On the use of a loop-tree decomposition method for the elimination of solenoidal error in time marching

Time-domain integral-equation methods for the simulation of electromagnetic wave scattering have historically been subject to two sources of instability. The first source of instability causes the solution yielded by the process to oscillate wildly, and is caused by spatial integrations that are unable to capture the rapid change in the integrand at shadow boundaries. The second source of instability results in a slow growth of the current on the structure, and is due to the ill-conditioned nature of the electric-field integral equation at low frequencies. In this work, the shadow region instability is eliminated using a convolution quadrature method, and the low-frequency difficulties are improved using a loop-tree decomposition. Numerical results will demonstrate the efficacy of the combination.