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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Domain decomposition with nonmatching grids: augmented Lagrangian approach
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by Patrick Le Tallec and Taoufik Sassi PDF
Math. Comp. 64 (1995), 1367-1396 Request permission

Abstract:

We propose and study a domain decomposition method which treats the constraint of displacement continuity at the interfaces by augmented Lagrangian techniques and solves the resulting problem by a parallel version of the Peaceman-Rachford algorithm. We prove that this algorithm is equivalent to the fictitious overlapping method introduced by P.L. Lions. We also prove its linear convergence independently of the discretization step h, even if the finite element grids do not match at the interfaces. A new preconditioner using fictitious overlapping and well adapted to three-dimensional elasticity problems is also introduced and is validated on several numerical examples.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Math. Comp. 64 (1995), 1367-1396
  • MSC: Primary 65N55; Secondary 65M55, 73V20
  • DOI: https://doi.org/10.1090/S0025-5718-1995-1308457-5
  • MathSciNet review: 1308457