Optimal Modeling Parameters for Higher Order MoM-SIE and FEM-MoM Electromagnetic Simulations

General guidelines and quantitative recipes for adoptions of optimal higher order parameters for computational electromagnetics (CEM) modeling using the method of moments and the finite element method are established and validated, based on an exhaustive series of numerical experiments and comprehensive case studies on higher order hierarchical CEM models of metallic and dielectric scatterers. The modeling parameters considered are: electrical dimensions of elements (
$h$
-refinement), polynomial orders of basis functions (
$p$
-refinement), orders of Gauss-Legendre integration formulas (integration accuracy), and geometrical (curvature) orders of elements in the model. The goal of the study, which is the first such study of higher order parameters in CEM, is to reduce the dilemmas and uncertainties associated with the great modeling flexibility of higher order elements, basis and testing functions, and integration procedures (this flexibility is the principal advantage but also the greatest shortcoming of the higher order CEM), and to ease and facilitate the decisions to be made on how to actually use them, by both CEM developers and practitioners.