On the Regularization of the High Order Time Domain EFIE with Quasi-Helmholtz Projectors

In this work, we present a quasi-Helmholtz projector-based preconditioning and stabilization of the time domain electric field integral equation when discretized with high-order basis functions and high-order convolution quadrature schemes. The proposed approach effectively cures the ill-conditioning at large time steps that the original scheme suffers from along with the late time instabilities caused by the static solenoidal nullspace. This stabilization is achieved through a generalization of the quasi-Helmholtz projectors adapted to the high-order space basis functions and the high-order implicit schemes used by the convolution quadrature method.