Probability and Statistics in Complex Systems: Genomics, Networks, and Financial Engineering, September 1, 2003 - June 30, 2004

Supported by the Department of Energy.

This workshop is at capacity and closed to further registration.

Organizers:

Douglas N. Arnold
IMA
University of Minnesota
director@ima.umn.edu
http://www.ima.umn.edu/~arnold

Pavel B. Bochev
Computational Mathematics and Algorithms Department
Sandia National Laboratories
pbboche@sandia.gov

Richard B. Lehoucq
Computational Mathematics and Algorithms Department
Sandia National Laboratories
rblehou@sandia.gov
http://www.cs.sandia.gov/~rlehoucq

Roy A. Nicolaides
Department of Mathematical Sciences
Carnegie-Mellon University
dept.head@math.cmu.edu
http://www.math.cmu.edu/people/fac/nicolaides.html

Mikhail Shashkov
MS-B284, Group T-7, Theoretical Division
Los Alamos National Laboratory
shashkov@lanl.gov
http://cnls.lanl.gov/~shashkov

Workshop will begin 9:00 AM Tuesday and end by 3:15 PM Saturday. Participants should plan to attend the entire workshop.

Description:

The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop is to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic instrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE.

Particular points of emphasis will include:

• Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical simulations.
• Identification and design of compatible spatial discretizations of PDEs, their classification, analysis, and relations.
• Relationships between different compatible spatial discretization methods and concepts which have been developed;
• Impact of compatible spatial discretizations upon physical fidelity, verification and validation of simulations, especially in large-scale, multiphysics settings.
• How solvers address the demands placed upon them by compatible spatial discretizations.

