamiltonJacobi (HJ)
equations and ideal MHD equations. Originally introduced for hyperbolic
conservation laws, central DG methods combine ideas in central schemes
and DG methods. They avoid the use of exact or approximate Riemann
solvers, while evolving two copies of approximating solutions on
overlapping meshes. To devise Galerkin type methods for HJ equations, the main difficulty is that these equations in general are not in the divergence form. By recognizing a weightedresidual or stabilizationbased formulation of central DG methods when applied to hyperbolic conservation laws, we propose a central DG method for HJ equations. Though the stability and the error estimate are established only for linear cases, the accuracy and reliability of the method in approximating the viscosity solutions are demonstrated through general numerical examples. This work is jointly done with Sergey Yakovlev. In the second part of the talk, we introduce a family of central DG methods for ideal MHD equations which provide the exactly divergencefree magnetic field. Ideal MHD system consists of a set of nonlinear hyperbolic equations, with a divergencefree constraint on the magnetic field. Though such constraint holds for the exact solution as long as it does initially, neglecting this condition numerically may lead to nonphysical features of approximating solutions or numerical instability. This work is jointly done with Liwei Xu and Sergey Yakovlev. 

Guang Lin (Pacific Northwest National Laboratory)  Pointwise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws 
Abstract: We develop a new hierarchical reconstruction (HR) method for limiting solutions of the discontinuous Galerkin and finite volume methods up to fourth order without local characteristic decomposition for solving hyperbolic nonlinear conservation laws on triangular meshes. The new HR utilizes a set of point values when evaluating polynomials and remainders on neighboring cells, extending the technique introduced in Hu, Li and Tang. The pointwise HR simplifies the implementation of the previous HR method which requires integration over neighboring cells and makes HR easier to extend to arbitrary meshes. We prove that the new pointwise HR method keeps the order of accuracy of the approximation polynomials. Numerical computations for scalar and system of nonlinear hyperbolic equations are performed on twodimensional triangular meshes. We demonstrate that the new hierarchical reconstruction generates essentially nonoscillatory solutions for schemes up to fourth order on triangular meshes.  
Alexei Lozinski (Université de Toulouse III (Paul Sabatier))  Multiscale finite element method in perforated domains 
Abstract: We present an adaptation of a Multiscale Finite Element Method (MsFEM by T. Hou et al.) to a simplified context of pollution dissemination in urban area in a real time marching simulation code. To avoid the use of a complex unstructured mesh that perfectly fits any building of the urban area a penalization technique is used. The physical model becomes a diffusion+penalization equation with highly heterogeneous and discontinuous coefficients. MsFEM is adapted by developing a new basis function oversampling technique. This is tested on a genuine urban area. We also present new variants of MsFEM inspired by the non conforming finite elements à la CrouzeixRaviart.  
Yvon Jean Maday (Université de Paris VI (Pierre et Marie Curie))  Two grids approximation of non linear eigenvalue problems 
Abstract: Approximation of non linear eigenvalue problems represent the key ingredient in quantum chemistry. These approximation are much computer demanding and these approximations saturate the ressources of many HPC centers. Being nonlinear, the approximation methods are iterative and a way to reduce the cost is to use different grids as has been proposed in fluid mechanics for various non linear problems as the Navier Stokes problem. We explain the basics of the approximation, present the numerical analysis and numerical results that illustrate the good behavior of the two grids scheme. This work has been done in collaboration with Eric Cancès and Rachida Chakir. 

Niall Madden (National University of Ireland, Galway)  Computational aspects of a twoscale finite element method for singularly perturbed problems 
Abstract: We consider the numerical solution linear, two dimensional singularly
perturbed reactiondiffusion problem posed on a unit square with homogeneous
Dirichlet boundary conditions. In [1], it is shown that a twoscale sparse
grid finite element method applied to this problem achieves the same order of
accuracy as a standard Galerkin finite element method, while reducing
the number of degrees of freedom from O(N^{2}) to O(N^{3/2}). In this presentation, we discuss implementation aspects of the algorithm, particularly regarding the computational cost. We also compare the method with the related "combination" technique. [1] F. Liu, N. Madden, M. Stynes & A. Zhou, A twoscale sparse grid method for a singularly perturbed reactiondiffusion problem in two dimensions, IMA J. Numer. Anal. 29 (2009), 9861007. 

Niall Madden (National University of Ireland, Galway)  Robust numerical solution of singularly perturbed problems 
Abstract: Singularly perturbed differential equations are usually posed with a
small positive (perturbation) parameter multiplying the highest derivative.
Their solutions typically exhibit boundary or interior layers. In recent years
much effort has been directed towards constructing and analysing socalled
"parameter robust" methods. Such methods should yield solutions whose accuracy
does not depend on the perturbation parameter, and should resolve any layers
present. In this talk I will survey some of these methods, and the mathematics behind them, with particular emphasis on finite differences for coupled systems. 

Jan Mandel (University of Colorado)  Coupled atmosphere  wildland fire numerical simulation by WRFFire 
Abstract: WRFFire consists of a firespread model, implemented by the level set method, coupled with the Weather Research and Forecasting model (WRF). In every time step, the fire model inputs the surface wind and outputs the heat flux from the fire. The level set method allows submesh representation of the burning region and flexible implementation of various ignition modes. This presentation will address the numerical methods in the fire module, solving the HamiltonJacobi level set equation, modeling real wildfire experiments, visualization, and experimental data assimilation with spatial displacement and representation of smooth random fields by FFT. Visualizations by Bedrich Sousedik, Erik Anderson, and Joel Daniels. Jan Mandel, Jonathan D. Beezley, Janice L. Coen, and Minjeong Kim, Data Assimilation for Wildland Fires: Ensemble Kalman filters in coupled atmospheresurface models, IEEE Control Systems Magazine 29, Issue 3, June 2009, 4765 Jan Mandel, Jonathan D. Beezley, and Volodymyr Y. Kondratenko, Fast Fourier Transform Ensemble Kalman Filter with Application to a Coupled AtmosphereWildland Fire Model. Anna M. GilLafuente, Jose M. Merigo (Eds.) Computational Intelligence in Business and Economics (Proceedings of the MS'10 International Conference, Barcelona, Spain, 1517 July 2010), World Scientific, pp. 777784. Also available at arXiv:1001.1588 

Thomas A. Manteuffel (University of Colorado)  A Parallel, Adaptive, FirstOrder System LeastSquares (FOSLS) Algorithm for Incompressible, Resistive Magnetohydrodynamics 
Abstract: Magnetohydrodynamics (MHD) is a fluid theory that describes Plasma Physics by treating the plasma as a fluid of charged particles. Hence, the equations that describe the plasma form a nonlinear system that couples NavierStokes with Maxwell's equations. We describe how the FOSLS method can be applied to incompressible resistive MHD to yield a wellposed, H$^1$equivalent functional minimization. To solve this system of PDEs, a nestediterationNewtonFOSLSAMGLAR approach is taken. Much of the work is done on relatively coarse grids, including most of the linearizations. We show that at most one Newton step and a few Vcycles are all that is needed on the finest grid. Estimates of the local error and of relevant problem parameters that are established while ascending through the sequence of nested grids are used to direct local adaptive mesh refinement (LAR), with the goal of obtaining an optimal grid at a minimal computational cost. An algebraic multigrid solver is used to solve the linearization steps. A parallel implementation is described that uses a binning strategy. We show that once the solution is sufficiently resolved, refinement becomes uniform which essentially eliminates load balancing on the finest grids. The ultimate goal is to resolve as much physics as possible with the least amount of computational work. We show that this is achieved in the equivalent of a few dozen work units on the finest grid. (A work unit equals a fine grid residual evaluation). Numerical results are presented for two instabilities in a large aspectratio tokamak, the tearing mode and the island coalescence mode. 

Jens Markus Melenk (Technische Universität Wien)  Wavenumberexplicit convergence analysis for the Helmholtz equation: hpFEM and hpBEM 
Abstract: We consider boundary value problems for the Helmholtz equation
at large
wave numbers k. In order to understand how the wave number
k affects
the convergence properties of discretizations of such problems,
we develop a regularity theory for the Helmholtz equation that
is explicit
in k. At the heart of our analysis is the decomposition of
solutions
into two components: the first component is an analytic, but
highly oscillatory function and the second one has finite
regularity but
features wavenumberindependent bounds. This understanding of the solution structure opens the door to the analysis of discretizations of the Helmholtz equation that are explicit in their dependence on the wavenumber k. As a first example, we show for a conforming high order finite element method that quasioptimality is guaranteed if (a) the approximation order p is selected as p = O(log k) and (b) the mesh size h is such that kh/p is small. As a second example, we consider combined field boundary integral equation arising in acoustic scattering. Also for this example, the same scale resolution conditions as in the high order finite element case suffice to ensure quasioptimality of the Galekrin discretization. This work presented is joint work with Stefan Sauter (Zurich) and Maike Löhndorf (Vienna). 

