High-order quadratures for the solution of scattering problems in two dimensions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Duan, Ran¹  Rokhlin, Vladimir^1,2,3 

[1] Yale Univ, Dept Phys, New Haven, CT 06511 USA

[2] Yale Univ, Dept Comp Sci, New Haven, CT 06511 USA

[3] Yale Univ, Dept Math, New Haven, CT 06511 USA

关键词: High-order;    Quadratures;    Scattering;    Helmholtz;    Singular;    Hankel;    Lippmann-Schwinger;   

DOI  :  10.1016/j.jcp.2008.11.033

来源: Elsevier

【 摘 要 】

We construct an iterative algorithm for the solution of forward scattering problems in two dimensions. The scheme is based on the combination of high-order quadrature formulae, fast application of integral operators in Lippmann-Schwinger equations, and the stabilized bi-conjugate gradient method (BI-CGSTAB). While the FFT-based fast application of integral operators and the BI-CGSTAB for the solution of linear systems are fairly standard, a large part of this paper is devoted to constructing a class of high-order quadrature formulae applicable to a wide range of singular functions in two and three dimensions; these are used to obtain rapidly convergent discretizations of Lippmann-Schwinger equations. The performance of the algorithm is illustrated with several numerical examples. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free