A well-conditioned time domain EFIE for densely discretized low frequency problems

The time domain electric field integral equation (TD-EFIE) models transient scattering by perfect electric conductors. Upon discretization, this equation yields an ill-conditioned system matrix when the time step is large (low frequency breakdown), or the mesh is dense (dense discretization breakdown). Furthermore, its solution suffers from spurious static loop currents (DC instability). The quasi-Helmholtz projected TD-EFIE (qHP-TDEFIE) is an alternative formulation of the TD-EFIE which is immune to both low frequency breakdown and DC instability. In this contribution, a multiplicative Calderón preconditioner is constructed for the qHP-TDEFIE, which renders it immune to dense discretization breakdown. This ensures that transient electromagnetic scattering problems can be solved efficiently and accurately, even for slowly varying fields in the presence of small geometrical features.