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2018 | OriginalPaper | Chapter

Robust Block Preconditioners for Biot’s Model

Authors : James H. Adler, Francisco J. Gaspar, Xiaozhe Hu, Carmen Rodrigo, Ludmil T. Zikatanov

Published in: Domain Decomposition Methods in Science and Engineering XXIV

Publisher: Springer International Publishing

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Abstract

In this paper, we design robust and efficient block preconditioners for the two-field formulation of Biot’s consolidation model, where stabilized finite-element discretizations are used. The proposed block preconditioners are based on the well-posedness of the discrete linear systems. Block diagonal (norm-equivalent) and block triangular preconditioners are developed, and we prove that these methods are robust with respect to both physical and discretization parameters. Numerical results are presented to support the theoretical results.

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next chapter An Additive Schwarz Analysis for Multiplicative Schwarz Methods: General Case
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Metadata
Title
Robust Block Preconditioners for Biot’s Model
Authors
James H. Adler
Francisco J. Gaspar
Xiaozhe Hu
Carmen Rodrigo
Ludmil T. Zikatanov
Copyright Year
2018
Book
Domain Decomposition Methods in Science and Engineering XXIV

Print ISBN: 978-3-319-93872-1

Electronic ISBN: 978-3-319-93873-8

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-93873-8_1

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