A Domain Decomposition Approach for Uncertainty Analysis

Abstract

This paper proposes a decomposition approach for uncertainty analysis of systems governed by partial differential equations (PDEs). The system is split into local components using domain decomposition. Our domain-decomposed uncertainty quantification (DDUQ) approach performs uncertainty analysis independently on each local component in an “offline" phase, and then assembles global uncertainty analysis results using precomputed local information in an “online" phase. At the heart of the DDUQ approach is importance sampling, which weights the precomputed local PDE solutions appropriately so as to satisfy the domain decomposition coupling conditions. To avoid global PDE solves in the online phase, a proper orthogonal decomposition reduced model provides an efficient approximate representation of the coupling functions.