High-Order Modeling for Computational Electromagnetics

This paper provides a brief review of the most recent advances in computational electromagnetics regarding simple techniques for the systematic construction of high-order vector bases used by advanced numerical codes. The technique to build higher-order vector bases here discussed uses only scalar interpolating or hierarchical functions together with vector functions of the zeroth order (the lowest possible order). The higher order models thus obtained are used in the numerical solution of differential and integro-differential equations by application of the Method of Moments and the Finite Elements Method. First we consider divergence and curl-conforming polynomial vector bases, and then introduce substitutive and additive vector bases able to model the field singularities in the vicinity of edges or vertices. The advantages offered by the use of these higher order models are illustrated by numerical results. Several other numerical results were shown during the oral presentation of this paper.