Peter Monk (University of Delaware)  The solution of time harmonic wave equations using complete families of elementary solutions 
Abstract: This presentation is devoted to plane wave methods for approximating the timeharmonic wave equation paying particular attention to the Ultra Weak Variational Formulation (UWVF). This method is essentially an upwind Discontinuous Galerkin (DG) method in which the approximating basis functions are special traces of solutions of the underlying wave equation. In the classical UWVF, due to Cessenat and Després, sums of plane wave solutions are used element by element to approximate the global solution. For these basis functions, convergence analysis and considerable computational experience shows that, under mesh refinement, the method exhibits a high order of convergence depending on the number of plane wave used on each element. Convergence can also be achieved by increasing the number of basis functions on a fixed mesh (or a combination of the two strategies). However illconditioning arising from the plane wave basis can ultimately destroy convergence. This is particularly a problem near a reentrant corner where we expect to need to refine the mesh. The presentation will start with a summary of the UWVF and some typical analytical and numerical results for the Hemholtz equation. An alternative to plane waves, is to use polynomial basis functions on small elements. Using mixed finite element methods, we can view the UWVF as a hybridization strategy and I shall also present theoretical and numerical results for this approach. Although neither the Bessel function or the plane wave UWVF are free of dispersion error (pollution error) they can provide a method that can use large elements and small number of degrees of freedom per wavelength to approximate the solution. It has been extended to Maxwell's equations and elasticity. Perhaps the main open problems are how to improve on the biconjugate gradient method that is currently used to solve the linear system, and how to adaptively refine the approximation scheme. 

Brian Edward Moore (University of Central Florida)  Conformal conservation laws and geometric integration for Hamiltonian PDE with added dissipation 
Abstract: Conformal conservation laws are defined and derived for a class of multisymplectic equations with added dissipation. In particular, the conservation laws of symplecticity, energy and momentum are considered, along with others that arise from linear symmetries. Numerical methods that preserved these conformal conservation laws are presented. The nonlinear Schrödinger equation and semilinear wave equation with added dissipation are used as examples to demonstrate the results.  
Michael Joseph Neilan (Louisiana State University)  Finite element methods for the MongeAmpere equation 
Abstract: The MongeAmpere equation is a fully nonlinear second order PDE that arises in various application areas such as differential geometry, meteorology, reflector design, economics, and optimal transport. Despite its prevalence in many applications, numerical methods for the MongeAmpere equation are still in their infancy. In this work, I will discuss a new approach to construct and analyze several finite element methods for the MongeAmpere equation. As a first step, I will show that a key feature in developing convergent discretizations is to construct schemes with stable linearizations. I will then describe a methodology for constructing finite elements that inherits this trait and provide two examples: C^0 finite element methods and discontinuous Galerkin methods. Finally, I will present some promising application areas to apply this methodology including mesh generation and computing a manifold with prescribed Gauss curvature.  
NgocCuong Nguyen (Massachusetts Institute of Technology)  HDG methods for multiphysics simulation 
Abstract: We present a recent development of hybridizable discontinuous Galerkin (HDG) methods for continuum mechanics. The HDG methods inherit the geometric flexibility, highorder accuracy, and multiphysics capability of discontinuous Galerkin (HDG) methods. They also possess several unique features which distinguish themselves from other DG methods: (1) the global unknowns are the numerical traces of the field variables; (2) all the approximate variables converge with the optimal order k+1 for diffusiondominated problems; (3) in such cases, local postprocessing can be developed to increase the convergence rate to k+2 for the approximation of the field variables; (4) they can deal with noncompatible boundary conditions; (5) they result in a compact matrix system and (6) they are somewhat easier to implement and provide a single code for solving multiphysics problems.  
NgocCuong Nguyen (Massachusetts Institute of Technology)  HDG methods for CFD applications 
Abstract: We extend hybridizable discontinuous Galerkin (HDG) methods to CFD applications. The HDG methods inherit the geometric flexibility and highorder accuracy of discontinuous Galerkin methods, and offer a significant reduction in the computational cost. In order to capture shocks, we employ an artificial viscosity model based on an extension of existing artificial viscosity methods. In order to integrate the SpalartAllmaras turbulence model using highorder methods, some modification of the model is necessary. Mesh adaptation based on shock indicator is used to improve shock profiles. Several test cases are presented to illustrate the proposed approach.  
Sylvain Nintcheu Fata (Oak Ridge National Laboratory)  The generalized fundamental theorem of calculus and its applications to boundary element methods 
Abstract: An effective technique which employs only the underlying surface discretization to calculate domain integrals
appearing in boundary element methods has been developed. The proposed approach first converts a domain
integral with continuous or weaklysingular integrand into a boundary integral. The resulting surface integral
is then computed via standard quadrature rules commonly used for boundary elements. This transformation of a
domain integral into a boundary counterpart is accomplished through a systematic generalization of the
fundamental theorem of calculus to higher dimension. In addition, it is established that the higherdimensional
version of the first fundamental theorem of calculus corresponds to the classical Poincaré lemma. This research was supported by the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under contract DEAC0500OR22725 with UTBattelle, LLC. 

Sylvain Nintcheu Fata (Oak Ridge National Laboratory)  3D boundary integral analysis by a precorrected fast Fourier transform algorithm 
Abstract: An acceleration of a Galerkin boundary integral equation (BIE)
method for solving the threedimensional Laplace equation is
investigated in the context of the precorrected fast Fourier
transform (PFFT) scheme. The PFFT technique is an
algorithm for rapid computation of the
dense matrixvector products arising in an iterative solution
of discretized integral equations. In the PFFT method, the
problem domain is overlaid with a
regular Cartesian grid that serves as an auxiliary platform for
computation. With the aid of the fast Fourier transform (FFT)
procedure, the necessary influence matrices of the discretized
problem are rapidly evaluated on the Fourier grid in a
sparse manner resulting in a significant reduction in execution
time and computer memory requirements. This research was supported by the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under contract DEAC0500OR22725 with UTBattelle, LLC. 

Ricardo H. Nochetto (University of Maryland)  Adaptive finite element methods 
Abstract: Adaptivity is an essential tool in modern scientific and engineering computation that allows one to optimize the computational effort by locating the degrees of freedom where they are most needed, that is in regions of rapid solution variation. Adaptive finite element methods (AFEM) are the most popular and effective numerical methods to solve elliptic PDE, and are driven by a posteriori error estimators. In this tutorial we will discuss the basic structure of AFEM and its main properties, analyze its convergence (contraction property), and derive convergence rates.  
Ricardo H. Nochetto (University of Maryland)  Convergence rates of AFEM with H ^{1} Data 
Abstract: In contrast to most of the existing theory of adaptive
finite
element methods (AFEM), we design an AFEM for Δ u =
f with right hand side f in H^{ 1} instead of
L^{2}. This
has
two important consequences. First we formulate our AFEM in
the
natural space for f, which is nonlocal. Second, we show
that
decay rates for the data estimator are dominated by those
for the
solution u in the energy norm. This allows us to conclude
that
the performance of AFEM is solely dictated by the
approximation
class of u. This is joint work with A. Cohen and R. DeVore. 

EunHee Park (Louisiana State University)  Twolevel additive Schwarz preconditioners for a weakly overpenalized symmetric interior penalty method 
Abstract: The weakly overpenalized symmetric interior penalty (WOPSIP) method was introduced for second order elliptic problems by Brenner et al. in 2008. It belongs to the family of discontinuous Galerkin methods. We will discuss twolevel additive Schwarz preconditioners for the WOPSIP method. The key ingredient of the twolevel additive Schwarz preconditioner is the construction of the subdomain solvers and the coarse solver. In our approach, we consider different choices of coarse spaces and intergrid transfer operators. It is shown that the condition number estimates previously obtained for classical finite element methods also hold for the WOPSIP method. Numerical results will be presented, which illustrate the parallel performance of these preconditioners. This is joint work with Andrew T. Barker, Susanne C. Brenner, and Liyeng Sung. 

Ilaria Perugia (Università di Pavia)  Trefftzdiscontinuous Galerkin methods for timeharmonic wave problems 
Abstract: Several finite element methods used in the numerical discretization of wave problems in frequency domain are based on incorporating a priori knowledge about the differential equation into the local approximation spaces by using Trefftztype basis functions, namely functions which belong to the kernel of the considered differential operator. For the Helmholtz equation, for instance, examples of Trefftz basis functions are plane waves, FourierBessel functions and Hankel functions, and there are in the literature several methods based on them: the Plane Wave/Bessel Partition of Unit Method by Babuška and Melenk, the Ultra Weak Variational Formulation by Cessenat and Després, the Plane Wave/Bessel Least Square Method by Monk and Wang, the Discontinuous Enrichment Method by Farhat and coworkers, the Method of Fundamental Solutions by Stojek, to give some examples. These methods differ form one another not only for the type of Trefftz basis functions used in the approximating spaces, but also for the way of imposing continuity at the interelement boundaries: partition of unit, least squares, Lagrange multipliers or discontinuous Galerkin techniques. In this talk, the construction of Trefftzdiscontinuous Galerkin methods for both the Helmholtz and the timeharmonic Maxwell problems will be reviewed and their abstract error analysis will be presented. It will also be shown how to derive best approximation error estimates for Trefftz functions, needed to complete the convergence analysis, by using Vekua's theory. Some explicit estimates in the case of plane waves will be given. These results have been obtained in collaboration with Ralf Hiptmair and Andrea Moiola form ETH Zürich. 

