A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics

Frigo, Matteo; Castelletto, Nicola; Ferronato, Massimiliano

doi:10.1137/18M120645X

Title: A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics

Abstract

In this work, 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. Lastly, numerical experiments in both theoretical benchmarks and real-world applications are presented and discussed to investigate the RPF properties, performance, and robustness.

Authors:

Frigo, Matteo ^[1]; Castelletto, Nicola ^[2];

^[1]

Univ. of Padova (Italy)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: 2019-07-11

Research Org.:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1548353

Report Number(s):: LLNL-JRNL-756041
Journal ID: ISSN 1064-8275; 943354

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: SIAM Journal on Scientific Computing

Additional Journal Information:: Journal Volume: 41; Journal Issue: 4; Journal ID: ISSN 1064-8275

Publisher:: SIAM

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; preconditioning; Krylov subspace methods; mixed finite elements; poromechanics

Citation Formats


                    Frigo, Matteo, Castelletto, Nicola, and Ferronato, Massimiliano. A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics.  United States: N. p., 2019. 
Web.  doi:10.1137/18M120645X.

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                    Frigo, Matteo, Castelletto, Nicola, & Ferronato, Massimiliano. A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics.  United States.  https://doi.org/10.1137/18M120645X

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                    Frigo, Matteo, Castelletto, Nicola, and Ferronato, Massimiliano. Thu .  
"A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics".  United States.  https://doi.org/10.1137/18M120645X.  https://www.osti.gov/servlets/purl/1548353.

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@article{osti_1548353,

  title        = {A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics},

  author       = {Frigo, Matteo and Castelletto, Nicola and Ferronato, Massimiliano},

  abstractNote = {In this work, 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. Lastly, numerical experiments in both theoretical benchmarks and real-world applications are presented and discussed to investigate the RPF properties, performance, and robustness.},

  doi          = {10.1137/18M120645X},

  journal      = {SIAM Journal on Scientific Computing},

  number       = 4,

  volume       = 41,

  place        = {United States},

  year         = {2019},

  month        = {7}

}

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Cited by: 9 works

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Figures / Tables:

Algorithm 3.1: RPF preconditioner computation: pre-processing stage.

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Algorithm 3.1 (p. 12)

Fig. 1 (p. 12)

Algorithm 3.2 (p. 13)

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