Integral accuracy and the stability of time domain integral equations for electromagnetic scattering
Date
2018
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Publisher
University of Delaware
Abstract
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, numerical integrals are assumed exact and higher integral orders are assumed to deliver higher accuracy. The lack of attention to this detail has led to inaccurate conclusions about the stability of different solution methods. In this work, we examine the complicated relationship between the actual accuracy of integral computation and the resulting stability of integral equations. Numerical results show that numerical integrals are not as exact as expected, and 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.