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A domain decomposition method based on augmented Lagrangian with a Penalty term. (English) Zbl 1183.65163

Bercovier, Michel (ed.) et al., Domain decomposition methods in science and engineering XVIII. Selected papers based on the presentations at the 18th international conference of domain decomposition methods, Jerusalem, Israel, January 12–17, 2008. Berlin: Springer (ISBN 978-3-642-02676-8/hbk; 978-3-642-04466-3/ebook). Lecture Notes in Computational Science and Engineering 70, 339-346 (2009).
Summary: An iterative substructuring method with Lagrange multipliers is considered for the second order elliptic problem, which is a variant of the finite element tearing and interconnecting dual-primal (FETI-DP) method. The standard FETI-DP formulation is associated with a saddle-point problem which is induced from the minimization problem with a constraint for imposing the continuity across the interface. Starting from the slightly changed saddle-point problem by addition of a penalty term with a positive penalization parameter \(\eta\), we propose a dual substructuring method which is implemented iteratively by the conjugate gradient method. In spite of the absence of any preconditioners, it is shown that the proposed method is numerically scalable in the sense that for a large value of \(\eta\), the condition number of the resultant dual problem is bounded by a constant independent of both the subdomain size \(H\) and the mesh size \(h\). We discuss computational issues and present numerical results.
For the entire collection see [Zbl 1178.65001].

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
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