Scheduling massively parallel multigrid for multilevel Monte Carlo methods

Rüde U, Drzisga DP, Gmeiner B, Wohlmuth BI, Scheichl R (2016)

Publication Language: English

Publication Type: Other publication type

Publication year: 2016

Publisher: arXiv

Article Number: 1607.03252


Open Access Link:


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, but to exploit them fully in a parallel environment, sophisticated scheduling strategies are needed. Often fast algorithms that are executed in parallel are essential to compute fine level samples in 3D, whereas to compute individual coarse level samples only moderate numbers of processors can be employed efficiently. We make use of multiple instances of a parallel multigrid solver combined with advanced load balancing techniques. In particular, we optimize the concurrent execution across the three layers of the MLMC method: parallelization across levels, across samples, and across the spatial grid. The overall efficiency and performance of these methods will be analyzed. Here the ”scalability window” of the multigrid solver is revealed as being essential, i.e., the property that the solution can be computed with a range of process numbers while maintaining good parallel efficiency. We evaluate the new scheduling strategies in a series of numerical tests, and conclude the paper demonstrating large 3D scaling experiments.

Authors with CRIS profile

Involved external institutions

How to cite


Rüde, U., Drzisga, D.P., Gmeiner, B., Wohlmuth, B.I., & Scheichl, R. (2016). Scheduling massively parallel multigrid for multilevel Monte Carlo methods. arXiv.


Rüde, Ulrich, et al. Scheduling massively parallel multigrid for multilevel Monte Carlo methods. arXiv, 2016.

BibTeX: Download