TY - JOUR

T1 - Integral equations requiring small numbers of krylov-subspace iterations for two-dimensional smooth penetrable scattering problems

AU - Boubendir, Yassine

AU - Bruno, Oscar

AU - Levadoux, David

AU - Turc, Catalin

N1 - Funding Information:
Oscar Bruno thanks NSF (contracts DMS-1008631 and DMS-1411876 ) and AFOSR (contracts FA9550-11-1-0193 and FA9550-15-1-0043 ) for their support during the preparation of this work. Yassine Boubendir gratefully acknowledges support from NSF through contract DMS-1016405 . Catalin Turc gratefully acknowledge support from NSF through contract DMS-1008076 .
Publisher Copyright:
© 2015 IMACS. Published by Elsevier B.V. All rights reserved.

PY - 2015/5/26

Y1 - 2015/5/26

N2 - 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.

AB - 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.

KW - Combined field integral equations

KW - Electromagnetic scattering

KW - Pseudo-differential operators

KW - Regularizing operators

KW - Transmission problems

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U2 - 10.1016/j.apnum.2015.01.005

DO - 10.1016/j.apnum.2015.01.005

M3 - Article

AN - SCOPUS:84929710496

SN - 0168-9274

VL - 95

SP - 82

EP - 98

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -