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Approximate inverse-based block preconditioners in poroelasticity

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Abstract

We focus on the fully implicit solution of the linear systems arising from a three-field mixed finite element approximation of Biot’s poroleasticity equations. The objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. In this work, we investigate the use of approximate inverse-based techniques to decouple the native system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning of the unknowns by field type. The proposed methods are tested in various numerical experiments including real-world applications dealing with petroleum and geotechnical engineering.

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Acknowledgments

Portions of this work are developed within the 2019 GNCS project “Innovative and parallel techniques for large size linear and non-linear systems, matrix functions and equations, with applications.” Portions of this work were performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

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Authors and Affiliations

  1. Energy Resources Engineering, Stanford University, Stanford, CA, USA

    Andrea Franceschini

  2. Atmospheric, Earth and Energy Division, Lawrence Livermore National Laboratory, Livermore, CA, USA

    Nicola Castelletto

  3. Department of Civil, Environmental and Architectural Engineering, University of Padova, Padova, Italy

    Massimiliano Ferronato

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  1. Andrea Franceschini
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  2. Nicola Castelletto
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  3. Massimiliano Ferronato
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Correspondence to Massimiliano Ferronato.

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Franceschini, A., Castelletto, N. & Ferronato, M. Approximate inverse-based block preconditioners in poroelasticity. Comput Geosci 25, 701–714 (2021). https://doi.org/10.1007/s10596-020-09981-2

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