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

Authors:
Ran Duan;Vladimir Rokhlin
Affiliations:
Department of Physics, Yale University, New Haven, CT 06511, USA;Department of Physics, Yale University, New Haven, CT 06511, USA and Department of Computer Science, Yale University, New Haven, CT 06511, USA and Department of Mathematics, Yale University, New H ...
Venue:
Journal of Computational Physics
Year:
2009

Citing 4
Cited 1

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Abstract

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.