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

Yassine Boubendir, Oscar Bruno, David Levadoux, Catalin Turc

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)82-98
Number of pages17
JournalApplied Numerical Mathematics
Volume95
DOIs
StatePublished - May 26 2015

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Combined field integral equations
  • Electromagnetic scattering
  • Pseudo-differential operators
  • Regularizing operators
  • Transmission problems

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