### Abstract

We present a new version of the regularized combined source integral equation (CSIE-AR) for the solution of electromagnetic scattering problems in the presence of perfectly conducting bodies. The integral equation is of the second kind and has no spurious resonances. It is well-conditioned at all frequencies for simply connected geometries. Reconstruction of the magnetic field, however, is subject to catastrophic cancellation due to the need for computing a scalar potential from magnetic currents. Here, we show that by solving an auxiliary (scalar) integral equation, we can avoid this form of low-frequency breakdown. The auxiliary scalar equation is used to solve a Neumanntype boundary value problem using data corresponding to the normal component of the magnetic field. This scalar equation is also of the second kind, non-resonant, and well-conditioned at all frequencies. A principal advantage of our approach, by contrast with hyper-singular EFIE, CFIE or CSIE formulations, is that the standard loop-star and related basis function constructions are not needed, and preconditioners are not required. This permits an easy coupling to fast algorithms such as the fast multipole method (FMM). Furthermore, the formalism is compatible with non-conformal mesh discretization and works well with singular (sharp) boundaries.

Original language | English (US) |
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Journal | IEEE Transactions on Antennas and Propagation |

DOIs | |

State | Accepted/In press - Jan 1 2019 |

### Fingerprint

### Keywords

- Boundary conditions
- Calderon preconditioning (CP)
- charge-current formulations
- electromagnetic (EM) scattering
- Electromagnetic scattering
- Geometry
- high frequency preconditioning
- Integral equations
- Magnetic resonance
- Mathematical model
- Maxwell equations
- Standards

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Antennas and Propagation*. https://doi.org/10.1109/TAP.2019.2891399

**An Augmented Regularized Combined Source Integral Equation for Nonconforming Meshes.** / Vico, Felipe; Greengard, Leslie; Ferrando-Bataller, Miguel; Antonino-Daviu, Eva.

Research output: Contribution to journal › Article

*IEEE Transactions on Antennas and Propagation*. https://doi.org/10.1109/TAP.2019.2891399

}

TY - JOUR

T1 - An Augmented Regularized Combined Source Integral Equation for Nonconforming Meshes

AU - Vico, Felipe

AU - Greengard, Leslie

AU - Ferrando-Bataller, Miguel

AU - Antonino-Daviu, Eva

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We present a new version of the regularized combined source integral equation (CSIE-AR) for the solution of electromagnetic scattering problems in the presence of perfectly conducting bodies. The integral equation is of the second kind and has no spurious resonances. It is well-conditioned at all frequencies for simply connected geometries. Reconstruction of the magnetic field, however, is subject to catastrophic cancellation due to the need for computing a scalar potential from magnetic currents. Here, we show that by solving an auxiliary (scalar) integral equation, we can avoid this form of low-frequency breakdown. The auxiliary scalar equation is used to solve a Neumanntype boundary value problem using data corresponding to the normal component of the magnetic field. This scalar equation is also of the second kind, non-resonant, and well-conditioned at all frequencies. A principal advantage of our approach, by contrast with hyper-singular EFIE, CFIE or CSIE formulations, is that the standard loop-star and related basis function constructions are not needed, and preconditioners are not required. This permits an easy coupling to fast algorithms such as the fast multipole method (FMM). Furthermore, the formalism is compatible with non-conformal mesh discretization and works well with singular (sharp) boundaries.

AB - We present a new version of the regularized combined source integral equation (CSIE-AR) for the solution of electromagnetic scattering problems in the presence of perfectly conducting bodies. The integral equation is of the second kind and has no spurious resonances. It is well-conditioned at all frequencies for simply connected geometries. Reconstruction of the magnetic field, however, is subject to catastrophic cancellation due to the need for computing a scalar potential from magnetic currents. Here, we show that by solving an auxiliary (scalar) integral equation, we can avoid this form of low-frequency breakdown. The auxiliary scalar equation is used to solve a Neumanntype boundary value problem using data corresponding to the normal component of the magnetic field. This scalar equation is also of the second kind, non-resonant, and well-conditioned at all frequencies. A principal advantage of our approach, by contrast with hyper-singular EFIE, CFIE or CSIE formulations, is that the standard loop-star and related basis function constructions are not needed, and preconditioners are not required. This permits an easy coupling to fast algorithms such as the fast multipole method (FMM). Furthermore, the formalism is compatible with non-conformal mesh discretization and works well with singular (sharp) boundaries.

KW - Boundary conditions

KW - Calderon preconditioning (CP)

KW - charge-current formulations

KW - electromagnetic (EM) scattering

KW - Electromagnetic scattering

KW - Geometry

KW - high frequency preconditioning

KW - Integral equations

KW - Magnetic resonance

KW - Mathematical model

KW - Maxwell equations

KW - Standards

UR - http://www.scopus.com/inward/record.url?scp=85059802269&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059802269&partnerID=8YFLogxK

U2 - 10.1109/TAP.2019.2891399

DO - 10.1109/TAP.2019.2891399

M3 - Article

AN - SCOPUS:85059802269

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

ER -