Approximate inverse-based block preconditioners in poroelasticity

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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Correspondence to Massimiliano Ferronato.

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Franceschini, A., Castelletto, N. & Ferronato, M. Approximate inverse-based block preconditioners in poroelasticity. Comput Geosci (2020). https://doi.org/10.1007/s10596-020-09981-2

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Keywords

  • Approximate inverses
  • Poroelasticity
  • Iterative methods
  • Preconditioning

Mathematics Subject Classification (2010)

  • 65F08
  • 65F10