The boundary element method in electrodynamics; techniques and lessons from elastostatics and elastodynamics

This paper describes a curvilinear, isoparametric method for discretisation and solution of the magnetic field integral equation in the analysis of electromagnetic scattering from a perfect conductor. Geometry representation is via curvilinear triangular or quadrilateral patches, of the kind developed for and widely applied in finite element treatments in solid mechanics. The field representation employs these same quadratic shape functions, giving an isoparametric treatment, able to represent field and geometry variations with considerable smoothness. This is in contrast to the "flat facets" approach more common in electrodynamics. Two parallel codes are described, in the frequency domain and the time domain. Such accurate representations make more pressing the proper treatment of the singular and hypersingular integrands present in the integral equation, and techniques based on singularity supression and subtraction have been adapted from solid mechanics. In the time domain the temporal representation of the field employs similar smooth modelling, with shape functions quadratic in intrinsic time. The treatment is implicit; timesteps are unconstrained by nodal spacing. This is common in elastodynamics, and is in contrast to the explicit treatments usual in electrodynamics. Besides computational cost savings, this has the benefit of removing stability difficulties. An example of the performance of the approach is given, involving scattering from a large, stealthy RCS target.