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

被引：24
|
作者：
Duan, Ran [1 ]
Rokhlin, Vladimir [1 ,2 ,3 ]
机构：
[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
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2009年 / 228卷 / 06期
关键词：
High-order; Quadratures; Scattering; Helmholtz; Singular; Hankel; Lippmann-Schwinger;
D O I：
10.1016/j.jcp.2008.11.033
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
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.
引用
收藏
页码：2152 / 2174
页数：23
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