An Efficient Intrusive Uncertainty Propagation Method For Multi-Physics System With Random Inputs

摘要: Coupled partial differential equation (PDE) systems, which often represent multi-physics models, are naturally suited for modular numerical solution methods. However, several challenges yet remain in extending the benefits of modularization practices to task uncertainty propagation. Since cost each deterministic PDE solve can be usually expected quite significant, statistical sampling based methods like Monte-Carlo (MC) inefficient because they do not take advantage mathematical structure problem, and suffer poor convergence properties. On other hand, even if module contains a moderate number uncertain parameters, implementing spectral on combined high-dimensional parameter space prohibitively expensive due curse dimensionality. In this work, we present module-based efficient intrusive projection (ISP) method our proposed method, subproblem is separated modularized via block Gauss-Seidel (BGS) techniques, such that only needs tackle local stochastic space. Moreover, computational costs significantly mitigated by constructing reduced chaos approximations input data enter module. We demonstrate implementations its gains over standard ISP using examples.