Partial Differential Equations

Friday, June 10, 2016 - 9:00am - 10:00am
Benham Jafarpour (University of Southern California)
In this talk, I will present an overview of sparse representations and their applications in solving inverse modeling problems involving PDEs that describe multi-phase flow in heterogeneous porous media. The related PDE-constrained inverse problems are often formulated to infer spatially distributed material properties from dynamic response measurements at scattered source/sink locations.
Friday, March 18, 2016 - 9:00am - 9:30am
Ekkehard Sachs (Universität Trier)
In this talk we consider modern developments of the neoclassical growth model developed by Ramsey almost 90 years ago. One example is the extension to peer-to-peer banking, which leads to a vector optimization problem. Another aspect we consider is the extension of the model with a finite number of households which leads to an optimal control problem with partial differential equations including nonlocal effects. We give theoretical results obtained from optimal control and compare it to their economical interpretation supported by numerical results.
Wednesday, March 16, 2016 - 10:30am - 11:00am
John Singler (Missouri University of Science and Technology)
Balanced POD is a data-based model reduction algorithm that has been widely used for linearized fluid flows and other linear PDE systems with inputs and outputs. We discuss recent work on balanced POD for such systems, including the case of unbounded input and output operators as can occur when control actuators and sensors are located on the boundary of the physical domain. We also discuss challenges for model reduction of linear and nonlinear PDE systems.
Tuesday, November 3, 2015 - 9:00am - 10:00am
Yanyan Li (Rutgers, The State University of New Jersey)
The classic and pioneering work of Nirenberg, in collaboration with
Gidas and Ni, on symmetries of solutions of partial differential equations
has generated enormous research activities, and the method of moving planes has
become a powerful and user-friendly tool in the study of partial differential
equations. In this talk, we will discuss some analytic aspects
of second order elliptic or degenerate elliptic conformally invariant
equations, in particular on some results where the method of
Tuesday, November 30, 2010 - 2:00pm - 2:45pm
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 user-friendly fashion.
Tuesday, November 30, 2010 - 11:00am - 11:45am
Irad Yavneh (Technion-Israel Institute of Technology)

Thursday, August 5, 2010 - 2:30pm - 3:00pm
Jingfang Huang (University of North Carolina, Chapel Hill)
In this talk, we discuss a numerical scheme for the accurate and efficient
solution of time dependent partial differential equations. The technique
first discretizes the temporal direction using Gaussian type nodes and
spectral integration, and applies low-order time marching schemes to
form a preconditioned elliptic system. The better conditioned system is
then solved iteratively using Jacobi-Free Newton–Krylov techniques, and
each function evaluation is simply one low-order time-stepping
Monday, August 2, 2010 - 9:30am - 10:00am
Per-Gunnar Martinsson (University of Colorado)
The talk will describe recently developed fast solvers for the
linear systems arising upon the discretization of elliptic
PDEs. While most existing fast methods tend to be based on
iterative solvers such as GMRES, the new techniques directly
construct an approximate inverse (or LU factorization) of the
coefficient matrix. This makes the techniques robust and
particularly fast for problems involving multiple right hand
sides. Such fast direct solvers have been developed both for
Thursday, February 4, 2016 - 11:00am - 12:00pm
Kirsten Morris (University of Waterloo)
There are essentially two approaches to controller design for systems modeled by a partial differential equation: direct and indirect. In direct controller design, the original model is used design the controller. In indirect controller design, a finite-dimensional approximation of the system is obtained and controller design is based on this approximation. The chief drawback of direct controller design is that a representation of the solution suitable for calculation is required.
Friday, October 24, 2014 - 9:00am - 9:45am
Franco Brezzi (Istituto Universitario di Studi Superiori)
The talk will review the Virtual Element spaces, recently introduced by the speaker and co-authors in order to approximate spaces of the type H(div) or H(curl) on polygonal and polyhedral decompositions. As is well known, these spaces are needed in the approximation of boundary value problems for (systems of) Partial Differential Equations in mixed form. The Virtual Element spaces are defined locally as solutions of systems of PDE's, that however don't need to be solved (not even in an approximate way).


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