The Path from Monadic to Tetradic Green’s Functions

Field responses to Dirac delta function sources are referred to as the Green's functions (GFs) associated with a given boundary value problem. Scalar (monadic) and dyadic GFs characterizing, respectively, isotropic/anisotropic, and bi-anisotropic media are pervasive in computational engineering. This paper considers comprehensively the coupling between electromagneticand thermoelastic fields in fully tetra-anisotropic and inhomogeneous media and inaugurates the notions of triadic and tetradic GFs and their spatial derivatives in 3-D. To this end, the governing (G) and constitutive (C) equations, describing tetradic coupled fields, are judiciously partitioned into the diagonalized (D) and the corresponding supplementary (S) equations. The resulting D- and S systems, being consistent and sharply complementary, are equivalent with the originating combined (G, C) equations. The D- and S equations transformed into spectral domain enable the calculation of the tetradic GFs and their spatial derivatives with a unifying stroke. A glimpse at future work includes the applicability of Per-Olov Loewdin's partitioning technique to the D-form to generate perturbation expressions for nadic GFs at any arbitrary point in spectral domain.