Resumen de Efficient implementation of box-relaxation multigrid methods for the poroelasticity problem on semi-structured grids

Francisco José Gaspar Lorenz , Francisco Javier Lisbona Cortés , Carmen Rodrigo Cardiel

• We consider the numerical solution of a poroelasticity problem using a stabilized finite element method (FEM), based on the perturbation of the flow equation. Semistructured triangular grids and stencil-based implementation of the linear FEM for displacements and pressure are used. An efficient procedure to construct the stencils associated with the basic diferential operators involved in the poroelasticity equations, using some reference stencils computed on a canonical hexagon, is presented.

  To solve the algebraic system of saddle point type, geometric multigrid methods based on box-relaxation are proposed which result to have a good performance for the considered problem. Numerical results are presented to show the behavior of the method.