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Numerical comparison of different choices of interface weights in the BDDC method
Čertíková, M. ; Burda, P. ; Šístek, Jakub
Balancing Domain Decomposition by Constraints (BDDC) belongs to the class of primal substructuring Domain Decomposition (DD) methods. DD methods are iterative methods successfully used in engineering to parallelize solution of large linear systems arising from discretization of second order elliptic problems. Substructuring DD methods represent an important class of DD methods. Their main idea is to divide the underlying domain into nonoverlapping subdomains and solvemany relatively small, local problems on subdomains instead of one large problem on the whole domain. In primal methods, it has to be specified how to distribute interface residuals among subdomains and how to obtain global, interface values of solution from local values on adjacent subdomains. Usually a weighted average is used with some simple choice of weights.
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Approaches to parallel implementation of the BDDC method
Šístek, Jakub ; Burda, P. ; Čertíková, M. ; Novotný, J.
During past several years, we have implemented and tested various approaches to domain decomposition methods, especially the Balancing Domain Decomposition Method by Constraints (BDDC). The goal of this paper is to summarize our experience with parallel implementation of such algorithms and to suggest ways to an implementation of the BDDC method that would be efficient on very large number of cores of computers of near future.
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On selections of constraints for the BDDC method
Čertíková, M. ; Šístek, Jakub ; Novotný, J. ; Burda, P.
The Balancing Domain Decomposition by Constraints (BDDC) method is an iterative substructuring domain decomposition method which uses a coarse space. The choice of coarse constraints on continuity has strong influence on convergence of the method. The goal of this paper is to compare the performance of several algorithms for selection of the coarse constraints applied to both test and industrial 3D linear elasticity problems and confront results obtained for typical test problems with results for industrial problems.
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