Jingmei Qiu (Colorado School of Mines)  High order integral deferred correction method based on Strang split semiLagrangian WENO method for Vlasov Poisson simulations 
Abstract: We apply the very high order Strang split semiLagrangian WENO algorithm for kinetic equations. The spatial accuracy of the current Strang split finite difference WENO algorithm is very high (as high as ninth order), however the temporal error is dominated by the dimensional splitting, which is only second order accurate. It is therefore very important to overcome this splitting error, in order to have a consistently high order numerical algorithm. We are currently working on using the IDC framework to overcome the `at best' second order Strang splitting error. Specifically, the dimensional splitting error is overcomed by iteratively correcting the numerical solution via the error function, which is solved by approximating the error equation. We will show numerically that if one embeds a first order dimensional splitting algorithm into the IDC framework, there will be first order increase in order of accuracy when one applies a correction loop in IDC algorithm. Applications to the VlasovPoisson system will be presented.  
Gianluigi Rozza (École Polytechnique Fédérale de Lausanne (EPFL))  A reduced basis hybrid method for viscous flows in parametrized complex networks 
Abstract: Model order reduction techniques provide an efficient and reliable way
of solving partial differential equations in the manyquery or real
time context, such as (shape) optimization, characterization,
parameter estimation and control. The reduced basis (RB) approximation is used for a rapid and reliable solution of parametrized partial differential equations (PDEs). The reduced basis method is crucial to find the solution of parametrized problems as projection of previously precomputed solutions for certain instances of the parameters. It consists on rapidly convergent Galerkin approximations on a space spanned by “snapshots” on a parametrically induced solution manifold; rigorous and sharp a posteriori error estimators for the outputs/quantities of interest; efficient selection of quasioptimal samples in general parameter domains; and OfflineOnline computational procedures for rapid calculation in the manyquery and realtime contexts. The error estimators play an important role in efficient and effective sampling procedures: the inexpensive error bounds allow to explore much larger subsets of parameter domain in search of most representative or best “snapshots”, and to determine when we have just enough basis functions. Extensions of the RB method have been combined with domain decomposition tecniques: this approach, called reduced basis element method (RBEM), is suitable for the approximation of the solution of problems described by partial differential equations within domains which are decomposable into smaller similar blocks and properly coupled. The goal is to speed up the computational time with rapid and efficient numerical strategies to deal with complex and realistic configurations, where topology features are recurrent. The construction of the map from the reference shapes to each corresponding block of the computational domain is done by the generalized transfinite maps. The empirical interpolation procedure has been applied to the geometrical nonaffine transformation terms to re cast the problem in an affine setting. Domain decomposition techniques are important to enable the use of parallel architectures in order to speed up the computational time, compared to a global approach, and also to increase the geometric complexity dealing with independent smaller tasks on each subdomain, where the approximated solution is recovered as projection of local previously computed solutions and then properly glued through different domains by some imposed coupling conditions to guarantee the continuity of stresses and velocities in viscous flows, for example. The Offline/Online decoupling of the reduced basis procedure and the computational decomposition of the method allow to reduce considerably the problem complexity and the simulation times. We propose here an option for RBEM, called reduced basis hybrid method (RBHM) where we focus on different coupling conditions to guarantee the continuity of velocity and pressure. Each basis function in each reference subdomain is computed considering zero stress condition at the interfaces, the continuity of the stresses (nonzero) at the interfaces is recovered by a coarse finite element solution on the global domain, while the continuity of velocities is guaranteed by Lagrange multipliers. This computational procedure allows to reduce considerably the problem complexity and the computational times which are dominated online by the coarse finite element solution, while all the RB offline calculations may be carried out by a parallel computing approach. Applications and results are shown on several combinations of geometries representing cardiovascular networks made up of stenosis, bifurcation, ect. 

Ulrich Rüde (FriedrichAlexanderUniversität ErlangenNürnberg)  Towards Exascale Computing: Multilevel Methods and Flow Solvers for Millions of Cores 
Abstract: We will report on our experiences implementing PDE solvers on PetaScale computers, such as the 290 000 core IBM Blue Gene system in the Jülich Supercomputing Center. The talk will have two parts, the first one reporting on our Hierarchical Hybrid Grid method, a prototype Finite Element Multigrid Solver scaling up to a trillion (10^12) degrees of freedom on a tetrahedral mesh by using a carefully designed matrixfree implementation. The second part of the talk will present our work on simulating complex flow phenomena using the LatticeBoltzmann algorithm. Our software includes parallel algorithms for treating free surfaces with the goal of simulating fully resolved bubbly flows and foams. Additionally, we will report on a parallel fluidstructureinteraction technique with many moving rigid objects. This work is directed towards the modeling of particulate flows that we can represent using fully resolved geometric models of each individual particle embedded in the flow. The talk will end with some remarks on the challenges that algorithm developers will be facing on the path to exascale in the coming decade.


Giancarlo Sangalli (Università di Pavia)  Isogeometric Analysis for electromagnetic problems 
Abstract: The concept of Isogeometric Analysis (IGA) was first applied to the approximation of Maxwell equations in [A. Buffa, G. Sangalli, R. Vázquez, Isogeometric analysis in electromagnetics: Bsplines approximation, CMAME, doi:10.1016/j.cma.2009.12.002.]. The method is based on the construction of suitable Bspline spaces such that they conform a De Rham diagram. Its main advantages are that the geometry is described exactly with few elements, and the computed solutions are smoother than those provided by finite elements. We present here the theoretical background to the approximation of vector fields in IGA. The key point of our analysis is the definition of suitable projectors that render the diagram commutative. The theory is then applied to the numerical approximation of Maxwell source and eigen problem, and numerical results showing the good behavior of the scheme are also presented.  
Christoph Schwab (ETH Zürich)  Sparse tensor Galerkin discretizations for first order transport problems 
Abstract: Joint with R. Hiptmair, Konstantin Grella, Eividn Fonn of SAM, ETH. We report on an ongoing project on Sparse Tensor Finite Element Discretizations for High Dimensional Linear Transport Problems. After reviewing several wellposed variational formulations and the regularity of weak solutions of these problems, we discuss their stable discretizations, with a focus on hierarchic, multilevel type discretizations. Particular examples include (multi)wavelet and shearlet discretizations. We discuss sparse tensor discretizations for Least Squares Formulations of first order transport equations on high dimensional parameter spaces. The formulation is due to Manteuffel etal. (SINUM2000). We present preliminary numerical results for both, sparse tensor spectral as well as for wavelet discretizations. Results are report from ongoing work at the Seminar for Applied Mathematics at ETH Zurich which is supported by the Swiss National Science Foundation (SNF) and from joint work with the groups of W. Dahmen and of G. Kutyniok within the Priority Research Programme (SPP) No. 1324 of the German Research Foundation. http://www.dfgspp1324.de 

Marc Alexander Schweitzer (Rheinische FriedrichWilhelmsUniversität Bonn)  Stable enrichment and treatment of complex domains in the particle–partition of unity method 
Abstract: We are concerned with the stability and approximation properties of enriched meshfree methods for the discretization of PDE on arbitrary domains. In particular we focus on the particlepartition of unity method (PPUM) yet the presented results hold for any partition of unity based enrichment scheme. The goal of our enrichment scheme is to recover the optimal convergence rate of the uniform hversion independent of the regularity of the solution. Hence, we employ enrichment not only for modeling purposes but rather to improve the approximation properties of the numerical scheme. To this end we enrich our PPUM function space in an enrichment zone hierarchically near the singularities of the solution. This initial enrichment however can lead to a severe illconditioning and can compromise the stability of the discretization. To overcome the illconditioning of the enriched shape functions we present an appropriate local preconditioner which yields a stable basis independent of the employed initial enrichment. The construction of this preconditioner is of linear complexity with respect to the number of discretization points. The treatment of general domains with meshbased methods such as the finite element method is rather involved due to the necessary meshgeneration. In collocation type meshfree methods this complex preprocessing step is completely avoided by construction. However, in Galerkin type meshfree discretization schemes we must compute domain and boundary integrals and thus must be concerned with the meshfree treatment of arbitrary domains. Here, we present a cutcelltype scheme for the partition of unity method and ensure stability by enforcing the flattop condition in a simple postprocessing step. 