"HOT TOPICS" WORKSHOP SCHEDULE
Tuesday Wednesday Thursday Friday Saturday
TUESDAY, MAY 11 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30	Coffee and Registration	Reception Room EE/CS 3-176
9:15	IMA Directors and Organizers	Welcome and Introduction
9:30	Douglas N. Arnold IMA	Differential Complexes and Stability of Finite Element Methods Slides:   pdf
10:20	Discussion and break
11:00	Roy Nicolaides Carnegie Mellon University	Compatible Discretizations, Covolume Algorithms and Differential Forms
11:50	Discussion and lunch break
1:30	Mikhail Shashkov Los Alamos National Laboratory	Mimetic Finite Difference Methods for Partial Differential Equations and Discrete Vector and Tensor Analysis Slides:   pdf
2:20	Discussion and break
3:00	SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, re-frame their main points, look toward future directions.
3:30	Group Photo  here
3:40	IMA Tea and more (Reception and Poster Session) 400 Lind Hall Peter Arbenz Institute of Computational Science, ETH Zurich Eigenvalue Solvers for Electromagnetic Fields in Cavities Martin Berggren Uppsala University A Vertex-Centered Dual Discontinuous Galerkin Method Slides:   pdf Panagiotis Chatzipantelidis Texas A&M University A Finite Volume Element Method for a Nonlinear Elliptic Problem Snorre H. Christiansen University of Oslo Div-curl Lemma for Edge Elements Slides:   pdf    ps Leszek Demkowicz The University of Texas at Austin De Rham Diagram for Projection-Based Interpolation. 3D Optimal p- and hp-Error Estimates Slides:   pdf    ps Yalchin Efendiev Texas A&M University Numerical Homogenization of Nonlinear Partial Differential Equations and its Applications Juergen Geiser University of Heidelberg Mixed Discretisation Methods for Discontinuous Galerkin Method with Analytical Test-Functions Paper:   pdf   ps Anil N. Hirani Caltech Discrete Exterior Calculus and its Applications in Mechanics and Computer Science Slides:   pdf P. Robert Kotiuga Boston University Intuitive vs. Computable Topological Aspects of Computational Electromagnetics Slides:   html    pdf    ps    ppt Melvin Leok California Institute of Technology Discrete Connections on Principal Bundles Slides:   pdf Konstantin Lipnikov Los Alamos National Laboratory New Mimetic Discretizations of Diffusion-Type Problems on Polygonal Meshes Poster size a0:   pdf    ps Poster size a4:   pdf   ps Elizabeth L. Mansfield University of Kent, UK Towards a Variational Complex of the Finite Element Method Slides:   pdf    ps Ilia D. Mishev Exxon-Mobil Why Mixed Finite Elements are not used in the Petroleum Industry and what can we do about it? Slides:   html    pdf    ps    ppt J. David Moulton Los Alamos National Laboratory Mimetic Preconditioners for Mixed Discretizations of the Diffusion Equation Slides:   pdf Ilaria Perugia Università di Pavia Discontinuous Galerkin Methods for Maxwell's Equations in Frequency-Domain Slides:   pdf Robert N. Rieben Lawrence Livermore National Laboratory High Order Symplectic Integration Methods for Finite Element Solutions to Time Dependent Maxwell Equations Slides:   html    pdf    ps    ppt Beatrice Riviere University of Pittsburgh Two-Phase Flow Modeling Allen C. Robinson Sandia National Laboratories Compatible Discretizations in Lagrangian/Eulerian Resistive MHD Modeling for Z-pinch Applications Slides:   pdf Rolf Schuhmann Technische Universität Darmstadt Institut für Theorie Elektromagnetischer Felder (TEMF) Consistent Material Operators for Geometrical Discretization Methods on Generalized Grids Slides:   pdf Rajen Kumar Sinha Texas A&M University Finite Volume Element Methods for Parabolic Integro-Differential Equation with Nonsmooth Initial Data Paper:   pdf Jean-Marie Thomas University of Pau, France Finite Element Methods for Non-elliptic but Coercive Problems Jukka Tuomela University of Joensuu Formal Theory of PDEs and simulation of Fluid Flows Poster size a0:   imaposteri.pdf    imaposteri.ps Poster size a4:   imaposteria4.pdf   imaposteria4.ps Jing Wang IMA Numerical Simulation of Contraints Preserving Boundary Conditions for Constrainted Hyperbolic Equations Slides:   pdf
