Galerkin based generalized ANOVA for the solution of stochastic steady state diffusion problems

Abstract

This work presents a novel approach, referred here as Galerkin based generalized analysis of variance decomposition (GG-ANOVA), for the solution of stochastic steady state diffusion problems. The proposed approach utilizes generalized ANOVA (G-ANOVA) expansion to represent the unknown stochastic response and Galerkin projection to decompose the stochastic differential equation into a set of coupled differential equations. The coupled set of partial differential equations obtained are solved using finite difference method and homotopy algorithm. Implementation of the proposed approach for solving stochastic steady state diffusion problems has been illustrated with three numerical examples. For all the examples, results obtained are in excellent agreement with the benchmark solutions. Additionally, for the second and third problems, results obtained have also been compared with those obtained using polynomial chaos expansion (PCE) and conventional G-ANOVA. It is observed that the proposed approach yields highly accurate result outperforming both PCE and G-ANOVA. Moreover, computational time required using GG-ANOVA is in close proximity of G-ANOVA and less as compared to PCE.