Calder\'on Preconditioners for the TD-EFIE discretized with Convolution Quadratures

TL;DR

This paper introduces Calderón preconditioners to improve the stability and conditioning of the time domain electric field integral equation discretized with convolution quadratures, addressing issues like ill-conditioning and DC instability.

Contribution

It proposes a Calderón-based preconditioning method for the TD-EFIE with convolution quadratures, enhancing numerical stability and addressing DC instability problems.

Findings

Numerical results confirm improved conditioning.

Preconditioning reduces DC instability.

Enhanced stability for large time steps and refined meshes.

Abstract

This work focuses on the preconditioning and DC stabilization of the time domain electric field integral equation discretized in time with the convolution quadrature method. The standard formulation of the equation suffers from severe ill-conditioning for large time steps and refined meshes, in addition to DC instabilities plaguing standard solutions for late time steps. This work addresses all these issues by preconditioning the TD-EFIE operator matrices with a Calder\'on approach. Numerical results will corroborate the theory, showing the practical relevance of the proposed advancements.