Jie Shen (Purdue University)  New efficient spectral methods for highdimensional PDEs and for FokkerPlanck equation of FENE dumbbell model 
Abstract: Many scientific, engineering and financial applications require
solving highdimensional PDEs. However, traditional tensor product
based algorithms suffer from the so called "curse of dimensionality". We shall construct a new sparse spectral method for highdimensional problems, and present, in particular, rigorous error estimates as well as efficient numerical algorithms for elliptic equations. We shall also propose a new weighted weak formulation for the FokkerPlanck equation of FENE dumbbell model, and prove its wellposedness in weighted Sobolev spaces. Based on the new formulation, we are able to design simple, efficient, and unconditionally stable semiimplicit FourierJacobi schemes for the FokkerPlanck equation of FENE dumbbell model. It is hoped that the combination of the two new approaches would make it possible to directly simulate the five or six dimensional NavierStokes FokkerPlanck system. 

ChiWang Shu (Brown University)  Maximumprinciplesatisfying and positivitypreserving high order discontinuous Galerkin and finite volume schemes for conservation laws 
Abstract: We construct uniformly high order accurate discontinuous Galerkin (DG) and weighted essentially nonoscillatory (WENO) finite volume (FV) schemes satisfying a strict maximum principle for scalar conservation laws and passive convection in incompressible flows, and positivity preserving for density and pressure for compressible Euler equations. A general framework (for arbitrary order of accuracy) is established to construct a limiter for the DG or FV method with first order Euler forward time discretization solving one dimensional scalar conservation laws. Strong stability preserving (SSP) high order time discretizations will keep the maximum principle and make the scheme uniformly high order in space and time. One remarkable property of this approach is that it is straightforward to extend the method to two and higher dimensions. The same limiter can be shown to preserve the maximum principle for the DG or FV scheme solving twodimensional incompressible Euler equations in the vorticity streamfunction formulation, or any passive convection equation with an incompressible velocity field. A suitable generalization results in a high order DG or FV scheme satisfying positivity preserving property for density and pressure for compressible Euler equations. Numerical tests demonstrating the good performance of the scheme will be reported. This is a joint work with Xiangxiong Zhang.  
Rob Stevenson (Universiteit van Amsterdam)  Adaptive tensor product wavelet methods for solving wellposed operator equations 
Abstract: In this talk, we give an overview of adaptive wavelet methods for solving operator equations. In particular, we will focus on the following topics: The application of these methods to time evolution problems as parabolic problems and the instationary Stokes system; the advantage of the application of tensor product wavelets and the role of anisotropic regularity; the construction of piecewise tensor product wavelet bases on general domains; the application of the adaptive scheme to singularly perturbed problems.  
Tong Sun (Bowling Green State University)  Numerical smoothness and error analysis for RKDG on the scalar nonlinear conservation laws 
Abstract: The new concept of numerical smoothness is applied to the RKDG (RungeKutta/Discontinuous Galerkin) methods for scalar nonlinear conservations laws. The main result is an a posteriori error estimate for the RKDG methods of arbitrary order in space and time, with optimal convergence rate. Currently, the case of smooth solutions is the focus point. However, the error analysis framework is prepared to deal with discontinuous solutions in the future.  
Yi Sun (Statistical and Applied Mathematical Sciences Institute (SAMSI))  Numerical study of singular solutions of relativistic Euler equations 
Abstract: Singularity formation in relativistic flow is an open theoretical problem in relativistic hydrodynamics. These singularities can be either shock formation, violation of the subluminal conditions or concentration of the mass. We numerically investigate singularity formation in solutions of the relativistic Euler equations in (2+1)dimensional spacetime with smooth initial data. A hybrid method is used to solve the radially symmetric case. The hybrid method takes the Glimm scheme for an accurate treatment of nonlinear waves and a centralupwind scheme in other regions where the fluid flow is sufficiently smooth. The numerical results indicate that shock formation occurs in a certain parametric regime. This is a joint work with Pierre Gremaud.  
Vidar Thomée (Chalmers University of Technology)  Plenary talk: On the lumped mass finite element method for parabolic problems 
Abstract: We study the lumped mass method for the model homogeneous heat
equation
with homogeneous Dirichlet boundary conditions. We first recall
that the maximum
principle for the heat equation does not carry over to the the
spatially semidiscrete
standard Galerkin finite element method, using continuous,
piecewise linear approximating functions. However, for the lumped mass variant the
situation is more
advantageous. We present necessary and sufficient conditions on
the triangulation, expressed in terms of properties of the stiffness matrix,
for the semidiscrete
lumped mass solution operator to be a positive operator or a
contraction in the
maximumnorm. We then turn to error estimates in the L_{2}norm. Improving earlier results we show that known optimal order smooth initial data error estimates for the standard Galerkin method carry over to the lumped mass method, whereas nonsmooth initial data estimates require special assumptions on the triangulations. We also discuss the application to time discretization by the backward Euler and CrankNicolson methods. 

Ray S. Tuminaro (Sandia National Laboratories)  Energy minimization algebraic multigrid: Robustness and flexibility in multilevel software 
Abstract: Energy minimization provides a general framework for developing a family of multigrid algorithms.
The proposed strategy is applicable to Hermitian, nonHermitian, definite, and indefinite problems.
Each column of the grid transfer operator P is minimized in an energybased norm while enforcing two types of constraints: a defined sparsity pattern and preservation of specified modes in the range of P. A Krylovbased
strategy is used to minimize energy, which is equivalent to solving A P = 0 with the constraints ensuring a
nontrivial solution. For the Hermitian positive definite case, a conjugate gradientbased (CG)
method is utilized to construct grid transfers, while methods based on generalized minimum residual
(GMRES) and CG on the normal equations (CGNR) are explored for the general case. One of the main advantages of the approach is that it is flexible, allowing for arbitrary coarsenings, unrestricted sparsity patterns, straightforward long distance interpolation, and general use of constraints, either userdefined or autogenerated. We illustrate how this flexibility can be used to adapt an algebraic multigrid scheme to an extended finite element discretization suitable for modeling fracture. Computational results are presented illustrate that this particular energy minimization scheme gives rise to mesh independent convergence rates and is relatively insensitive to the number and location of cracks being modeled. 

Catalin Turc (Case Western Reserve University)  Efficient, accurate and rapidlyconvergent algorithms for the solution of three dimensional acoustic and electromagnetic scattering problems in domains with geometric singularities 
Abstract: We present novel discretization techniques based on boundary integral equations formulations for the solution of three dimensional acoustic and electromagnetic scattering problems in domains with corners and edges. Our method is based on three main components: (1) the use of regularization/preconditioning techniques to design wellconditioned boundary integral equations in domains with geometric singularities; (2) the use of ansatz formulations that explicitly account for the singular and possibly unbounded behavior of the quantities that enter the integral formulations; and (3) the use of a novel Nystrom discretization technique based on nonoverlapping integration patches and Chebyshev discretization together with ClenshawCurtistype integrations. We will illustrate the excellent performance of our solvers for a variety of challenging 3D configurations that include closed/open domains with corners and edges. Joint work with O. Bruno (Caltech) and A. Anand (IIT Kanpur).  
Andreas Michael Veeser (Università di Milano)  Local and global approximation of gradients with piecewise polynomials 
Abstract: The quality of a finite element solution hinges in particular on the approximation properties of the finite element space. In the first part of this talk we will consider the approximation of the gradient of a target function by continuous piecewise polynomials over a simplicial, 'shaperegular' mesh and prove the following result: the global best approximation error is equivalent to an appropriate sum in terms of the local best approximation errors on the elements, which do not overlap. This means in particular that, for gradient norms, the continuity requirement does not downgrade the local approximation potential on elements and that discontinuous piecewise polynomials do not offer additional approximation power. In the second part of the talk we will discuss the usefulness of this result in the context of adaptive methods for partial differential equations. Joint work with Francesco Mora (Milan). 

