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^12×12Ψ^12×1 = ∂_zΨ^12×1), and the associated supplementary differential equation (Φ^10×1 = K^10×12Ψ^12×1) can be constructed. This paper discusses important properties of LΨ = ∂_zΨ 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 = ∂_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.