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Parallel domain decomposition solver for flows in hydrostatic bearings
Hanek, Martin ; Šístek, Jakub ; Burda, P. ; Stach, E.
We perform simulations of oil flow in hydrostatic bearings. Stationary incompressible three-dimensional flow governed by the Navier-Stokes equations is considered. The finite element method is used for discretization. The arising nonlinear system of algebraic equations is linearized using the Picard’s iteration, and the Balancing Domain Decomposition based on Constraints (BDDC) method is used to solve the linear systems of equations. The solver is first validated with an experiment for the case of a bearing without motion, and it is then applied to simulation of flow in a sliding bearing.
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Some practical aspects of parallel adaptive BDDC method
Šístek, Jakub ; Mandel, J. ; Sousedík, B.
We describe a parallel implementation of the Balancing Domain Decomposition by Constraints (BDDC) method enhanced by an adaptive construction of coarse problem. The method is designed for numerically difficult problems, where standard choice of continuity of arithmetic averages across faces and edges of subdomains fails to maintain the low condition number of the preconditioned system. Problems of elasticity analysis of bodies consisting of different materials with rapidly changing stiffness may represent one class of such challenging problems. The adaptive selection of constraints is shown to significantly increase the robustness of the method for this class of problems. However, since the cost of the set-up of the preconditioner with adaptive constraints is considerably larger than for the standard choices, computational feasibility of the presented implementation is obtained only for large contrasts of material coefficients.
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An application of the BDDC method to the Navier-Stokes equations in 3-D cavity
Hanek, M. ; Šístek, Jakub ; Burda, P.
We deal with numerical simulation of incompressible flow governed by the Navier-Stokes equations. The problem is discretised using the finite element method, and the arising system of nonlinear equations is solved by Picard iteration. We explore the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to nonsymmetric problems arising from such linearisation. One step of BDDC is applied as the preconditioner for the stabilized variant of the biconjugate gradient (BiCGstab) method. We present results for a 3-D cavity problem computed on 32 cores of a parallel supercomputer.
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Different approaches to interface weights in the BDDC method in 3D
Čertíková, M. ; Šístek, Jakub ; Burda, P.
In this paper, we discuss the choice of weights in averaging of local (subdomain) solutions on the interface for the BDDC method (Balancing Domain Decomposition by Constraints). We try to find relations among different choices of the interface weights and compare them numerically on model problems of the Poisson equation and linear elasticity in 3D. Problems with jumps in coefficients of material properties are considered and both regular and irregular interfaces between subdomains are tested.
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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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