A high order accurate, low frequency stable convolution quadrature method for the solution of time-domain electromagnetics problems

Convolution quadrature (CQ) methods are one of a host of new techniques for creating stable implementations of time domain integral equations. Like all such methods, CQ methods provide an accurate approach for spatial integration in view of the natural shadow region created by the Galerkin testing process. The success of CQ in this regard, however, does nothing to eliminate the slowly growing instability connected with the separation of electromagnetic problems into electrostatic and magnetostatic problems at low frequency. In this work, therefore, we add the loop-tree low frequency stabilization technique to the CQ method. Numerical results demonstrate the stability and accuracy of the technique.