On adaptive BDDC for the flow in heterogeneous porous media
Links to Fileshttps://arxiv.org/abs/1901.02090
MetadataShow full item record
Type of Work21 pages
journal artilces preprints
Citation of Original PublicationBedřich Sousedík , On adaptive BDDC for the flow in heterogeneous porous media, Numerical Analysis , 2019, https://arxiv.org/abs/1901.02090
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balancing domain decomposition
balancing domain decomposition by constraints (BDDC)
flow in porous media
SPE 10 benchmark
We study a method based on Balancing Domain Decomposition by Constraints (BDDC) for a numerical solution of a single-phase flow in heterogenous 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 number of iterations of conjugate gradients at a small additional cost.