Past Event: Oden Institute Seminar

Guaranteed-Accuracy Fast Algorithms for the Evaluation of Layer Potentials using 'Quadrature by Expansion'

Andreas Klöckner, Assistant Professor, Computer Science Department, University of Illinois at Urbana-Champaign

Abstract

Quadrature by Expansion, or 'QBX', is a systematic, high-order approach to singular quadrature that applies to layer potential integrals with general kernels on curves and surfaces. The efficient and accurate evaluation of layer potentials, in turn, is a key building block in the construction of solvers for elliptic PDEs based on integral equation methods. I will present a new fast algorithm incorporating QBX that evaluates layer potentials on and near surfaces in two and three dimensions with user-specified accuracy, along with supporting theoretical and empirical results on complexity and accuracy. A series of examples on unstructured geometry across a variety of applications in two and three dimensions demonstrates the applicability of the method. Bio Dr. Klockner is an assistant professor in the scientific computing group within the Computer Science Department at the University of Illinois at Urbana-Champaign. Prior to being at UIUC, he was at the Courant Institute of Mathematical Sciences at NYU working with Leslie Greengard on various problems in computational electromagnetics and integral equation methods for solving PDEs. Earlier still, he worked on his PhD at the Division of Applied Mathematics at Brown University with Jan Hesthaven on a variety of issues involving linear and nonlinear hyperbolic PDEs and discontinuous Galerkin finite element method. Dr. Klockner studies high-order numerical methods for Partial Differential Equations, in particular for elliptic and hyperbolic problems, as well as parallel computing and the software engineering needed to build useful, robust simulation codes.