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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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Uniform preconditioners for high order finite element approximations of planar linear elasticity
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by Mark Ainsworth and Charles Parker;
Math. Comp. 93 (2024), 2067-2102
DOI: https://doi.org/10.1090/mcom/3926
Published electronically: November 17, 2023

Abstract:

A new overlapping Additive Schwarz preconditioner is developed for high order finite element approximation of planar linear elastic problems on triangular meshes. The new preconditioner results in a condition number that is bounded independently of the degree $p$, the mesh-size $h$ and the ratio $\lambda /\mu$. The resulting condition number is reduced to roughly $6.0$ for all values of the parameters and discretization parameters on standard test problems. Crucially, the overall cost of the new preconditioner is comparable to the cost of applying standard domain decomposition based preconditioners.
References
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Bibliographic Information
  • Mark Ainsworth
  • Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island
  • MR Author ID: 261514
  • Email: mark_ainsworth@brown.edu
  • Charles Parker
  • Affiliation: Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, United Kingdom
  • MR Author ID: 1382837
  • ORCID: 0000-0003-0767-5732
  • Email: charles.parker@maths.ox.ac.uk
  • Received by editor(s): January 9, 2023
  • Received by editor(s) in revised form: September 27, 2023
  • Published electronically: November 17, 2023
  • Additional Notes: This material is based upon work supported by the National Science Foundation under Award No. DMS-2201487.
  • © Copyright 2023 American Mathematical Society
  • Journal: Math. Comp. 93 (2024), 2067-2102
  • MSC (2020): Primary 65N30, 65N55, 65F08, 74S05
  • DOI: https://doi.org/10.1090/mcom/3926
  • MathSciNet review: 4759370