Optimal higher order modeling methodology based on method of moments and finite element method for electromagnetics

Abstract

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 (subdivisions) in the model (h-refinement), polynomial orders of basis and testing functions (p-refinement), orders of Gauss-Legendre integration formulas (numbers of integration points - integration accuracy), and geometrical orders of elements (orders of Lagrange-type curvature) 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. The ultimate goal is to close the large gap between the rising academic interest in higher order CEM, which evidently shows great numerical potential, and its actual usefulness and application to electromagnetics research and engineering applications.