Analysis and Applied Mathematics Seminar
Guaranteed-Accuracy Fast Algorithms for the Evaluation of Layer Potentials using `Quadrature by Expansion'
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.
Monday April 16, 2018 at 4:00 PM in SEO 636