A block-diagonal preconditioner for a four-field mixed finite element method for Biot's equations

Abstract

In this paper, we explore an efficient preconditioning method for the saddle point system resulting from a four-field mixed finite element method applied to Biot's consolidation model. The proposed preconditioner is a block diagonal preconditioner based on the Schur complement. We obtain bounds on the eigenvalues of the preconditioned matrix that are clustered away from 0. To reduce the computational expense, this preconditioner is inverted approximately. Some numerical results are provided to show the efficiency of our preconditioning strategy when applied to a poroelasticity problem in a layered medium.