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

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-12x12 Psi(12x1) = partial derivative(z)Psi(12x1)), and the associated supplementary differential equation (Phi(10x1) = K-10x12 Psi(12x1)) can be constructed. This paper discusses important properties of L Psi =partial derivative(z)Psi and Phi = K Psi, respectively, their corresponding 12x12 and 10x12 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 L Psi = partial derivative(z)Psi and Phi = K Psi 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.