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000874426 037__ $$aFZJ-2020-01436
000874426 041__ $$aEnglish
000874426 1001_ $$0P:(DE-HGF)0$$aHuber, Markus$$b0$$eCorresponding author
000874426 1112_ $$aNIC Symposium 2020$$cJülich$$d2020-02-27 - 2020-02-28$$wGermany
000874426 245__ $$aMassively Parallel Multigrid with Direct Coarse Grid Solvers
000874426 260__ $$aJülich$$bForschungszentrum Jülich GmbH Zentralbibliothek, Verlag$$c2020
000874426 29510 $$aNIC Symposium 2020
000874426 300__ $$a335 - 344
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000874426 3367_ $$0PUB:(DE-HGF)8$$2PUB:(DE-HGF)$$aContribution to a conference proceedings$$bcontrib$$mcontrib$$s1583851625_498
000874426 3367_ $$0PUB:(DE-HGF)7$$2PUB:(DE-HGF)$$aContribution to a book$$mcontb
000874426 4900_ $$aPublication Series of the John von Neumann Institute for Computing (NIC) NIC Series$$v50
000874426 520__ $$aMultigrid methods play an important role in the numerical approximation of partial differential equations. As long as only a moderate number of processors is used, many alternatives can be used as solver for the coarsest grid. However, when the number of processors increases, then standard coarsening will stop while the problem is still large and the communication overhead for solving the corresponding coarsest grid problem may dominate. In this case, the coarsest grid must be agglomerated to only a subset of the processors. This article studies the use of sparse direct methods for solving the coarsest grid problem as it arises in a multigrid hierarchy. We use as test case a Stokes-type model and solve algebraic saddle point systems with up to O(10$^{11}$) degrees of freedom on a current peta-scale supercomputer. We compare the sparse direct solver with a preconditioned minimal residual iteration and show that the sparse direct method can exhibit better parallel efficiency.
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000874426 7001_ $$0P:(DE-HGF)0$$aKohl, Nils$$b1
000874426 7001_ $$0P:(DE-HGF)0$$aLeleux, Philippe$$b2
000874426 7001_ $$0P:(DE-HGF)0$$aRüde, Ulrich$$b3
000874426 7001_ $$0P:(DE-HGF)0$$aThönnes, Dominik$$b4
000874426 7001_ $$0P:(DE-HGF)0$$aWohlmuth, Barbara$$b5
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000874426 8564_ $$uhttps://juser.fz-juelich.de/record/874426/files/NIC_2020_Wohlmuth.pdf$$yOpenAccess
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000874426 9101_ $$0I:(DE-588b)36241-4$$6P:(DE-HGF)0$$aTechnische Universität München$$b0$$kTUM
000874426 9101_ $$0I:(DE-HGF)0$$6P:(DE-HGF)0$$aFriedrich-Alexander Universität$$b1
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000874426 9101_ $$0I:(DE-HGF)0$$6P:(DE-HGF)0$$aFriedrich-Alexander Universität$$b3
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000874426 9101_ $$0I:(DE-HGF)0$$6P:(DE-HGF)0$$aFriedrich-Alexander Universität$$b4
000874426 9101_ $$0I:(DE-588b)36241-4$$6P:(DE-HGF)0$$aTechnische Universität München$$b5$$kTUM
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000874426 9141_ $$y2020
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000874426 9201_ $$0I:(DE-Juel1)NIC-20090406$$kNIC$$lJohn von Neumann - Institut für Computing$$x0
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