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Balancing domain decomposition for mixed finite elements. (English) Zbl 0828.65135
The convergence rate of the balancing domain decomposition method applied to mixed finite element discretizations of second-order elliptic equations is analyzed.
The balancing domain decomposition method was introduced by J. Mandel. It is a substructuring method that involves at each iteration the solution of a local problem with Dirichlet data, a local problem with Neumann data, and a “coarse grid” problem to propagate information globally and to insure the consistency of the Neumann problem. It is shown that the condition number grows at work like the logarithm squared of the ratio of the subdomain size to the element size, both in two and three dimensions. Computational results on an INTEL-Delta machine demonstrate the scalability properties of the method.

MSC:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65Y05 Parallel numerical computation
35J25 Boundary value problems for second-order elliptic equations
Software:
PICL
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References:
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