The Decoupled Potential Integral Equation for Time-Harmonic Electromagnetic Scattering

Felipe Vico, Miguel Ferrando, Leslie Greengard, Zydrunas Gimbutas

Research output: Contribution to journalArticle

Abstract

We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials A,φ in the Lorenz gauge, we establish boundary conditions on the potentials themselves rather than on the field quantities. This permits the development of a well-conditioned second-kind Fredholm integral equation that has no spurious resonances, avoids low-frequency breakdown, and is insensitive to the genus of the scatterer. The equations for the vector and scalar potentials are decoupled. That is, the unknown scalar potential defining the scattered field, φscat, is determined entirely by the incident scalar potential φinc. Likewise, the unknown vector potential defining the scattered field, Ascat is determined entirely by the incident vector potential Ainc. This decoupled formulation is valid not only in the static limit but for arbitrary ω≥0$.

Original languageEnglish (US)
Pages (from-to)771-812
Number of pages42
JournalCommunications on Pure and Applied Mathematics
Volume69
Issue number4
DOIs
StatePublished - Apr 1 2016

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Electromagnetic Scattering
Integral equations
Integral Equations
Harmonic
Scalar
Scattering
Vector Potential
Electric conductors
Unknown
Formulation
Resonance Frequency
Fredholm Integral Equation
Conductor
Gages
Breakdown
Low Frequency
Electric Field
Gauge
Genus
Magnetic Field

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

The Decoupled Potential Integral Equation for Time-Harmonic Electromagnetic Scattering. / Vico, Felipe; Ferrando, Miguel; Greengard, Leslie; Gimbutas, Zydrunas.

In: Communications on Pure and Applied Mathematics, Vol. 69, No. 4, 01.04.2016, p. 771-812.

Research output: Contribution to journalArticle

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