Error estimation and adaptive refinement for integral equations

Surface integral equation formulations are popular approaches for electromagnetic radiation and scattering problems. Unlike differential equation formulations, which are routinely implemented using adaptive refinement procedures to assist the analysis, there appears to be no widespread use of adaptive refinement techniques applied to integral equations. Adaptive refinement consists of adjusting cell sizes (h-refinement) or representation orders (p-refinement) to achieve a more accurate and efficient solution without user intervention. The approach reduces the need for user expertise and provides a more systematic solution procedure.