Integral Accuracy and the Stability of TDIEs

Stability of time domain integral equation approaches to the computation of electromagnetic scattering is profoundly affected by the accuracy of the underlying numerical integration methods used for computation of the kernel elements. In most publications, the accuracy of the quadratures used to compute kernel elements is never measured, and higher order computation is assumed to deliver high accuracy. In this paper, we examine the complicated relationship between the actual accuracy of kernel element computation and the resulting stability of integral equations. Numerical results show that stability may be improved for a higher integral accuracy. Moreover, while integral accuracy is not always improved by higher order integration rules, more careful integration (as delivered by adaptive integration methods) is often helpful. Numerical results for a range of problems demonstrate these contentions.