Graduate Student / Postdoc Seminar
Fast, Accurate Tools for Physical and Biophysical Modeling in Complex Geometries
Speaker: Leslie Greengard, Courant Institute
Location: Warren Weaver Hall 1302
Date: Friday, April 6, 2018, 1 p.m.
If the future of scientific computing and computational engineering lies in "design by simulation", it will require not only that a single problem be solved accurately and rapidly, but that an entire sequence of problems be solved, with varying geometry, material parameters, etc. In addition to the advance in high-performance computing environments, recent developments in numerical methods have allowed for a vast increase in the number of degrees of freedom which can be considered. In this talk, I will give an overview of the analytical and numerical foundations of methods that permit the construction of fast, high-order accurate, and robust methods for a variety of problems in science and engineering. Critical issues include the derivation of well-conditioned integral equation formulations for the governing PDE, high-order geometry representations, accurate quadrature rules for singular functions, and suitable fast algorithms. I will touch on the application of these techniques to problems drawn from classical mathematical physics, including acoustics, elasticity, electromagnetics, and heat flow.