In this talk, we discuss a numerical scheme for the accurate and efficientsolution of time dependent partial differential equations. The techniquefirst discretizes the temporal direction using Gaussian type nodes andspectral integration, and applies low-order time marching schemes toform a preconditioned elliptic system. The better conditioned s...
Creator:
Huang, Jingfang (University of North Carolina, Chapel Hill)
Created:
2010-08-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 pr...
Creator:
Sachs, Ekkehard W. (Universität Trier)
Created:
2016-03-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 bo...
Creator:
Singler, John (Missouri University of Science and Technology)
Created:
2016-03-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 meas...
Creator:
Jafarpour, Benham (University of Southern California)
Created:
2016-06-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The talk will describe recently developed fast solvers for thelinear systems arising upon the discretization of ellipticPDEs. While most existing fast methods tend to be based oniterative solvers such as GMRES, the new techniques directlyconstruct an approximate inverse (or LU factorization) of thecoefficient matrix. This makes the techniques ro...
Creator:
Martinsson, Per-Gunnar J. (University of Colorado)
Created:
2010-08-02
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
I shall talk about how to design fast spectral-Galerkin algorithms forsome prototypical partial differential equations. We shall start withalgorithms in one dimension, then using a tensor product approach fortwo and three dimensions, and hyperbolic cross/spectral sparse gridfor higher dimensional problems.
Creator:
Shen, Jie (Purdue University)
Created:
2010-10-31
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Several numerical techniques will be presented for solvingdiscretized partial differential equations (PDEs) by special multilevelmethods based on one or no grid with nearly optimal computationalcomplexity in a user-friendly fashion.
Creator:
Xu, Jinchao
Created:
2010-11-30
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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...
Creator:
Yavneh, Irad (Technion-Israel Institute of Technology)
Created:
2010-11-30
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The classic and pioneering work of Nirenberg, in collaboration withGidas and Ni, on symmetries of solutions of partial differential equationshas generated enormous research activities, and the method of moving planes hasbecome a powerful and user-friendly tool in the study of partial differentialequations. In this talk, we will discuss some anal...
Creator:
Li, Yanyan (Rutgers, The State University of New Jersey)
Created:
2015-11-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This is joint work with Viorel Barbu (Romanian Academy, Iasi).We extend the approach of variational inequalities (VI) to partial differential equations (PDE) with singular coefficients, to the stochastic case. As a model case we concentrate on the parabolic 1-Laplace equation (a PDE with highly singular diffusivity) on a bounded convex domain in...
Creator:
Röckner, Michael (Universität Bielefeld)
Created:
2012-10-24
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.