期刊
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
卷 21, 期 2, 页码 239-255出版社
WILEY
DOI: 10.1002/nla.1924
关键词
iterative methods; algebraic multigrid; smoothed aggregation; stochastic PDEs; stochastic Galerkin
资金
- Department of Energy, Office of Advanced Scientific Computing Research (ASCR), Applied Mathematics Program (AM), Modeling and Simulation of High Dimensional Stochastic Multiscale PDE Systems at the Exascale under DOE ASCR AM [FG02-03ER25574]
- Lawrence Livermore National Laboratory [B568677]
- National Science Foundation [CBET-1249858]
- Department of Energy [DE-SC0006402]
- U.S. Department of Energy (DOE) [DE-SC0006402] Funding Source: U.S. Department of Energy (DOE)
- Directorate For Engineering
- Div Of Chem, Bioeng, Env, & Transp Sys [1249858] Funding Source: National Science Foundation
We consider two algebraic multilevel solvers for the solution of discrete problems arising from PDEs with random inputs. Our focus is on problems with large jumps in material coefficients. The model problem considered is that of a diffusion problem with uncertainties in the diffusion coefficients and realization values differing dramatically between different layers in the spatial domain, with the location of the interfaces between the layers assumed to be known. The stochastic discretization is based on the generalized polynomial chaos, and the spatial problem is discretized using conforming finite elements. A multigrid solver based on smoothed aggregation is presented, and numerical experiments are provided demonstrating convergence properties of the multigrid solver. The observed convergence is shown to depend only weakly on the stochastic discretization and, for the discretized stochastic PDE problem, generally mimics that of the corresponding deterministic problem. Copyright (c) 2014 John Wiley & Sons, Ltd.
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