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A Low-Frequency Stable, Excitation Agnostic Discretization of the Right-Hand Side for the Electric Field Integral Equation on Multiply-Connected Geometries
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  • Bernd Hofmann,
  • Thomas F. Eibert,
  • Francesco P. Andriulli,
  • Simon Adrian
Bernd Hofmann
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Thomas F. Eibert
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Francesco P. Andriulli
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Simon Adrian
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Abstract

In order to accurately compute scattered and radiated fields in the presence of arbitrary excitations, a low-frequency stable discretization of the right-hand side (RHS) of a quasi-Helmholtz preconditioned electric field integral equation (EFIE) on multiply-connected geometries is introduced, which avoids an ad-hoc extraction of the static contribution of the RHS when tested with solenoidal functions. To obtain an excitation agnostic approach, our approach generalizes a technique to multiply-connected geometries where the testing of the RHS with loop functions is replaced by a testing of the normal component of the magnetic field with a scalar function. To this end, we leverage orientable global loop functions that are formed by a chain of Rao-Wilton-Glisson (RWG) functions around the holes and handles of the geometry, for which we introduce cap surfaces that allow to uniquely define a suitable scalar function. We show that this approach works with open and closed, orientable and non-orientable geometries. The numerical results demonstrate the effectiveness of this approach.
16 Apr 2024Submitted to TechRxiv
18 Apr 2024Published in TechRxiv
2023Published in IEEE Transactions on Antennas and Propagation on pages 1-1. 10.1109/TAP.2023.3234704