MINIMIZING THE CONDITION NUMBER OF BOUNDARY INTEGRAL OPERATORS IN ACOUSTIC AND ELECTROMAGNETIC SCATTERING

1 January 1985

journal article
Published by Oxford University Press (OUP) in The Quarterly Journal of Mechanics and Applied Mathematics

Vol. 38 (2) , 323-341
https://doi.org/10.1093/qjmam/38.2.323

Abstract

The question of non-uniqueness in boundary integral equation formulations of exterior boundary-value problems in time-harmonic acoustic and electromagnetic scattering can be resolved by seeking the solutions in the form of a combined single and double-layer potential in acousties or a combined electric- and magnetic-dipole field in electromagnetics. We present an analysis of the appropriate choice of the coupling parameters which is optimal in the sense of minimizing the condition number of the boundary integral operators.

Keywords

MAXWELL EQUATION
BOUNDARY VALUE PROBLEM
CONDITION NUMBER
HELMHOLTZ EQUATION
INTEGRAL EQUATION
EIGENVALUES

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