期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
卷 92, 期 4, 页码 370-398出版社
WILEY
DOI: 10.1002/nme.4341
关键词
stochastic partial differential equations; parametrized partial differential equations; polynomial chaos; Galerkin projection; reduced-order modeling
资金
- United Kingdom Engineering and Physical Sciences Research Council (EPSRC) [EP/F006802/1]
- NSERC
- Canada Research Chairs program
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.
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