Integral equations requiring small numbers of krylov-subspace iterations for two-dimensional smooth penetrable scattering problems

Document Type

Article

Publication Date

5-26-2015

Abstract

This paper presents a class of boundary integral equations for the solution of problems of electromagnetic and acoustic scattering by two-dimensional homogeneous penetrable scatterers with smooth boundaries. The new integral equations, which, as is established in this paper, are uniquely solvable Fredholm equations of the second kind, result from representations of fields as combinations of single and double layer potentials acting on appropriately chosen regularizing operators. As demonstrated in this text by means of a variety of numerical examples (that resulted from a high-order Nyström computational implementation of the new equations), these "regularized combined equations" can give rise to important reductions in computational costs, for a given accuracy, over those resulting from previous iterative boundary integral equation solvers for transmission problems.

Identifier

84929710496 (Scopus)

Publication Title

Applied Numerical Mathematics

External Full Text Location

https://doi.org/10.1016/j.apnum.2015.01.005

ISSN

01689274

First Page

82

Last Page

98

Volume

95

Grant

1312169

Fund Ref

National Science Foundation

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