Abstract
The performance of the parallel domain decomposition methods (DDM) for solving very large systems of linear algebraic equations with non-symmetric sparse matrices depends on the convergence of the iterative algorithms as well as on the efficiency of the computational technologies. Usually in DDM approach the number of iterations grows together with a growth of the degree of freedom. We consider the algorithms for increasing the convergence rate based on the preconditioning with using deflation and aggregation techniques which take low rank approximations of the original systems of linear algebraic equations. The efficiency of the proposed approaches is demonstrated on the representative set of model tasks.
The work is supported partially by Russian Science Foundation grant N 14-11-00485. The experimental part of the paper is supported by the RFBR grant N 14-07-00128.
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Saad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publications, New York (2002)
Toselli, A., Widlund, O.: Domain Decomposition Methods - Algorithms and Theory. Springer, Heidelberg (2005)
Chapman, A., Saad, Y.: Deflated and augmented krylov subspace technique. Numer. Linear Algebra Applic. 4(1), 43–66 (1997)
Il’in, V.P.: Parallel Methods and Technologies of Domain Decomposition (in Russian). Vestnik YuUrGU. Series Computational mathematics and informatics. 46(305), 31–44 (2012)
Dubois, O., Gander, M.J., St-Cyr, A., Loisel, S., Szyld, D.: The optimized schwarz method with a coarse grid correction. SIAM J. Sci. Comput. 34(1), 421–458 (2012)
Il’in, V.P.: Finite Difference and Finite Volume Methods for Elliptic Equations. ICMMG Publisher, Novosibirsk (2001). (in Russian)
Il’in, V.P.: Finite Element Methods and Technologies. ICMMG Publisher, Novosibirsk (2007). (in Russian)
Official page of Domain Decomposition Methods. http://www.ddm.org
Butyugin, D.S., Gurieva, Y.L., Il’in, V.P., Perevozkin, D.V., Petukhov, A.V.: Functionality and Algebraic Solvers Technologies in Krylov Library (in Russian). Vestnik YuUrGU. Series Computational mathematics and informatics. 2(3), 92–105 (2013)
Gander, M.J., Halpern, L., Santugini, K.: Domain decomposition methods in science and engineering XXI. In: Erhel, J., Gander, M.J., Halpern, L., Pichot, G., Sassi, T., Widlund, O. (eds.) A New Coarse Grid Correction for RAS/AS. LNCSE. Springer-Verlag, Switzerland (2013)
Siberian Supercomputer Centre. http://www2.sscc.ru
Intel Math Kernel Library (Intel MKL). http://software.intel.com/en-us/intel-mkl
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Gurieva, Y.L., Il’in, V.P. (2015). On Parallel Computational Technologies of Augmented Domain Decomposition Methods. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2015. Lecture Notes in Computer Science(), vol 9251. Springer, Cham. https://doi.org/10.1007/978-3-319-21909-7_4
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DOI: https://doi.org/10.1007/978-3-319-21909-7_4
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