Algebraic preconditioning for poroelasticity

Tomáš Luber

May 15, 2018, 3:30 p.m. S2 416-1

Poroelasticity is a fundamental model model of a fluid flow in a deformable
porous media. It couples the description of mechanical deformation of the
matrix with the fluid flow through pores in the matrix. Deformation is
described by linear elasticity, fluid flow by Darcy's law. This relatively
simple model is limited to description of quasistacionary processes. However,
its application is suitable in different fields. The formulation of the
poroelastic model will be presented in a variant that uses three fields to
describe the state of the porous environment: displacement, pore pressure and
fluid flow. This formulation will be discretized by the mixed finite element
method in space and implicit Euler method time. For the resulting system block
preconditioners based on algebraic properties will be proposed and analyzed
with respect to dependence on material parameters of the model.