TY  - CONF
AU  - Huber, Markus
AU  - Kohl, Nils
AU  - Leleux, Philippe
AU  - Rüde, Ulrich
AU  - Thönnes, Dominik
AU  - Wohlmuth, Barbara
TI  - Massively Parallel Multigrid with Direct Coarse Grid Solvers
VL  - 50
CY  - Jülich
PB  - Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag
M1  - FZJ-2020-01436
T2  - Publication Series of the John von Neumann Institute for Computing (NIC) NIC Series
SP  - 335 - 344
PY  - 2020
AB  - Multigrid 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.
T2  - NIC Symposium 2020
CY  - 27 Feb 2020 - 28 Feb 2020, Jülich (Germany)
Y2  - 27 Feb 2020 - 28 Feb 2020
M2  - Jülich, Germany
LB  - PUB:(DE-HGF)8 ; PUB:(DE-HGF)7
UR  - https://juser.fz-juelich.de/record/874426
ER  -