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Math Colloquium
Sivaram Ambikasaran
Courant Institute, New York University
Title: Fast solvers for elliptic partial differential equations

Abstract: Numerical methods for solving elliptic PDE broadly fall into the following categories: (i) Local schemes (finite difference, finite element, etc.) (ii) Global schemes (Green’s function based integral approach). One of the challenges for both is the scaling of the algorithms as the underlying degrees of freedom become large. In this talk, I shall focus on some of my contributions in reducing the computational complexity of these algorithms. To be specific, I will discuss structured matrix computations that exploit the underlying analytic property of the local and global operators to achieve linear or almost linear complexity. I will elaborate on how these enable constructing high accuracy (more than 10 digits), direct (as opposed to iterative) solvers, thereby facilitating real time simulation and design.

Date: Friday, October 3, 2014
Time: 4:30 pm
Location: Wean Hall 7500
Submitted by:  Bohman
Note: Refreshments at 4:00 pm, Math Lounge.