Robust block preconditioners for biot’s model

James H. Adler, Francisco J. Gaspar, Xiaozhe Hu, Carmen Rodrigo, Ludmil Tomov Zikatanov

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Citations (Scopus)

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.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computational Science and Engineering
PublisherSpringer Verlag
Pages3-16
Number of pages14
DOIs
StatePublished - Jan 1 2018

Publication series

NameLecture Notes in Computational Science and Engineering
Volume125
ISSN (Print)1439-7358

Fingerprint

Preconditioner
Consolidation
Linear systems
Stabilized Finite Elements
Equivalent Norm
Robust Design
Finite Element Discretization
Discrete Systems
Well-posedness
Triangular
Discretization
Linear Systems
Model
Numerical Results
Formulation

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

Cite this

Adler, J. H., Gaspar, F. J., Hu, X., Rodrigo, C., & Zikatanov, L. T. (2018). Robust block preconditioners for biot’s model. In Lecture Notes in Computational Science and Engineering (pp. 3-16). (Lecture Notes in Computational Science and Engineering; Vol. 125). Springer Verlag. https://doi.org/10.1007/978-3-319-93873-8_1
Adler, James H. ; Gaspar, Francisco J. ; Hu, Xiaozhe ; Rodrigo, Carmen ; Zikatanov, Ludmil Tomov. / Robust block preconditioners for biot’s model. Lecture Notes in Computational Science and Engineering. Springer Verlag, 2018. pp. 3-16 (Lecture Notes in Computational Science and Engineering).
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Adler, JH, Gaspar, FJ, Hu, X, Rodrigo, C & Zikatanov, LT 2018, Robust block preconditioners for biot’s model. in Lecture Notes in Computational Science and Engineering. Lecture Notes in Computational Science and Engineering, vol. 125, Springer Verlag, pp. 3-16. https://doi.org/10.1007/978-3-319-93873-8_1

Robust block preconditioners for biot’s model. / Adler, James H.; Gaspar, Francisco J.; Hu, Xiaozhe; Rodrigo, Carmen; Zikatanov, Ludmil Tomov.

Lecture Notes in Computational Science and Engineering. Springer Verlag, 2018. p. 3-16 (Lecture Notes in Computational Science and Engineering; Vol. 125).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Adler JH, Gaspar FJ, Hu X, Rodrigo C, Zikatanov LT. Robust block preconditioners for biot’s model. In Lecture Notes in Computational Science and Engineering. Springer Verlag. 2018. p. 3-16. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-319-93873-8_1