3D Diagonalization and Supplementation in Thermo-Elasto-Electro-Magnetics: Dyadic Green's Functions and Algebraic and Exponential Regularization

摘要

In an accompanying paper in this proceedings it is rigorously shown that the governing and constitutive equations in fully quad-anisotropic and inhomogeneous media, capable of supporting coupled thermo-elasto-electro-magnetic fields, can be diagonalized (L~(12×12)Ψ~(12×1) = {partial deriv}_z Ψ~(12×1)), and the associated supplementary differential equation (Φ~(10×1) = K~(10×12)Ψ~(12×1)) can be constructed. This paper discusses important properties of LΨ = {partial deriv}_z Ψ and Φ = KΨ, respectively, their corresponding 12 × 12 and 10 × 12 algebraic counterparts in spectral domain, by resourcing to the simplest possible two-and three-dimensional boundary value problems, which permit closed-forms solutions. Distinctively desirable consequences of LΨ = {partial deriv}_zΨ and Φ = KΨ for renormalizing (regularizing) divergence behaviors of dyadic Greens functions in the near- and far-field will be illuminated, and consequences thereof for robust and accelerated algorithm design will be alluded to in terms of canonical examples.