WEDNESDAY, MAY 12 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:00	Coffee	Reception Room EE/CS 3-176
9:30	Pavel Bochev Sandia National Laboratories	Variational and Geometric Aspects of Compatible Discretizations Slides:   html   pdf    ps    ppt
10:20	Discussion and break
11:00	Alain Bossavit Laboratoire de Génie Electrique de Paris (LGEP)	Computational Electromagnetism and Whitney Forms Slides:   IMA1.pdf    IMA2.pdf
11:50	Discussion and lunch break
1:30	Ralf Hiptmair Seminar of Applied Mathematics	Higher Order Whitney Forms (pdf version) Slides:   pdf
2:20	Discussion and break
3:00	Daniel A. White Lawrence Livermore National Laboratory	Development and Application of Compatible Discretizations of Maxwell's Equations Slides:   pdf
4:00	SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, re-frame their main points, look toward future directions.
THURSDAY, MAY 13 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:00	Coffee	Reception Room EE/CS 3-176
9:30	Ivan Yotov University of Pittsburgh	Superconvergence in Some Locally Conservative Discretization Methods Slides:   pdf
10:20	Discussion and break
11:00	Thomas F. Russell National Science Foundation	Relationships Among Some Locally Conservative Discretization Methods Which Handle Discontinuous Anisotropic Coefficients on Deformed Grids Slides:   pdf|color-pdf`
11:50	Discussion and lunch break
1:30	Mary Fanett Wheeler The University of Texas at Austin	Coupling of MFE or Mimetic Finite Differences with Discontinuous Galerkin for Poro-Elasticity Slides:   html    pdf    ps    ppt
2:20	Discussion and break
3:00	Ivar Aavatsmark University of Bergen	MPFA Discretization on Quadrilateral Grids Slides:   pdf
4:00	SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, re-frame their main points, look toward future directions.
FRIDAY, MAY 14 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:00	Coffee	Reception Room EE/CS 3-176
9:30	Eitan Tadmor University of Maryland, College Park	Entropy Stability Theory For Difference Approximations of Quasilinear Problems Slides:   pdf
10:20	Discussion and break
11:00	Timothy J. Barth NASA Ames Research Center	Entropy Stable FEM Discretization of First-Order Systems of Conservation Laws Slides:   pdf
11:50	Discussion and lunch break
1:30	Thomas J. R. Hughes University of Texas at Austin	"Consider a Spherical Cow" - Conservation of Geometry in Analysis: Implications for Computational Methods in Engineering
2:20	Discussion and break
3:00	Blair Perot University of Massachusetts	Compatible Reconstructions of Vectors and their Application to the Navier-Stokes Equations Slides:   pdf    pps
4:00	SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, re-frame their main points, look toward future directions.
6:00	Workshop Dinner	Bona Vietnamese Restaurant 802 Washington Avenue SE, Minneapolis Phone: 612-331-5011
SATURDAY, MAY 15 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:00	Coffee	Reception Room EE/CS 3-176
9:30	Jim E. Morel Los Alamos National Laboratory	Asymptotic-Preserving Discretization Schemes Slides:   pdf
10:20	Discussion and break
11:00	Daniele Boffi Università di Pavia	Compatible Discretizations for Eigenvalue Problems Slides:   pdf
11:50	Discussion and lunch break
1:30	Ragnar Winther University of Oslo, Norway	From the de Rham Sequence to Mixed Elasticity Slides:   pdf
2:30	SECOND CHANCES, i.e., speakers of the day respond to further questions, suggestions, re-frame their main points, look toward future directions.
3:15	End of Workshop

