A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics
Abstract
In this paper, we introduce a relaxed physical factorization (RPF) preconditioner for the efficient iterative solution of the linearized algebraic system arising from the mixed finite element discretization of coupled poromechanics equations. The preconditioner is obtained by using a proper factorization of the $3\times3$ block matrix and setting a relaxation parameter $\alpha$. The preconditioner is inspired by the relaxed dimensional factorization introduced by Benzi et al. [J. Comput. Phys., 230 (2011), pp. 6185--6202; Comput. Methods Appl. Mech. Engrg., 300 (2016), pp. 129--145]. A stable algorithm is advanced to compute the optimal value of $\alpha$, along with a lower bound to control the possible ill-conditioning of the $\alpha$ dependent inner blocks. Numerical experiments in both theoretical benchmarks and real-world applications are presented and discussed to investigate the RPF properties, performance, and robustness.
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Information
Published In
SIAM Journal on Scientific Computing
Pages: B694 - B720
DOI: 10.1137/18M120645X
ISSN (online): 1095-7197
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© 2019, Society for Industrial and Applied Mathematics.
History
Submitted: 9 August 2018
Accepted: 7 May 2019
Published online: 11 July 2019
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Lawrence Livermore National Laboratory https://doi.org/10.13039/100006227 : DE-AC52-07NA27344
Università degli Studi di Padova https://doi.org/10.13039/501100003500
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