Robust solution of time-domain integral equations using loop-tree decomposition and bandlimited extrapolation

A stabilization method that eradicates low frequency instabilities in the solution of the time-domain integral equations of electromagnetic scattering is presented. The method uses the loop-tree decomposition originally suggested for the solution of low frequency scattering problems via the method of moments. Specifically, a temporally differentiated form of the pertinent integral equation is tested using tree basis functions, and the undifferentiated form is tested using solenoidal basis functions. The underlying solution method uses bandlimited interpolation functions (BLIFs) and the higher-order divergence-conforming vector bases of Graglia et al. for the temporal and spatial discretization of the integral equations, respectively. An extrapolation technique has been implemented to overcome the noncausality introduced into the system by the BLIFs. Numerical results will demonstrate the stability and accuracy of the proposed technique.