Algebraic preconditioning for Biot-Barenblatt poroelastic systems

Radim Blaheta; Tomáš Luber

Applications of Mathematics (2017)

  • Volume: 62, Issue: 6, page 561-577
  • ISSN: 0862-7940

Abstract

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Poroelastic systems describe fluid flow through porous medium coupled with deformation of the porous matrix. In this paper, the deformation is described by linear elasticity, the fluid flow is modelled as Darcy flow. The main focus is on the Biot-Barenblatt model with double porosity/double permeability flow, which distinguishes flow in two regions considered as continua. The main goal is in proposing block diagonal preconditionings to systems arising from the discretization of the Biot-Barenblatt model by a mixed finite element method in space and implicit Euler method in time and estimating the condition number for such preconditioning. The investigation of preconditioning includes its dependence on material coefficients and parameters of discretization.

How to cite

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Blaheta, Radim, and Luber, Tomáš. "Algebraic preconditioning for Biot-Barenblatt poroelastic systems." Applications of Mathematics 62.6 (2017): 561-577. <http://eudml.org/doc/294179>.

@article{Blaheta2017,
abstract = {Poroelastic systems describe fluid flow through porous medium coupled with deformation of the porous matrix. In this paper, the deformation is described by linear elasticity, the fluid flow is modelled as Darcy flow. The main focus is on the Biot-Barenblatt model with double porosity/double permeability flow, which distinguishes flow in two regions considered as continua. The main goal is in proposing block diagonal preconditionings to systems arising from the discretization of the Biot-Barenblatt model by a mixed finite element method in space and implicit Euler method in time and estimating the condition number for such preconditioning. The investigation of preconditioning includes its dependence on material coefficients and parameters of discretization.},
author = {Blaheta, Radim, Luber, Tomáš},
journal = {Applications of Mathematics},
keywords = {poroelasticity; double permeability; preconditioning; Schur complement},
language = {eng},
number = {6},
pages = {561-577},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Algebraic preconditioning for Biot-Barenblatt poroelastic systems},
url = {http://eudml.org/doc/294179},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Blaheta, Radim
AU - Luber, Tomáš
TI - Algebraic preconditioning for Biot-Barenblatt poroelastic systems
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 6
SP - 561
EP - 577
AB - Poroelastic systems describe fluid flow through porous medium coupled with deformation of the porous matrix. In this paper, the deformation is described by linear elasticity, the fluid flow is modelled as Darcy flow. The main focus is on the Biot-Barenblatt model with double porosity/double permeability flow, which distinguishes flow in two regions considered as continua. The main goal is in proposing block diagonal preconditionings to systems arising from the discretization of the Biot-Barenblatt model by a mixed finite element method in space and implicit Euler method in time and estimating the condition number for such preconditioning. The investigation of preconditioning includes its dependence on material coefficients and parameters of discretization.
LA - eng
KW - poroelasticity; double permeability; preconditioning; Schur complement
UR - http://eudml.org/doc/294179
ER -

References

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