Peter Edward Vincent (Stanford University)  The flux reconstruction approach to highorder methods: Theory and application 
Abstract: Highorder flux reconstruction (FR) schemes are efficient, simple to implement, and allow various highorder methods, such as the nodal discontinuous Galerkin (DG) method and any spectral difference method, to be cast within a single unifying framework. Recently, we have identified a new class of 1D linearly stable FR schemes. Identification of such schemes offers significant insight into why certain FR schemes are stable, whereas other are not. Also, from a practical standpoint, the resulting linearly stable formulation provides a simple prescription for implementing an infinite range of intuitive and apparently robust highorder methods. We are currently extending the 1D formulation to multiple dimensions (including to simplex elements). We are also developing CPU/GPU enabled unstructured highorder inviscid and viscous compressible flow solvers based on the range of linearly stable FR schemes. Details of both the mathematical theory and the practical implementation will be presented in the poster.  
Shawn W. Walker (Louisiana State University)  Shape optimization of chiral propellers in 3D stokes flow 
Abstract: Locomotion at the microscale is important in biology and in industrial applications such as targeted drug delivery and microfluidics. We present results on the optimal shape of a rigid body locomoting in 3D Stokes flow. The actuation consists of applying a fixed moment and constraining the body to only move along the moment axis; this models the effect of an external magnetic torque on an object made of magnetically susceptible material. The shape of the object is parametrized by a 3D centerline with a given crosssectional shape. No a priori assumption is made on the centerline. We show there exists a minimizer to the infinite dimensional optimization problem in a suitable infinite class of admissible shapes. We develop a variational (constrained) descent method which is wellposed for the continuous and discrete versions of the problem. Sensitivities of the cost and constraints are computed variationally via shape differential calculus. Computations are accomplished by a boundary integral method to solve the Stokes equations, and a finite element method to obtain descent directions for the optimization algorithm. We show examples of locomotor shapes with and without different fixed payload/cargo shapes.  
Wei Wang (Florida International University)  High order wellbalanced schemes for nonequilibrium flows 
Abstract: We studied the wellbalancedness properties of the high order finite difference WENO schemes and high order low dissipative filter schemes based on a fivespecies onetemperature reacting flow model. Both 1d and 2d results are shown to demonstrate the advantages of using wellbalanced schemes for nonequilibrium flows.  
Timothy C. Warburton (Rice University)  GPU accelerated discontinuous Galerkin methods 
Abstract: This poster will describe recent progress in adapting discontinuous Galerkin methods to obtain high efficiency on modern graphics processing units. A new low storage version of the methods allows unstructured meshes where all elements to be curvilinear without incurring the usual expensive memory overhead of the traditional scheme. Some performance tests reveal that a modest workstation can generate teraflop performance. Simulation results from timedomain electromagnetics and also compressible flows will demonstrate the promise of this new formulation.  
Olof B. Widlund (New York University)  An introduction to domain decomposition algorithms 
Abstract: Variational formulation and piecewise linear finite element approximations
of Poisson's problem. Dirichlet and Neumann boundary conditions and
Poincaré's and Friedrichs's inequalities. A word about linear elasticity.
Condition numbers of finite element matrices and the preconditioned conjugate
gradient method. Domains and subdomains. Subdomain matrices as building blocks for domain decomposition methods and the related Schur complements. The twosubdomain case: the NeumannDirichlet and Schwarz alternating algorithms; they can be placed in a unified framework and written in terms of Schur complements. Extension to the case of many subdomains; coloring, the problems of singular subdomain matrices, and the need to use a coarse, global problem. Three assumptions and the basic result on the condition number of additive Schwarz algorithms. Classical and more recent twolevel additive Schwarz methods. Remarks on the effect of irregular subdomains. Extensions to elasticity problems including the almost incompressible case. Modern iterative substructuring methods: FETI–DP and BDDC. An introduction in terms of blockCholesky for problems only partially assembled. The equivalence of the spectra. Results on elasticity including incompressible Stokes problems. 

Olof B. Widlund (New York University)  New Domain Decomposition Algorithms from Old 
Abstract: In recent years, variants of the twolevel Schwarz algorithm
have been developed in collaboration between Clark Dohrmann of SandiaAlbuquerque and a group at the Courant Institute. By a modification of the coarse component of the preconditioner, borrowed in part from older domain decomposition methods of iterative substructuring type, the new methods are easier to implement for general subdomain geometries and can be made insensitive to large variations on the coefficients of the partial differential equation across the interface between the subdomains. After an introduction to the design of these methods, results on applications to almost incompressible elasticity and ReissnerMindlin plates  solved by using mixed finite elements  and problems posed in H(div) and H(curl) will be discussed. Some of these results will appear in the doctoral dissertations of Jong Ho Lee and Duksoon Oh, two PhD candidates at the Courant Institute. 

Barbara Wohlmuth (Technical University of Munich )  Variational consistent discretization schemes and numerical algorithms for contact problems 
Abstract: We consider variationally consistent discretization schemes for mechanical contact problems. Most of the results can also be applied to other variational inequalities such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance.
The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddlepoint problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain.
Having a uniform infsup bound, one can then establish optimal loworder a priori convergence rates for the discretization error in the primal and dual variables. In addition to the abstract framework of the linear saddlepoint theory, complementarity terms have to be taken into account. The resulting inequality system is solved by rewriting it equivalently by means of the nonlinear complementarity function as a system of equations.
Although it is not differentiable in the classical sense, semismooth Newton methods, yielding superlinear convergence rates, can be applied and easily implemented in terms of a primaldual active set strategy. Quite often the solution of contact problems has a low regularity, and the efficiency of the approach can be improved by using adaptive refinement techniques. Different standard types, such as residual and equilibrated based a posteriori error estimators, can be designed based on the interpretation of the dual variable as Neumann boundary condition. For the fully dynamic setting it is of interest to apply energypreserving time integration schemes.
However, the differential algebraic character of the system can result in high oscillations if standard methods are applied. A possible remedy is to modify the fully discretized system by a local redistribution of the mass. Numerical results in two and three dimensions illustrate the wide range of possible applications and show the performance of the space discretization scheme, nonlinear solver, adaptive refinement process and time integration.


Carol S. Woodward (Lawrence Livermore National Laboratory)  Implicit Solution Approaches: Why We Care and How We Solve the Systems 
Abstract: Parallel computers with large storage capacities have paved the way for increasing both the fidelity and complexity of largescale simulations. Increasing fidelity leads to tighter constraints on time steps for stability of explicit methods. Increasing complexity tends to also increase the number of physics models and variations in time scales. Providing both a stable solution process which can accurately capture nonlinear coupling between dynamically relevant phenomena while stepping over fast waves or rapid adjustments leads us toward implicit solution approaches.
This presentation provides an overview of issues arising in large scale, multiphysics simulations and some of the motivators for looking at implicit approaches. We discuss several popular implicit nonlinear solver technologies and show examples of uses of them within the context of problems found in supernova, subsurface simulation, fusion, and nonlinear diffusion problems. 

Dexuan Xie (University of Wisconsin)  Finite element analysis and a fast solver approach to a nonlocal dielectric continuum model 
Abstract: The nonlocal continuum dielectric model is an important extension of the classical Poisson dielectric model. This poster will report some recent results we made on the finite element analysis and fast solver development for one commonlyused nonlocal continuum dielectric model. We first prove that the finite element equation of this model has the unique solution but leads to a dense linear system, which is very expansive to be solved. Surprisingly, we then discover and prove that such a dense linear system can be converted to a system of two sparse finite element equations in a form similar to the standard mixed finite element equation. In this way, fast numerical solvers can be developed to solve the nonlocal continuum dielectric model in an optimal order. Some numerical results in free energy calculation will also be presented to demonstrate the great promise of nonlocal dielectric modeling in improving the accuracy of the classic Poisson dielectric model in computing electrostatic potential energies. This project is a joined work with Prof. Ridgeway Scott, Peter Brune, (both from University of Chicago), and Yi Jiang under the support of NSF grant #DMS0921004.  
Jinchao Xu (Pennsylvania State University)  Multilevel iterative methods for PDEs based on one or no grid 
Abstract: Several numerical techniques will be presented for solving discretized partial differential equations (PDEs) by special multilevel methods based on one or no grid with nearly optimal computational complexity in a userfriendly fashion.  
Liwei Xu (Rensselaer Polytechnic Institute)  Numerical simulation of threedimensional nonlinear water waves 
Abstract: We present an accurate and efficient numerical model for the simulation of fully nonlinear (nonbreaking), threedimensional surface water waves on infinite or finite depth. As an extension of the work of Craig and Sulem (1993), the numerical method is based on the reduction of the problem to a lowerdimensional Hamiltonian system involving surface quantities alone. This is accomplished by introducing the DirichletNeumann operator which is described in terms of its Taylor series expansion in homogeneous powers of the surface elevation. Each term in this Taylor series can be computed efficiently using the fast Fourier transform. An important contribution of this paper is the development and implementation of a symplectic implicit scheme for the time integration of the Hamiltonian equations of motion, as well as detailed numerical tests on the convergence of the DirichletNeumann operator. The performance of the model is illustrated by simulating the longtime evolution of twodimensional steadily progressing waves, as well as the development of threedimensional (shortcrested) nonlinear waves, both in deep and shallow water. This is a joint work with Philippe Guyenne at the University of Delaware.  
Liwei Xu (Rensselaer Polytechnic Institute)  Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergencefree magnetic field 
Abstract: We present a central discontinuous Galerkin method for solving ideal magnetohydrodynamic (MHD) equations. The methods are based on the original central discontinuous Galerkin methods designed for hyperbolic conservation laws on overlapping meshes, and they use different discretization for magnetic induction equations. The resulting schemes carry many features of standard central discontinuous Galerkin methods such as high order accuracy and being free of exact or approximate Riemann solvers. And more importantly, the numerical magnetic field is exactly divergencefree. Such property, desired in reliable simulations of MHD equations, is achieved by first approximating the normal component of the magnetic field through discretizing induction equations on the mesh skeleton, namely, the element interfaces. And then it is followed by an elementbyelement divergencefree reconstruction with the matching accuracy. Numerical examples are presented to demonstrate the high order accuracy and the robustness of the schemes. This is a joint work with Fengyan Li and Sergey Yakovlev at Rensselaer Polytechnic Institute.  
Guangri Xue (University of Texas at Austin)  A multipoint flux mixed finite element method on general hexahedra: Multiscale mortar extension and applications to multiphase flow in porous media 
Abstract: Joint work with Mary Wheeler (University of Texas) and Ivan
Yotov (University of Pittsburgh). We develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cellcentered finite difference scheme. A special nonsymmetric quadrature rule is employed that yields a positive definite cellcentered system for the scalar by eliminating local fluxes. The method is shown to be accurate on highly distorted rough quadrilateral and hexahedral grids, including hexahedra with nonplanar faces. Theoretical and numerical results indicate firstorder convergence for the scalar and face fluxes. We also develop multiscale mortar method that utilize multipoint flux mixed finite element method as the fine scale discretization. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. We present applications to muliphase flow in porous media. 

