On adaptive BDDC for the flow in heterogeneous porous media

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dc.contributor.authorSousedik, Bedrich
dc.date.accessioned2019-02-14T16:08:32Z
dc.date.available2019-02-14T16:08:32Z
dc.date.issued2019-04-23
dc.description.abstractWe 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.en_US
dc.description.sponsorshipSupported by the U.S. National Science Foundation under grant DMS1521563.en_US
dc.description.urihttps://link.springer.com/article/10.21136/AM.2019.0222-18en_US
dc.format.extent26 pagesen_US
dc.genrejournal articlesen_US
dc.genrepreprints
dc.identifierdoi:10.13016/m2ilje-bqy7
dc.identifier.citationSousedík, B. On adaptive BDDC for the flow in heterogeneous porous media. Appl Math 64, 309–334 (2019). https://doi.org/10.21136/AM.2019.0222-18en_US
dc.identifier.urihttp://hdl.handle.net/11603/12791
dc.identifier.urihttps://doi.org/10.21136/AM.2019.0222-18
dc.language.isoen_USen_US
dc.publisherSpringer
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
dc.subjectiterative substructuringen_US
dc.subjectbalancing domain decompositionen_US
dc.subjectbalancing domain decomposition by constraints (BDDC)en_US
dc.subjectmultiscale methodsen_US
dc.subjectadaptive methodsen_US
dc.subjectflow in porous mediaen_US
dc.subjectreservoir simulationen_US
dc.subjectSPE 10 benchmarken_US
dc.titleOn adaptive BDDC for the flow in heterogeneous porous mediaen_US
dc.typeTexten_US
dcterms.creatorhttps://orcid.org/0000-0002-8053-8956

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