Green's function for random media

Random coefficients in partial differential equations and boundary conditions pose a computational challenge. The stochastic finite element formulation is involved because the Tatarski convection like terms must be captured via stochastic strain-displacement matrices. Once the stochastic Green's Function is obtained, standard packages for boundary element analysis, e.g., BEASY, can be employed. Here, for random constitutive properties, a stationary iteration scheme is demonstrated via Fourier transform of distributions. The deterministic Green's function associated with a uniform medium provides the kernel. There is no such analog for stochastic finite elements. In a current bio-engineering stress analysis program a computer algebra environment, viz. Mathematica, is used to approximate stochastic Green's Functions.