2016/07/12 by Björn Gmeiner, Daniel Drzisga, Gmeiner, Björn +7
Decision Sciences · Mathematics · #Computational Engineering #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Finance #G.1.8 #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Mathematical Software (cs.MS) #Numerical Analysis (math.NA) #Parallel #Probabilistic and Robust Engineering Design #Statistical Methods and Inference #and Cluster Computing (cs.DC) #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.1607.03252
openalex publication_date 2016/07/12 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
The computational complexity of naive, sampling-based uncertainty\nquantification for 3D partial differential equations is extremely high.\nMultilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the\ncomplexity significantly, but to exploit them fully in a parallel environment,\nsophisticated scheduling strategies are needed. Often fast algorithms that are\nexecuted in parallel are essential to compute fine level samples in 3D, whereas\nto compute individual coarse level samples only moderate numbers of processors\ncan be employed efficiently. We make use of multiple instances of a parallel\nmultigrid solver combined with advanced load balancing techniques. In\nparticular, we optimize the concurrent execution across the three layers of the\nMLMC method: parallelization across levels, across samples, and across the\nspatial grid. The overall efficiency and performance of these methods will be\nanalyzed. Here the scalability window of the multigrid solver is revealed as\nbeing essential, i.e., the property that the solution can be computed with a\nrange of process numbers while maintaining good parallel efficiency. We\nevaluate the new scheduling strategies in a series of numerical tests, and\nconclude the paper demonstrating large 3D scaling experiments.\n