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

0427664 - ÚGN 2015 RIV NE eng J - Článek v odborném periodiku
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
Grant CEP: GA MŠMT ED1.1.00/02.0070
Institucionální podpora: RVO:68145535
Klíčová slova: poroelasticity * saddle point matrices * preconditioning * stability of discretization
Kód oboru RIV: BA - Obecná matematika
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.
Trvalý link: http://hdl.handle.net/11104/0233156