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We present a new approach to the construction of Domain Decomposition (DD) preconditioners for the conjugate gradient method applied to the solution of symmetric and positive definite finite element equations. The DD technique is based on a non-overlapping decomposition of the domain Ω intop subdomains connected later with thep processors of a MIMD(More)
We describe a preconditioned conjugate gradient solution strategy for a multiprocessor system with message passing architecture. The preconditioner combines two techniques, a Schurcomplement preconditioning over “coupling boundaries” between the subdomains and an arbitrary choice of classic preconditioning for the inner degrees of freedom on each subdomain.(More)
In the first part of this article series, we had derived Domain Decomposition (DD) preconditioners containing three block matrices which must be specified for specific applications. In the present paper, we consider finite element equations arising from the DD discretization of plane, symmetric, 2nd-order, elliptic b.v.p.s and specify the matrices involved(More)
After some remarks on the parallel implementation of the Finite Element package FEAP, our realisation of the parallel CG{algorithm is sketched. From a technical point of view, a hierarchical preconditioner with and without additional global crosspoint preconditioning is presented. The numerical properties of this preconditioners are discussed and compared(More)
Zusammenfassung Der Einsatz der Finite-Element-Methode bei linearen piezoelektrischen Problemen führt auf eine Systemmatrix der Struktur " C B B T −K « mit positiv definiten Blockmatrizen C und K. Zur Lösung indefiniter Gleichungssy-steme, die diese symmetrische Blockstruktur besitzen, kann der Bramble–Pasciak–CG eingesetzt werden. Entscheidend für eine(More)