A fast algorithm for Quadrature by Expansion in three dimensions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:388

Article

Wala, Matt¹  Klockner, Andreas¹ 

[1] Univ Illinois, Dept Comp Sci, Champaign, IL 61820 USA

关键词: Fast algorithms;    Fast multipole method;    Integral equations;    Quadrature;    Singular integrals;    Three dimensional problems;   

DOI  :  10.1016/j.jcp.2019.03.024

来源: Elsevier

【 摘 要 】

This paper presents an accelerated quadrature scheme for the evaluation of layer potentials in three dimensions. Our scheme combines a generic, high order quadrature method for singular kernels called Quadrature by Expansion (QBX) with a modified version of the Fast Multipole Method (FMM). Our scheme extends a recently developed formulation of the FMM for QBX in two dimensions, which, in that setting, achieves mathematically rigorous error and running time bounds. In addition to generalization to three dimensions, we highlight some algorithmic and mathematical opportunities for improved performance and stability. Lastly, we give numerical evidence supporting the accuracy, performance, and scalability ofthe algorithm through a series of experiments involving the Laplace and Helmholtz equations. (c) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free