High-order Calderón multiplicative preconditioner for time domain electric field integral equations

Marching-on-in-time (MOT) time domain electric field integral equation (TDEFIE) solvers are often used to analyze scattering of transient electromagnetic fields from perfect electrically conducting (PEC) surfaces. Unfortunately, just like their frequency domain counterparts, MOT-TDEFIE solvers suffer from dense-mesh breakdown when the linear dimensions of the patches in a surface mesh are small compared to the space time step and/or the order of the spatial basis functions used to expand the surface currents is high. This breakdown phenomenon manifests itself in the form of ill conditioned MOT system matrices and slow convergence rates of the MOT iterative solver.