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Abstract
The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly when they are combined with a fast multigrid solver, but to exploit them fully in a parallel environment, sophisticated scheduling strategies are needed. We optimize the concurrent execution across the three layers of the MLMC method: parallelization across levels, across samples, and across the spatial grid. In a series of numerical tests, the influence on the overall performance of the “scalability window” of the multigrid solver (i.e., the range of processor numbers over which good parallel efficiency can be maintained) is illustrated. Different homogeneous and heterogeneous scheduling strategies are proposed and discussed. Finally, large 3D scaling experiments are carried out, including adaptivity.
Original language | English |
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Pages (from-to) | S873-S897 |
Journal | SIAM Journal on Scientific Computing |
Volume | 39 |
Issue number | 5 |
DOIs | |
Publication status | Published - 26 Oct 2017 |
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Dive into the research topics of 'Scheduling Massively Parallel Multigrid for Multilevel Monte Carlo Methods'. Together they form a unique fingerprint.Projects
- 2 Finished
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Multiscale Modelling of Aerospace Composites
Butler, R. (PI) & Scheichl, R. (CoI)
Engineering and Physical Sciences Research Council
6/01/14 → 5/02/18
Project: Research council
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Multilevel Monte Carlo Methods for Elliptic Problems
Scheichl, R. (PI)
Engineering and Physical Sciences Research Council
1/07/11 → 30/06/14
Project: Research council