A fast algorithm with error bounds for Quadrature by Expansion

JOURNAL OF COMPUTATIONAL PHYSICS

卷:374

Article

Wala, Matt¹  Klockner, Andreas¹ 

[1] Univ Illinois, Dept Comp Sci, 201 North Goodwin Ave, Urbana, IL 61801 USA

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

DOI  :  10.1016/j.jcp.2018.05.006

来源: Elsevier

【 摘 要 】

Quadrature by Expansion (QBX) is a quadrature method for approximating the value of the singular integrals encountered in the evaluation of layer potentials. It exploits the smoothness of the layer potential by forming locally-valid expansions which are then evaluated to compute the near or on-surface value of the potential. Recent work towards coupling of a Fast Multipole Method (FMM) to QBX yielded a first step towards the rapid evaluation of such integrals (and the solution of related integral equations), albeit with only empirically understood error behavior. In this paper, we improve upon this approach with a modified algorithm for which we give a comprehensive analysis of error and cost in the case of the Laplace equation in two dimensions. For the same levels of (user-specified) accuracy, the new algorithm empirically has cost-per-accuracy comparable to prior approaches. We provide experimental results to demonstrate scalability and numerical accuracy. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free