Effects of integration rule choice on time domain integral equation stability

Abstract

Sources of instability are one of the unresolved mysteries of the numerical solution of the time domain integral equations of electromagnetics, and finding these sources is difficult due to the complexity of the numerical analysis of these equations. Even though the approaches that are studied in this thesis, namely Finite Difference Delay Modeling and Bandlimited Interpolation and Extrapolation, generally work well and are much more stable than their predecessors, implementation issues may affect the stability of these schemes. Hence, computational experiments plays a key role in evaluation of their stability properties. This thesis, therefore, investigates in detail the influence of integration rule choice on time domain integral equations stability with computational experiments. Numerical results confirm that the stabilization of the methods depends on the choice of integration rules, but it is not always improved by increasing the order of integration.