Physics-Based Performance Enhancement in Computational Electromagnetics: A Review

Maxwell´s electrodynamic differential equations in general bi-anisotropic media have been split into an independent 4×4 diagonalized and a dependent 2×4 supplementary system of equations, referred to as the D-and S-forms, respectively. The forms have been utilized to construct standard singular Dyadic Green´s functions (DGFs). Problem-tailored expressions for the Dirac´s delta-function have been obtained using Fourier integral representations for the DGFs. The resulting expressions for the delta-function have been used to regularize the originating DGFs exponentially. On the other hand, employing standard finite-support basis- and testing functions, the DGFs have been regularized algebraically. Since the geneses of the exponential and algebraic regularization techniques are conceptually different they can be employed independently or in unison. Finally, frequency-, material- and geometry independent universal functions have been constructed for accelerated and highly performance-enhanced computation of the self- and mutual interactions in the method of moments applications.