A Low-Frequency and Refinement Stable Impedance Boundary Condition EFIE

TL;DR

This paper introduces a discretisation method for the impedance boundary condition EFIE that remains accurate and stable at very low frequencies and with dense meshes, improving computational robustness.

Contribution

A novel discretisation approach for the impedance boundary condition EFIE that ensures stability and accuracy at low frequencies and dense meshes.

Findings

Correct solution at arbitrarily small frequencies

Bounded matrix-vector products as frequency approaches zero

Enhanced stability with dense mesh discretisation

Abstract

In this contribution, a discretisation of the IBC EFIE is introduced that (i) yields the correct solution at arbitrarily small frequencies, (ii) requires for its solution a number of matrix vector products bounded as the frequency tends to zero and as the mesh density increases. The low frequency stabilisation is based on a projector-based discrete Helmholtz splitting, rescaling, and recombination that depends on the low frequency behaviour of both the EFIE operator and the surface impedance condition. The dense mesh stabilisation is a modifcation of the Perfect Electric Conductor operator preconditioning approach taking into account the effect on the singular value spectrum of the IBC term.