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Stable discretization of poroelasticity problems and efficient preconditioners for arising saddle point type matrices
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SYSNO ASEP 0427664 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Ostatní články Title Stable discretization of poroelasticity problems and efficient preconditioners for arising saddle point type matrices Author(s) Axelsson, Owe (UGN-S) RID
Blaheta, Radim (UGN-S) RID, SAI, ORCID
Byczanski, Petr (UGN-S)Number of authors 3 Source Title Computing and Visualization in Science - ISSN 1432-9360
Roč. 15, č. 4 (2012), s. 191-207Number of pages 17 s. Publication form Online - E Language eng - English Country NE - Niger Keywords poroelasticity ; saddle point matrices ; preconditioning ; stability of discretization Subject RIV BA - General Mathematics R&D Projects ED1.1.00/02.0070 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Institutional support UGN-S - RVO:68145535 DOI 10.1007/s00791-013-0209-0 Annotation Poroelastic models arise in reservoir modeling and many other important applications. Under certain assumptions, they involve a time-dependent coupled system consisting of Navier–Lamé equations for the displacements, Darcy’s flow equation for the fluid velocity and a divergence constraint equation. Stability for infinite time of the continuous problem and, second and third order accurate, time discretized equations are shown. Methods to handle the lack of regularity at initial times are discussed and illustrated numerically. After discretization, at each time step this leads to a block matrix system in saddle point form. Mixed space discretization methods and a regularization method to stabilize the system and avoid locking in the pressure variable are presented. A certain block matrix preconditioner is shown to cluster the eigenvalues of the preconditioned matrix about the unit value but needs inner iterations for certain matrix. Workplace Institute of Geonics Contact Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Year of Publishing 2015 Electronic address http://link.springer.com/article/10.1007/s00791-013-0209-0
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