### 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 |

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### 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