Toward a Nonintrusive Stochastic Multiscale Design System for Composite Materials
Wei Wu, Jacob Fish · International Journal for Multiscale Computational Engineering · 2010
In this paper we study a nonintrusive stochastic collocation method in combination with a reduced-order homogenization method for solving partial differential equations with oscillatory random coefficients. The method consists of the two-scale homogenization in space, eigendeformation-based model reduction, Galerkin approximation of the reduced-order problem in space, and collocation approximation based on a sparse grid in the probability space that naturally leads to a nonintrusive approach. By this approach the solution of the original stochastic partial differential equations is constructed from a set of decoupled deterministic solutions from which statistical information is obtained. Preliminary numerical experiments are conducted to determine the feasibility of the method for solving two-scale problems in heterogeneous media.