LIST OF CONFIRMED PARTICIPANTS

NAME	DEPARTMENT	AFFILIATION
Ivar Aavatsmark	Center for Integrated Petroleum Research	University of Bergen
Scot Adams	Institute for Mathematics and its Applications	University of Minnesota
Peter Arbenz	Institut für Wissenschaftliches Rechnen	Zentrum für Umfragen, Methoden und Analysen (ZUMA) e.V.
Douglas Arnold	Institute for Mathematics and its Applications	University of Minnesota
Donald Aronson	Institute for Mathematics and its Applications	University of Minnesota
Gerard Awanou	Institute for Mathematics and its Applications	University of Minnesota
Randolph Bank	Department of Mathematics	University of California, San Diego
Timothy Barth		NASA Ames Research Center
Martin Berggren	Department of Scientific Computing	Uppsala University
Pavel Bochev	Applied Mathematics and Applications	Sandia National Laboratories
Daniele Boffi	Dipartimento di Matematica	Università di Pavia
Alain Bossavit		Laboratoire de Génie Electrique de Paris
Olga Brezhneva	Institute for Mathematics and its Applications	University of Minnesota
Franco Brezzi	Dipartimento di Matematica	I. A. N. del C. N. R.
Zhiqiang Cai	Department of Mathematics	Purdue University
Jose Castillo	Department of Mathematics & Statistics	San Diego State University
Panagiotis Chatzipantelidis	Department of Mathematics	Texas A & M University
Snorre Christiansen	Department of Mathematics	Centre of Mathematics for Applications
Mark Christon		Sandia National Laboratories
Bernardo Cockburn	School of Mathematics	University of Minnesota
Robert Crone	Mechanical Research and Development	Seagate Technology
Leszek Demkowicz	Institute for Computational Engineering and Sciences	University of Texas at Austin
Yalchin Efendiev	Department of Mathematics	Texas A & M University
Richard Falk	Department of Mathematics	Rutgers University
Juergen Geiser	IWR	Texas A & M University
Anne Gundel	Institute for Mathematics	Humboldt-Universität
Hazem Hamdan	School of Mathematics	University of Minnesota
Bo He	Department of Electrical Engineering	Ohio State University
Jan Hesthaven	Division of Applied Mathematics	Brown University
Ulrich Hetmaniuk		Sandia National Laboratories
Ralf Hiptmair	Seminar of Applied Mathematics	Zentrum für Umfragen, Methoden und Analysen (ZUMA) e.V.
Anil Hirani	Department of Control and Dynamical Systems	California Institute of Technology
Michael Holst	Department of Mathematics	University of California, San Diego
Ronald Hoppe	Department of Mathematics	University of Houston
Paul Houston	Department of Mathematics and Computer Science	University of Leicester
Thomas Hughes	Institute for Computational Engineering and Sciences	University of Texas at Austin
E. Hyde	School of Mathematics	University of Minnesota
Lili Ju	Institute for Mathematics and its Applications	University of Minnesota
Ruben Juanes	Department of Petroleum Engineering	Stanford University
Hye-Ryoung Kim		Seoul National University
Joseph Koning	Department of Engineering	Lawrence Livermore National Laboratory
Robert Kotiuga	Department of Electrical and Computer Engineering	Boston University
Thomas Kurtz	Department of Mathematics	University of Wisconsin-Madison
Yuri Kuznetsov	Department of Mathematics	University of Houston
Raytcho Lazarov	Department of Mathematics	Texas A & M University
Richard Lehoucq	Computational Mathematics and Algorithms	Sandia National Laboratories
Melvin Leok	Department of Control and Dynamical Systems	California Institute of Technology
Konstantin Lipnikov		Los Alamos National Laboratory
Mitchell Luskin	School of Mathematics	University of Minnesota
Antoinette Maniatty	Department of Mechanical, Aerospace, and Nuclear Engineering	Rensselaer Polytechnic Institute
Elizabeth Mansfield	Institute of Mathematics and Statistics	University of Kent at Canterbury
Donatella Marini	Dipartimento di Matematica	Università di Pavia
Ilya Mishev		ExxonMobil
Julie Mitchell	Departments of Mathematics and Biochemistry	University of Wisconsin-Madison
Jim Morel		Los Alamos National Laboratory
J. Moulton		Los Alamos National Laboratory
Jean-Claude Nédélec	Centre de Mathématiques Appliquées	École Polytechnique
Roy Nicolaides	Department of Mathematical Sciences	Carnegie Mellon University
Philippe Pebay		Sandia National Laboratories
Blair Perot	Department of Mechanical and Industrial Engineering	University of Massachusetts
Ilaria Perugia	Dipartimento di Matematica	Università di Pavia
Edward Ratner	Department of Optical CD Metrology	KLA - Tencor
Fernando Reitich	School of Mathematics	University of Minnesota
Jean-Francois Remacle	Scientific Computation Research Center	Rensselaer Polytechnic Institute
Robert Rieben	Institute for Scienftic Computing Research	Lawrence Livermore National Laboratory
Beatrice Riviere	Department of Mathematics	University of Pittsburgh
Allen Robinson	Computational Physics Research and Development Department	Sandia National Laboratories
Thomas Russell	Division of Mathematical Sciences	National Science Foundation
Fadil Santosa	Institute for Mathematics and its Applications	University of Minnesota
Rolf Schuhmann	TEMF Laboratory	TU Darmstadt
Mikhail Shashkov	XCP - X-Computational Physics	Los Alamos National Laboratory
Shagi-Di Shih	Department of Mathematics	University of Wyoming
Rajen Sinha	Institute for Scientific Computation	Texas A & M University
Stanly Steinberg	Department of Mathematics & Statistics	University of New Mexico
Srdjan Stojanovic	Department of Mathematical Sciences	University of Cincinnati
Eitan Tadmor	CSCAMM	University of Maryland
Fernando Teixeira	Department of Electrical Engineering	Ohio State University
Jean-Marie Thomas	Laboratory of Applied Mathematics	Université de Pau et des Pays de l'Adour
Kathryn Trapp	Department of Mathematical Sciences	Carnegie Mellon University
Jukka Tuomela	Department of Mathematics	University of Joensuu
Panayot Vassilevski	Center for Applied Scientific Computing	Lawrence Livermore National Laboratory
Jing Wang	Institute for Mathematics and its Applications	University of Minnesota
Timothy Warburton	Department of Mathematics & Statistics	University of New Mexico
Mary Wheeler	Institute for Computational Engineering and Sciences	University of Texas at Austin
Daniel White	Center for Applied Scientific Computing	Lawrence Livermore National Laboratory
Ragnar Winther	Centre of Mathematics for Applications	University of Oslo
Jinchao Xu	Department of Mathematics	Pennsylvania State University
Ivan Yotov	Department of Mathematics	University of Pittsburgh
Jun Zhao	Institute of Mathematics and its Application	University of Minnesota