000874426 001__ 874426 000874426 005__ 20210130004655.0 000874426 0247_ $$2Handle$$a2128/24533 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 000874426 3367_ $$2ORCID$$aCONFERENCE_PAPER 000874426 3367_ $$033$$2EndNote$$aConference Paper 000874426 3367_ $$2BibTeX$$aINPROCEEDINGS 000874426 3367_ $$2DRIVER$$aconferenceObject 000874426 3367_ $$2DataCite$$aOutput Types/Conference Paper 000874426 3367_ $$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. 000874426 536__ $$0G:(DE-HGF)POF3-899$$a899 - ohne Topic (POF3-899)$$cPOF3-899$$fPOF III$$x0 000874426 7001_ $$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 000874426 7870_ $$0FZJ-2020-01353$$iIsPartOf 000874426 8564_ $$uhttps://juser.fz-juelich.de/record/874426/files/NIC_2020_Wohlmuth.pdf$$yOpenAccess 000874426 8564_ $$uhttps://juser.fz-juelich.de/record/874426/files/NIC_2020_Wohlmuth.pdf?subformat=pdfa$$xpdfa$$yOpenAccess 000874426 909CO $$ooai:juser.fz-juelich.de:874426$$pdnbdelivery$$pdriver$$pVDB$$popen_access$$popenaire 000874426 9101_ $$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 000874426 9101_ $$0I:(DE-HGF)0$$6P:(DE-HGF)0$$aCERFACS$$b2 000874426 9101_ $$0I:(DE-HGF)0$$6P:(DE-HGF)0$$aFriedrich-Alexander Universität$$b3 000874426 9101_ $$0I:(DE-HGF)0$$6P:(DE-HGF)0$$aCERFACS$$b3 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$$kTUM 000874426 9131_ $$0G:(DE-HGF)POF3-899$$1G:(DE-HGF)POF3-890$$2G:(DE-HGF)POF3-800$$3G:(DE-HGF)POF3$$4G:(DE-HGF)POF$$aDE-HGF$$bProgrammungebundene Forschung$$lohne Programm$$vohne Topic$$x0 000874426 9141_ $$y2020 000874426 915__ $$0StatID:(DE-HGF)0510$$2StatID$$aOpenAccess 000874426 915__ $$0LIC:(DE-HGF)CCBY4$$2HGFVOC$$aCreative Commons Attribution CC BY 4.0 000874426 9201_ $$0I:(DE-Juel1)NIC-20090406$$kNIC$$lJohn von Neumann - Institut für Computing$$x0 000874426 980__ $$acontrib 000874426 980__ $$aVDB 000874426 980__ $$aUNRESTRICTED 000874426 980__ $$acontb 000874426 980__ $$aI:(DE-Juel1)NIC-20090406 000874426 9801_ $$aFullTexts