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Title: On adaptive BDDC for the flow in heterogeneous porous media (English)
Author: Sousedík, Bedřich
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 64
Issue: 3
Year: 2019
Pages: 309-334
Summary lang: English
Category: math
Summary: We study a method based on Balancing Domain Decomposition by Constraints (BDDC) for numerical solution of a single-phase flow in heterogeneous porous media. The method solves for both flux and pressure variables. The fluxes are resolved in three steps: the coarse solve is followed by subdomain solves and last we look for a divergence-free flux correction and pressures using conjugate gradients with the BDDC preconditioner. Our main contribution is an application of the adaptive algorithm for selection of flux constraints. Performance of the method is illustrated on the benchmark problem from the 10th SPE Comparative Solution Project (SPE 10). Numerical experiments in both 2D and 3D demonstrate that the first two steps of the method exhibit some numerical upscaling properties, and the adaptive preconditioner in the last step allows a significant decrease in the number of iterations of conjugate gradients at a small additional cost. (English)
Keyword: iterative substructuring
Keyword: balancing domain decomposition
Keyword: BDDC
Keyword: multiscale methods
Keyword: adaptive methods, flow in porous media
Keyword: reservoir simulation
Keyword: SPE 10 benchmark
MSC: 65F08
MSC: 65F10
MSC: 65M55
MSC: 65N55
idZBL: Zbl 07088743
idMR: MR3956175
DOI: 10.21136/AM.2019.0222-18
Date available: 2019-05-24T08:51:42Z
Last updated: 2020-07-02
Stable URL:
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