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Mathematics of Computation

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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
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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Article copyright: © Copyright 1995 American Mathematical Society