Fast algorithms for Quadrature by Expansion I: Globally valid expansions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:345

Article

Rachh, Manas¹  Klockner, Andreas²  O'Neil, Michael^3,4 

[1] Yale Univ, Program Appl Math, 51 Prospect St, New Haven, CT 06511 USA

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

[3] NYU, Courant Inst, New York, NY USA

[4] NYU, Tandon Sch Engn, New York, NY USA

关键词: Layer potentials;    Singular integrals;    Quadrature;    High-order accuracy;    Integral equations;    Fast multipole method;   

DOI  :  10.1016/j.jcp.2017.04.062

来源: Elsevier

【 摘 要 】

The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast algorithms for solving the resulting dense linear systems. Classically, these tools were developed separately. In this work, we present a unified numerical scheme based on coupling Quadrature by Expansion, a recent quadrature method, to a customized Fast Multipole Method (FMM) for the Helmholtz equation in two dimensions. The method allows the evaluation of layer potentials in linear-time complexity, anywhere in space, with a uniform, user-chosen level of accuracy as a black-box computational method. Providing this capability requires geometric and algorithmic considerations beyond the needs of standard FMMs as well as careful consideration of the accuracy of multipole translations. We illustrate the speed and accuracy of our method with various numerical examples. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free