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Stable discretization of poroelasticity problems and efficient preconditioners for arising saddle point type matrices

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    0427664 - ÚGN 2015 RIV NE eng J - Journal Article
    Axelsson, Owe - Blaheta, Radim - Byczanski, Petr
    Stable discretization of poroelasticity problems and efficient preconditioners for arising saddle point type matrices.
    Computing and Visualization in Science. Roč. 15, č. 4 (2012), s. 191-207. ISSN 1432-9360
    R&D Projects: GA MŠk ED1.1.00/02.0070
    Institutional support: RVO:68145535
    Keywords : poroelasticity * saddle point matrices * preconditioning * stability of discretization
    Subject RIV: BA - General Mathematics
    http://link.springer.com/article/10.1007/s00791-013-0209-0

    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.
    Permanent Link: http://hdl.handle.net/11104/0233156
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