### 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, 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$.

Original language | English (US) |
---|---|

Pages (from-to) | 771-812 |

Number of pages | 42 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 69 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2016 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*69*(4), 771-812. https://doi.org/10.1002/cpa.21585

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

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 69, no. 4, pp. 771-812. https://doi.org/10.1002/cpa.21585

}

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

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

VL - 69

SP - 771

EP - 812

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 4

ER -