Ulrike Meier Yang (Lawrence Livermore National Laboratory)  A parallel computing tutorial 
Abstract: This tutorial will provide an overview of the concepts of parallel computing. Topics to be discussed comprise parallel programming models and computer architectures, including multicore architectures, as well as various issues that need to be considered when designing parallel programs. Several examples of parallel solvers will be presented to illustrate the challenges that need to be overcome to achieve an efficient implementation.  
Ulrike Meier Yang (Lawrence Livermore National Laboratory)  Hypre: A scalable linear solver library 
Abstract: Hypre is a software library for solving large, sparse linear systems of equations on massively parallel computers. The library was created with the primary goal of providing users with advanced parallel preconditioners. The library features parallel multigrid solvers for both structured and unstructured grid problems. For ease of use, these solvers are accessed from the application code via hypre’s conceptual linear system interfaces, which allow a variety of natural problem descriptions. The motivation for the design of hypre, an overview of its interfaces and some of its performance highlights are presented.  
Irad Yavneh (TechnionIsrael Institute of Technology)  Nonlinear Multigrid Revisited 
Abstract:
Multigrid algorithms for discretized nonlinear partial differential equations and systems are nearly as old as multigrid itself. Over the years several approaches and variants of nonlinear multigrid algorithms have been developed. Typically, for relatively easy problems the different approaches exhibit similar performance. However, for difficult problems the behavior varies, and it is not easy to predict which approach may prevail. In this talk we will consider nonlinear multigrid, focusing on the task of coarsegrid correction, in a general framework of variational coarsening. Such a view reveals clear relations between the various existing approaches and may suggest future variants. This study also sheds light on the choice of intergrid transfer operators, which are so important for obtaining fast multigrid convergence, and which have received much attention in linear multigrid algorithms but far less so in nonlinear multigrid. 

