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

Posted by Youngjoon Hong , part of the Analysis and Applied Mathematics Seminar.

At

April 9, 2018, 4 p.m.

In

SEO 636

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.