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

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.