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Magoulès F., Roux F. X. Lagrangian formulation of domain decomposition methods: a unified theory, Applied Mathematical Modeling , Vol. 30, No. 7, 2006, pp. 593–615. Roux F. X. Lagrangian

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. The finite element method in magnetics 2008 Kruis J. Domain decomposition methods for distributed computing , Kippen

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Abstract  

A new preconditioned conjugate gradient (PCG)-based domain decomposition method is given for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed method is in the recommended preconditioner which is constructed by using cyclic matrix. The resulting preconditioned algorithms are well suited to parallel computation.

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2001 50 1523 1544 Kruis J. Domain decomposition methods for distributed computing , First ed. Saxe

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Magoulés F. Mesh partitioning techniques and domain decomposition method , Kippen, Stirling, Scotland, Saxe-Coburg Publication, 2007. Magoulés F

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A preconditioned conjugate gradient (PCG)-based domain decomposition method was given in [11] and [12] for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed algorithm was that the recommended preconditioner was constructed by using symmetric-cyclic matrix. But we could give only the definitions of the entries of this cyclic matrix. Here we give a short description of this algorithm, the method of calculation of matrix entries and the results of calculation. The numerical experiments presented show, that this construction of precondition in the practice works well.

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Pollack Periodica 2010 5 57 68 Kruis J. Domain decomposition methods for distributed computing

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methods for elliptic partial differential equations 1996 Quarteroni A., Valli A. Domain decomposition methods for partial

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, 2003 . [6] Yao W. , Jin J. M. , Krein P. T. A highly efficient domain decomposition method applied to 3-D finite-element analysis

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Pollack Periodica
Authors: Miklós Kuczmann, Tamás Budai, Gergely Kovács, Dániel Marcsa, Gergely Friedl, Péter Prukner, Tamás Unger, and György Tomozi

method , Kippen Stirling, Scotland, Saxe-Coburg Publication, 2007. Magoulés F. Mesh partitioning techniques and domain decomposition method

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