Shangyou Zhang (University of Delaware)  A jumping multigrid method via finite element extrapolation 
Abstract: The multigrid method solves the finite element equations in optimal
order, i.e., solving a linear system of $O(N)$ equations in
$O(N)$ arithmetic operations.
Based on low level solutions, we can use finite element extrapolation
to obtain the highlevel finite element solution on some
coarselevel element boundary, at an higher accuracy $O(h_i4)$.
Thus, we can solve higher level $(h_j, junderset{sim}{<}2i)$
finite element problems locally on each such
coarselevel element.
That is, we can skip the finite element problem
on middle levels, $h_{i+1},h_{i+2},dots, h_{j1}$.
Roughly speaking,
such a jumping multigrid method solves an order $O(N)=O(2^{2di})$
linear system of equations by
a memory of $O(sqrt N)=O(2^{di})$, and by a parallel computation
of $O(sqrt N)$, where $d$ is the space dimension. 
Jeffrey Abell  General Motors  11/11/2010  11/12/2010 
Slimane Adjerid  Virginia Polytechnic Institute and State University  10/31/2010  11/5/2010 
Mark Ainsworth  University of Strathclyde  11/28/2010  12/4/2010 
Alexander Alekseenko  California State University  9/1/2010  12/31/2010 
Roman Andreev  ETH Zürich  10/31/2010  11/6/2010 
Paola Francesca Antonietti  Politecnico di Milano  11/27/2010  12/3/2010 
Todd Arbogast  University of Texas at Austin  10/31/2010  11/7/2010 
Douglas N. Arnold  University of Minnesota  9/1/2010  6/30/2011 
Donald G. Aronson  University of Minnesota  9/1/2002  8/31/2011 
Gerard Michel Awanou  Northern Illinois University  9/1/2010  6/10/2011 
Blanca Ayuso de Dios  Centre de Recerca Matemàtica  10/30/2010  12/18/2010 
Constantin Bacuta  University of Delaware  10/31/2010  11/7/2010 
Nusret Balci  University of Minnesota  9/1/2009  8/31/2011 
Uday Banerjee  Syracuse University  9/1/2010  12/3/2010 
Randolph E. Bank  University of California, San Diego  11/28/2010  12/2/2010 
Andrew T. Barker  Louisiana State University  10/31/2010  11/6/2010 
Andrew T. Barker  Louisiana State University  11/27/2010  12/3/2010 
Yuri Bazilevs  University of California, San Diego  10/31/2010  11/5/2010 
Pavel Belik  Augsburg College  11/29/2010  12/3/2010 
Christine Bernardi  Université de Paris VI (Pierre et Marie Curie)  10/31/2010  11/5/2010 
Pavel B. Bochev  Sandia National Laboratories  10/30/2010  11/7/2010 
Daniele Boffi  Università di Pavia  10/30/2010  11/7/2010 
Andrea Bonito  Texas A & M University  11/26/2010  12/4/2010 
Francesca Bonizzoni  Politecnico di Milano  10/15/2010  11/10/2010 
Carlos Eduardo Cardoso Borges  Worcester Polytechnic Institute  11/27/2010  12/4/2010 
James H. Bramble  Texas A & M University  11/5/2010  11/7/2010 
Susanne C. Brenner  Louisiana State University  9/1/2010  6/10/2011 
Peter Brune  University of Chicago  11/27/2010  12/6/2010 
XiaoChuan Cai  University of Colorado  11/30/2010  12/3/2010 
Claudio Canuto  Politecnico di Torino  10/17/2010  11/7/2010 
Varis Carey  Colorado State University  11/4/2010  11/7/2010 
Carsten Carstensen  Yonsei University  11/29/2010  12/4/2010 
Fatih Celiker  Wayne State University  9/1/2010  12/31/2010 
Aycil Cesmelioglu  University of Minnesota  9/30/2010  8/30/2011 
Chi Hin Chan  University of Minnesota  9/1/2009  8/31/2011 
Feng Chen  Purdue University  10/30/2010  11/4/2010 
Long Chen  University of California, Irvine  11/28/2010  12/3/2010 
Qiang Chen  University of Delaware  10/31/2010  11/6/2010 
Yanlai Chen  University of Massachusetts, Dartmouth  10/31/2010  11/7/2010 
Zhiming Chen  Chinese Academy of Sciences  10/31/2010  11/7/2010 
Yingda Cheng  Brown University  10/31/2010  11/7/2010 
Heejun Choi  Purdue University  11/28/2010  12/3/2010 
ShueSum Chow  Brigham Young University  10/31/2010  11/7/2010 
Bernardo Cockburn  University of Minnesota  9/1/2010  6/30/2011 
Jintao Cui  University of Minnesota  8/31/2010  8/30/2011 
Wolfgang Dahmen  RWTH Aachen  11/1/2010  11/6/2010 
Christopher Davis  University of North Carolina  Charlotte  11/4/2010  11/6/2010 
Clint Dawson  University of Texas at Austin  10/31/2010  11/4/2010 
Leszek Feliks Demkowicz  University of Texas at Austin  10/31/2010  11/7/2010 
Alan Demlow  University of Kentucky  11/2/2010  11/6/2010 
Alan Demlow  University of Kentucky  11/29/2010  12/3/2010 
Clark R. Dohrmann  Sandia National Laboratories  11/29/2010  12/3/2010 
Tobin A. Driscoll  University of Delaware  8/26/2010  12/20/2010 
Qiang Du  Pennsylvania State University  11/2/2010  11/7/2010 
Yalchin Efendiev  Texas A & M University  11/1/2010  11/5/2010 
Bjorn Engquist  University of Texas at Austin  11/1/2010  11/5/2010 
Randy H. Ewoldt  University of Minnesota  9/1/2009  8/31/2011 
Robert Falgout  Lawrence Livermore National Laboratory  11/27/2010  12/4/2010 
Richard S Falk  Rutgers University  9/19/2010  12/18/2010 
Sean Farley  Argonne National Laboratory  11/5/2010  11/7/2010 
Xiaobing Henry Feng  University of Tennessee  10/29/2010  12/15/2010 
Oscar E. Fernandez  University of Minnesota  8/31/2010  8/30/2011 
Donald A. French  University of Cincinnati  11/4/2010  11/7/2010 
Andreas Frommer  Bergische UniversitätGesamthochschule Wuppertal (BUGH)  11/28/2010  12/5/2010 
Martin J. Gander  Universite de Geneve  11/28/2010  12/3/2010 
Xinfeng Gao  Lawrence Berkeley National Laboratory  11/28/2010  12/3/2010 
Carlos Andres GaravitoGarzon  University of Minnesota  11/28/2010  11/29/2010 
Lucia Gastaldi  Università di Brescia  10/30/2010  11/7/2010 
Joscha Gedicke  HumboldtUniversität  10/30/2010  12/4/2010 
Marc Iwan Gerritsma  Technische Universiteit te Delft  10/30/2010  11/6/2010 
Andrew Kruse Gillette  University of Texas at Austin  10/31/2010  11/5/2010 
Matthias K. Gobbert  University of Maryland Baltimore County  11/28/2010  12/2/2010 
Jay Gopalakrishnan  University of Florida  9/1/2010  6/30/2011 
Shiyuan Gu  Louisiana State University  9/1/2010  6/30/2011 
Thirupathi Gudi  Indian Institute of Science  11/27/2010  12/3/2010 
Johnny Guzman  Brown University  11/1/2010  11/13/2010 
Xiaoming He  Missouri University of Science and Technology  11/3/2010  11/7/2010 
Xiaoming He  Missouri University of Science and Technology  11/28/2010  12/3/2010 
Ying He  Purdue University  11/29/2010  12/3/2010 
Yuan He  Columbia University  11/28/2010  12/4/2010 
Jan S. Hesthaven  Brown University  10/30/2010  11/6/2010 
Robert L. Higdon  Oregon State University  10/31/2010  11/5/2010 
Ronald H.W. Hoppe  University of Houston  9/6/2010  12/20/2010 
Raya Horesh  University of Minnesota  10/15/2010  11/6/2010 
Thomas Yizhao Hou  California Institute of Technology  10/30/2010  11/4/2010 
Jason Howell  Clarkson University  10/31/2010  11/7/2010 
Yulia Hristova  University of Minnesota  9/1/2010  8/31/2011 
Lili Hu  Georgia Institute of Technology  10/31/2010  11/5/2010 
Jae Woo Jeong  Miami University  11/5/2010  11/6/2010 
Sunnie Joshi  Texas A & M University  10/30/2010  11/5/2010 
Lili Ju  University of South Carolina  10/31/2010  11/4/2010 
Myungjoo Kang  Seoul National University  10/31/2010  11/5/2010 
Guido Kanschat  Texas A & M University  9/6/2010  12/20/2010 
ChiuYen Kao  Ohio State University  9/1/2010  12/20/2010 
Ohannes Karakashian  University of Tennessee  11/4/2010  11/6/2010 
Markus Keel  University of Minnesota  7/21/2008  6/30/2011 
David Keyes  King Abdullah University of Science & Technology  11/28/2010  12/3/2010 
Chisup Kim  Catholic University of America  11/5/2010  11/6/2010 
Hyunju Kim  University of North Carolina  Charlotte  11/4/2010  11/6/2010 
Seungil Kim  Southern Methodist University  11/4/2010  11/7/2010 
JungHan Kimn  South Dakota State University  11/29/2010  12/2/2010 
Axel Klawonn  Universität DuisburgEssen  11/27/2010  12/3/2010 
Jon Kleinberg  Cornell University  11/7/2010  11/10/2010 
Tzanio V Kolev  Lawrence Livermore National Laboratory  11/29/2010  12/3/2010 
Pawel Konieczny  University of Minnesota  9/1/2009  8/31/2011 
Ralf Kornhuber  Freie Universität Berlin  11/28/2010  12/5/2010 
Kristina Kraakmo  University of Central Florida  10/30/2010  11/3/2010 
Johannes Karl Kraus  Johann Radon Institute for Computational and Applied Mathematics  11/27/2010  12/3/2010 
Christian Kreuzer  Universität DuisburgEssen  11/28/2010  12/4/2010 
JaEun Ku  Oklahoma State University  11/4/2010  11/7/2010 
Angela Kunoth  Universität Paderborn  10/31/2010  11/7/2010 
Stig Larsson  Chalmers University of Technology  11/3/2010  11/6/2010 
Ilya Lashuk  Lawrence Livermore National Laboratory  10/29/2010  11/5/2010 
Anita Layton  Duke University  11/1/2010  11/4/2010 
Raytcho Lazarov  Texas A & M University  11/3/2010  11/7/2010 
Sabine Le Borne  Tennessee Technological University  11/28/2010  12/3/2010 
Jungho Lee  Argonne National Laboratory  11/29/2010  12/3/2010 
YoungJu Lee  Rutgers University  11/4/2010  11/7/2010 
Gilad Lerman  University of Minnesota  9/1/2010  6/30/2011 
Dmitriy Leykekhman  University of Connecticut  10/31/2010  11/7/2010 
Dmitriy Leykekhman  University of Connecticut  11/29/2010  12/3/2010 
Fengyan Li  Rensselaer Polytechnic Institute  9/1/2010  12/20/2010 
Hengguang Li  University of Minnesota  8/16/2010  8/15/2011 
Jichun Li  University of Nevada  11/2/2010  11/6/2010 
Jing Li  Kent State University  11/28/2010  12/4/2010 
Lizao (Larry) Li  University of Minnesota  11/28/2010  12/3/2010 
