Domain decomposition with nonmatching grids: augmented Lagrangian approach

Authors:
Patrick Le Tallec and Taoufik Sassi

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

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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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DOI:
https://doi.org/10.1090/S0025-5718-1995-1308457-5

Article copyright:
© Copyright 1995
American Mathematical Society