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The Fixed-Stress splitting scheme for Biot's equations as a modified Richardson iteration: Implications for optimal convergence

Storvik, Erlend; Both, Jakub; Nordbotten, Jan Martin; Radu, Florin Adrian
Journal article, Peer reviewed
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URI
https://hdl.handle.net/11250/2991799
Date
2021
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  • Department of Mathematics [801]
  • Registrations from Cristin [5513]
Original version
Lecture Notes in Computational Science and Engineering. 2021, 139, 909–917.   https://doi.org/10.1007/978-3-030-55874-1_90
Abstract
The fixed-stress splitting scheme is a popular method for iteratively solving the Biot equations. The method successively solves the flow and mechanics subproblems while adding a stabilizing term to the flow equation, which includes a parameter that can be chosen freely. However, the convergence properties of the scheme depend significantly on this parameter and choosing it carelessly might lead to a very slow, or even diverging, method. In this paper, we present a way to exploit the matrix structure arising from discretizing the equations in the regime of impermeable porous media in order to obtain a priori knowledge of the optimal choice of this tuning/stabilization parameter.
Publisher
Springer
Journal
Lecture Notes in Computational Science and Engineering
Copyright
Copyright Springer Nature Switzerland AG 2021

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