Fast methods for solving partial differential equations

Per-Gunnar J Martinsson
Assistant Professor of Applied Mathematics
University of Colorado at Boulder

Abstract

The development over the last several decades of powerful computers and fast algorithms has dramatically increased our capability to computationally model a broad range of phenomena in science and engineering. Our newfound ability to design complex systems (cars, new materials, city infrastructures, etc) via computer simulations rather than physical experiments has in many fields led to both cost savings and dramatically improved performance. Intense efforts are currently being made to extend these advances to biochemistry, physiology, and several other areas in the biological and medical sciences.

In many computational simulations, the most time consuming step is the construction of approximate solutions to partial differential equations. In this talk, we will focus on linear PDEs; we will give an overview of well-established fast solvers for such equations, and describe some recent advances that have the potential to profoundly increase our computational capabilities. Specifically, we will discuss new techniques for (1) representing functions and operators, (2) directly inverting the large matrices that arise upon the discretization of many integral and differential equations, and (3) constructing low-rank approximations to operators using randomized sampling techniques.

Thursday, January 17th
337 Towne Bldg.
2:00 – 3:00 p.m.