Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media

Nicola Castelletto, Sergey Klevtsov, Hadi Hajibeygi, Hamdi A. Tchelepi

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)

Abstract

We propose a two-stage preconditioner for accelerating the iterative solution by a Krylov subspace method of Biot’s poroelasticity equations based on a displacement-pressure formulation. The spatial discretization combines a finite element method for mechanics and a finite volume approach for flow. The fully implicit backward Euler scheme is used for time integration. The result is a 2 × 2 block linear system for each timestep. The preconditioning operator is obtained by applying a two-stage scheme. The first stage is a global preconditioner that employs multiscale basis functions to construct coarse-scale coupled systems using a Galerkin projection. This global stage is effective at damping low-frequency error modes associated with long-range coupling of the unknowns. The second stage is a local block-triangular smoothing preconditioner, which is aimed at high-frequency error modes associated with short-range coupling of the variables. Various numerical experiments are used to demonstrate the robustness of the proposed solver.

Original languageEnglish
Number of pages18
JournalComputational Geosciences
DOIs
Publication statusE-pub ahead of print - 1 Jan 2018

Keywords

  • Iterative methods
  • Multiscale methods
  • Poromechanics
  • Preconditioners

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