Green's function for random media

Random coefficients in partial differential equations and boundary conditio ns pose a computational challenge. The stochastic finite element formulatio n is involved because the Tatarski convection like terms must be captured v ia stochastic strain-displacement matrices. Once the stochastic Green's Fun ction is obtained, standard packages for boundary element analysis, e.g., B EASY, can be employed. Here, for random constitutive properties, a stationa ry iteration scheme is demonstrated via Fourier transform of distributions. The deterministic Green's function associated with a uniform medium provid es the kernel. There is no such analog for stochastic finite elements. In a current bio-engineering stress analysis program a computer algebra environ ment, viz. Mathematica, is used to approximate stochastic Green's Functions .