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 language | English |
---|---|
Pages (from-to) | 207–224 |
Number of pages | 18 |
Journal | Computational Geosciences |
Volume | 23 (2019) |
DOIs | |
Publication status | Published - 1 Jan 2018 |
Keywords
- Iterative methods
- Multiscale methods
- Poromechanics
- Preconditioners