Abstract
Some geometric and algebraic aspects of various domain decomposition methods (DDMs) are considered. They are applied to a parallel solution of very large sparse SLAEs resulting from approximation of multi-dimensional mixed boundary value problems on non-structured grids. DDMs are used with parameterized overlapping of subdomains and various types of boundary conditions at the inner boundaries. An algorithm for automatic construction of a balancing domain decomposition for overlapping subdomains is presented. Subdomain SLAEs are solved by a direct or iterative preconditioned method in Krylov subspaces, whereas external iterations are performed by the FGMRES method. An experimental analysis of the algorithms is carried out on a set of model problems.
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Butyugin, D.S., Gurieva, Y.L., Ilin, V.P., Perevozkin, D.V. (2016). Some Geometric and Algebraic Aspects of Domain Decomposition Methods. In: Dickopf, T., Gander, M., Halpern, L., Krause, R., Pavarino, L. (eds) Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-18827-0_10
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DOI: https://doi.org/10.1007/978-3-319-18827-0_10
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