Integral equation methods for electrostatics, acoustics, and electromagnetics in smoothly varying, anisotropic media

Lise Marie Imbert-Gerard, Felipe Vico, Leslie Greengard, Miguel Ferrando

Research output: Contribution to journalArticle

Abstract

We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic, or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach involves a minor modification of a classical formulation. In the electrostatic or acoustic setting, we introduce a new vector partial differential equation, from which the desired solution is easily obtained. It is the vector equation for which we derive a well-conditioned integral equation. In addition to providing a unified framework for these solvers, we illustrate their performance using iterative solution methods coupled with the FFT-based technique of [F. Vico, L. Greengard, M. Ferrando, J. Comput. Phys., 323 (2016), pp. 191–203] to discretize and apply the relevant integral operators.

Original languageEnglish (US)
Pages (from-to)1020-1035
Number of pages16
JournalSIAM Journal on Numerical Analysis
Volume57
Issue number3
DOIs
StatePublished - Jan 1 2019

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Anisotropic media
Integral Equation Method
Anisotropic Media
Electrostatics
Integral equations
Acoustics
Acoustic Scattering
Inhomogeneous Media
Electromagnetic Scattering
Levenberg-Marquardt
Iterative Solution
Scattering Problems
Integral Operator
Fast Fourier transforms
Partial differential equations
Minor
Integral Equations
Partial differential equation
Scattering
Formulation

Keywords

  • Acoustics
  • Anisotropic media
  • Electromagnetics
  • Electrostatics
  • Inhomogeneous media
  • Integral equations

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

Integral equation methods for electrostatics, acoustics, and electromagnetics in smoothly varying, anisotropic media. / Imbert-Gerard, Lise Marie; Vico, Felipe; Greengard, Leslie; Ferrando, Miguel.

In: SIAM Journal on Numerical Analysis, Vol. 57, No. 3, 01.01.2019, p. 1020-1035.

Research output: Contribution to journalArticle

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