Green's function for random media

Abstract

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.