The Influence of the Exact Evaluation of Radiation Fields in Finite Precision Arithmetic on the Stability of the Time Domain Integral Equation Method

Transient electromagnetic scattering phenomena can effectively be simulated with time domain integral equation methods. The stability and accuracy of the marching on in time scheme is usually established with exact evaluation of the radiation fields. Due to singularities in their analytical expressions, straightforward evaluation in finite precision arithmetic can jeopardize the accuracy of the radiation fields. Computational experiments confirm this and show that it can even lead to late-time instability of the numerical model. Hence, a reformulation is necessary to remove the singular behavior and obtain the robustness required for industrial application. To this end, highly accurate and well-behaved expressions for the quasi-exact integration method in finite precision arithmetic will be derived in this paper. Numerical experiments confirm the robustness and stability of the improved Marching on in Time scheme.