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The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering
Author(s) -
Vico Felipe,
Ferrando Miguel,
Greengard Leslie,
Gimbutas Zydrunas
Publication year - 2016
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21585
Subject(s) - vector potential , magnetic potential , scalar potential , scalar (mathematics) , electric field integral equation , integral equation , mathematics , mathematical analysis , spurious relationship , electromagnetic field , scattering , boundary value problem , scalar field , perfect conductor , physics , magnetic field , mathematical physics , quantum mechanics , geometry , statistics
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, φ scat , is determined entirely by the incident scalar potential φ inc . Likewise, the unknown vector potential defining the scattered field, A scat is determined entirely by the incident vector potential A inc . This decoupled formulation is valid not only in the static limit but for arbitrary ω ≥ 0$. © 2016 Wiley Periodicals, Inc.