Yan Li  University of Minnesota  10/30/2010  11/6/2010 
Zhilin Li  North Carolina State University  10/31/2010  11/5/2010 
Hyeona Lim  Mississippi State University  10/30/2010  11/4/2010 
Guang Lin  Pacific Northwest National Laboratory  10/29/2010  11/3/2010 
Runchang Lin  Texas A&M International University (TAMIU)  11/4/2010  11/6/2010 
Tao Lin  Virginia Polytechnic Institute and State University  11/5/2010  11/7/2010 
Zhi (George) Lin  University of Minnesota  9/1/2009  8/31/2011 
Hailiang Liu  Iowa State University  10/31/2010  11/5/2010 
Jiangguo (James) Liu  Colorado State University  10/31/2010  11/7/2010 
Xinfeng Liu  University of South Carolina  11/1/2010  11/4/2010 
Irene Livshits  Ball State University  11/28/2010  12/3/2010 
Alexei Lozinski  Université de Toulouse III (Paul Sabatier)  10/31/2010  11/5/2010 
Mitchell Luskin  University of Minnesota  9/1/2010  6/30/2011 
Lina Ma  Purdue University  10/31/2010  11/6/2010 
Scott MacLachlan  Tufts University  10/24/2010  12/3/2010 
Yvon Jean Maday  Université de Paris VI (Pierre et Marie Curie)  11/1/2010  11/4/2010 
Niall Madden  National University of Ireland, Galway  10/18/2010  12/10/2010 
Kara Lee Maki  University of Minnesota  9/1/2009  8/31/2011 
Jan Mandel  University of Colorado  11/29/2010  12/3/2010 
Thomas A. Manteuffel  University of Colorado  11/30/2010  12/3/2010 
Yu (David) Mao  University of Minnesota  8/31/2010  8/30/2011 
Maider Judith MarinMcGee  University of Puerto Rico  10/29/2010  11/6/2010 
Tarek P Mathew  University of Colorado  11/28/2010  12/4/2010 
Jens Markus Melenk  Technische Universität Wien  10/30/2010  11/7/2010 
Irina Mitrea  University of Minnesota  8/16/2010  6/14/2011 
Dimitrios Mitsotakis  University of Minnesota  10/27/2010  8/31/2011 
Peter Monk  University of Delaware  9/8/2010  12/10/2010 
Brian Edward Moore  University of Central Florida  10/31/2010  11/3/2010 
Zhe Nan  Louisiana State University  10/30/2010  11/7/2010 
Michael Joseph Neilan  Louisiana State University  10/29/2010  11/7/2010 
Michael Joseph Neilan  Louisiana State University  11/27/2010  12/4/2010 
NgocCuong Nguyen  Massachusetts Institute of Technology  10/31/2010  11/5/2010 
Nilima Nigam  Simon Fraser University  11/1/2010  11/6/2010 
Sylvain Nintcheu Fata  Oak Ridge National Laboratory  11/1/2010  1/29/2011 
Victor Nistor  Pennsylvania State University  11/4/2010  11/7/2010 
Ricardo H. Nochetto  University of Maryland  9/13/2010  12/15/2010 
Ioannis Nompelis  University of Minnesota  11/28/2010  12/3/2010 
HaeSoo Oh  University of North Carolina  Charlotte  11/4/2010  11/7/2010 
Minah Oh  James Madison University  11/4/2010  11/6/2010 
Minah Oh  James Madison University  11/28/2010  12/4/2010 
Luke Olson  University of Illinois at UrbanaChampaign  11/28/2010  12/5/2010 
Alexandra Ortan  University of Minnesota  9/16/2010  6/15/2011 
Cecilia OrtizDuenas  University of Minnesota  9/1/2009  8/31/2011 
MiaoJung Yvonne Ou  Oak Ridge National Laboratory  8/30/2010  12/10/2010 
Jeffrey Ovall  University of Kentucky  10/31/2010  11/7/2010 
Sevtap Ozisik  Rice University  11/2/2010  11/7/2010 
EunHee Park  Louisiana State University  10/30/2010  11/7/2010 
EunHee Park  Louisiana State University  11/27/2010  12/4/2010 
Joseph E. Pasciak  Texas A & M University  11/5/2010  11/6/2010 
Jaime Peraire  Massachusetts Institute of Technology  10/31/2010  11/5/2010 
Ilaria Perugia  Università di Pavia  10/30/2010  11/6/2010 
Petr Plechac  University of Tennessee  9/1/2010  12/10/2010 
Jingmei Qiu  Colorado School of Mines  10/31/2010  11/3/2010 
Weifeng (Frederick) Qiu  University of Minnesota  8/31/2010  8/30/2011 
Vincent QuennevilleBelair  University of Minnesota  9/16/2010  6/15/2011 
Rachel Quinlan  National University of Ireland, Galway  10/18/2010  12/10/2010 
Naveen Ramunigari  University of Texas  11/27/2010  11/30/2010 
Darsh Priya Ranjan  University of California, Berkeley  10/29/2010  11/6/2010 
S. S. Ravindran  University of Alabama  11/4/2010  11/7/2010 
Armin Reiser  Louisiana State University  9/1/2010  12/13/2010 
Fernando Reitich  University of Minnesota  9/1/2010  6/30/2011 
Gianluigi Rozza  École Polytechnique Fédérale de Lausanne (EPFL)  10/30/2010  11/6/2010 
Ulrich Rüde  FriedrichAlexanderUniversität ErlangenNürnberg  11/28/2010  12/3/2010 
Giancarlo Sangalli  Università di Pavia  10/30/2010  11/6/2010 
Fadil Santosa  University of Minnesota  7/1/2008  6/30/2011 
Marcus Sarkis  Worcester Polytechnic Institute  11/29/2010  12/3/2010 
FranciscoJavier Sayas  University of Delaware  10/28/2010  11/7/2010 
Alfred Schatz  Cornell University  11/4/2010  11/7/2010 
Reinhold Schneider  TU Berlin  10/30/2010  11/6/2010 
Joachim Schöberl  Technische Universität Wien  11/1/2010  11/7/2010 
Dominik M. Schoetzau  University of British Columbia  10/30/2010  11/7/2010 
Christoph Schwab  ETH Zürich  10/31/2010  11/7/2010 
Marc Alexander Schweitzer  Rheinische FriedrichWilhelmsUniversität Bonn  10/31/2010  11/7/2010 
Guglielmo Scovazzi  Sandia National Laboratories  10/29/2010  11/5/2010 
Francisco G Serpa  Booz Allen Hamilton Inc. (BAH)  11/27/2010  12/4/2010 
Shuanglin Shao  University of Minnesota  9/1/2009  8/31/2011 
Natasha Shilla Sharma  University of Houston  11/5/2010  11/7/2010 
Mikhail Shashkov  Los Alamos National Laboratory  10/31/2010  11/5/2010 
Jie Shen  Purdue University  10/30/2010  11/6/2010 
Jie Shen  Purdue University  11/30/2010  12/3/2010 
Ke Shi  University of Minnesota  10/30/2010  11/6/2010 
ChiWang Shu  Brown University  10/31/2010  11/6/2010 
Ari Stern  University of California, San Diego  10/31/2010  11/6/2010 
Rob Stevenson  Universiteit van Amsterdam  10/30/2010  11/6/2010 
Panagiotis Stinis  University of Minnesota  9/1/2010  6/30/2011 
Jiguang Sun  Delaware State University  10/31/2010  11/7/2010 
Pengtao Sun  University of Nevada  11/2/2010  11/6/2010 
Tong Sun  Bowling Green State University  10/30/2010  11/7/2010 
Yi Sun  Statistical and Applied Mathematical Sciences Institute (SAMSI)  10/31/2010  11/4/2010 
Liyeng Sung  Louisiana State University  9/1/2010  6/15/2011 
Nicolae Tarfulea  Purdue University, Calumet  9/1/2010  6/15/2011 
Radek Tezaur  Stanford University  11/29/2010  12/3/2010 
Vidar Thomée  Chalmers University of Technology  11/3/2010  11/7/2010 
Dimitar Trenev  University of Minnesota  9/1/2009  8/31/2011 
Ray S. Tuminaro  Sandia National Laboratories  11/29/2010  12/3/2010 
Catalin Turc  Case Western Reserve University  10/31/2010  11/5/2010 
Danail Vassilev  University of Pittsburgh  11/4/2010  11/6/2010 
Panayot S Vassilevski  Lawrence Livermore National Laboratory  10/31/2010  11/5/2010 
Panayot S Vassilevski  Lawrence Livermore National Laboratory  11/6/2010  11/7/2010 
Andreas Michael Veeser  Università di Milano  11/27/2010  12/4/2010 
Chad N Vidden  Iowa State University  10/31/2010  11/5/2010 
Peter Edward Vincent  Stanford University  10/31/2010  11/6/2010 
Michael Vogelius  Rutgers University  11/4/2010  11/7/2010 
Lars B. Wahlbin  Cornell University  11/4/2010  11/6/2010 
Shawn W. Walker  Louisiana State University  10/30/2010  11/6/2010 
Noel J. Walkington  Carnegie Mellon University  11/4/2010  11/7/2010 
Junping Wang  National Science Foundation  11/4/2010  11/7/2010 
Kening Wang  University of North Florida  11/29/2010  12/3/2010 
Wei Wang  Florida International University  10/31/2010  11/7/2010 
Yanqiu Wang  Oklahoma State University  11/4/2010  11/7/2010 
Ying Wang  University of Minnesota  11/1/2010  11/6/2010 
Timothy C. Warburton  Rice University  11/1/2010  11/4/2010 
Yaoguang Wei  University of Minnesota  11/28/2010  11/29/2010 
Olof B. Widlund  New York University  11/28/2010  12/3/2010 
Ragnar Winther  University of Oslo  10/17/2010  11/12/2010 
Barbara Wohlmuth  Technical University of Munich  10/30/2010  11/6/2010 
Carol S. Woodward  Lawrence Livermore National Laboratory  11/29/2010  12/3/2010 
Dexuan Xie  University of Wisconsin  11/28/2010  12/3/2010 
Yulong Xing  University of Tennessee  11/1/2010  11/7/2010 
Jinchao Xu  Pennsylvania State University  11/5/2010  11/7/2010 
Jinchao Xu  Pennsylvania State University  11/29/2010  12/2/2010 
Liwei Xu  Rensselaer Polytechnic Institute  10/31/2010  11/7/2010 
Guangri Xue  University of Texas at Austin  10/29/2010  11/7/2010 
Sergey Borisovich Yakovlev  Rensselaer Polytechnic Institute  9/8/2010  12/15/2010 
Jue Yan  Iowa State University  10/31/2010  11/7/2010 
Ulrike Meier Yang  Lawrence Livermore National Laboratory  11/28/2010  12/3/2010 
Xingzhou Yang  Mississippi State University  10/29/2010  11/4/2010 
Irad Yavneh  TechnionIsrael Institute of Technology  11/28/2010  12/4/2010 
Xiu Ye  University of Arkansas  10/31/2010  11/7/2010 
Haijun Yu  Purdue University  11/29/2010  12/3/2010 
Hui Yu  Iowa State University  10/31/2010  11/5/2010 
Suxing Zeng  Wright State University  11/28/2010  12/3/2010 
Shangyou Zhang  University of Delaware  11/5/2010  11/6/2010 
Shangyou Zhang  University of Delaware  11/28/2010  12/4/2010 
Yi Zhang  Louisiana State University  11/27/2010  12/4/2010 
Zhimin Zhang  Wayne State University  10/31/2010  11/7/2010 
Shan Zhao  University of Alabama  10/31/2010  11/2/2010 
Huiqing Zhu  University of Southern Mississippi  11/5/2010  11/7/2010 
Ludmil Zikatanov  Pennsylvania State University  11/27/2010  12/3/2010 