TY - JOUR
T1 - The Decoupled Potential Integral Equation for Time-Harmonic Electromagnetic Scattering
AU - Vico, Felipe
AU - Ferrando, Miguel
AU - Greengard, Leslie
AU - Gimbutas, Zydrunas
N1 - Publisher Copyright:
© 2016 Wiley Periodicals, Inc.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - 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$.
AB - We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials A,φ in the Lorenz gauge, we establish boundary conditions on the potentials themselves rather than on the field quantities. This permits the development of a well-conditioned second-kind Fredholm integral equation that has no spurious resonances, avoids low-frequency breakdown, and is insensitive to the genus of the scatterer. The equations for the vector and scalar potentials are decoupled. That is, the unknown scalar potential defining the scattered field, φscat, is determined entirely by the incident scalar potential φinc. Likewise, the unknown vector potential defining the scattered field, Ascat is determined entirely by the incident vector potential Ainc. This decoupled formulation is valid not only in the static limit but for arbitrary ω≥0$.
UR - http://www.scopus.com/inward/record.url?scp=84958669707&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84958669707&partnerID=8YFLogxK
U2 - 10.1002/cpa.21585
DO - 10.1002/cpa.21585
M3 - Article
AN - SCOPUS:84958669707
SN - 0010-3640
VL - 69
SP - 771
EP - 812
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
IS - 4
ER -