Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 92, Issue 4, Pages 370-398Publisher
WILEY
DOI: 10.1002/nme.4341
Keywords
stochastic partial differential equations; parametrized partial differential equations; polynomial chaos; Galerkin projection; reduced-order modeling
Funding
- United Kingdom Engineering and Physical Sciences Research Council (EPSRC) [EP/F006802/1]
- NSERC
- Canada Research Chairs program
Ask authors/readers for more resources
In this paper, we consider the problem of constructing reduced-order models of a class of time-dependent randomly parametrized linear partial differential equations. Our objective is to efficiently construct a reduced basis approximation of the solution as a function of the spatial coordinates, parameter space, and time. The proposed approach involves decomposing the solution in terms of undetermined spatial and parametrized temporal basis functions. The unknown basis functions in the decomposition are estimated using an alternating iterative Galerkin projection scheme. Numerical studies on the time-dependent randomly parametrized diffusion equation are presented to demonstrate that the proposed approach provides good accuracy at significantly lower computational cost compared with polynomial chaos-based Galerkin projection schemes. Comparison studies are also made against Nouy's generalized spectral decomposition scheme to demonstrate that the proposed approach provides a number of computational advantages. Copyright (c) 2012 John Wiley & Sons, Ltd.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available