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首页> 外文期刊>SIAM/ASA Journal on Uncertainty Quantification >Uncertainty Quantification by Multilevel Monte Carlo and Local Time-Stepping for Wave Propagation
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Uncertainty Quantification by Multilevel Monte Carlo and Local Time-Stepping for Wave Propagation

机译：波传播的多能级蒙特卡罗和局部时间步长的不确定性量化

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摘要

Because of their robustness, efficiency, and non intrusiveness, Monte Carlo methods are probably the most popular approach in uncertainty quantification for computing expected values of quantities of interest. Multilevel Monte Carlo (MLMC) methods significantly reduce the computational cost by distributing the sampling across a hierarchy of discretizations and allocating most samples to the coarser grids. For time dependent problems, spatial coarsening typically entails an increased time step. Geometric constraints, however, may impede uniform coarsening thereby forcing some elements to remain small across all levels. If explicit time-stepping is used, the time step will then be dictated by the smallest element on each level for numerical stability. Hence, the increasingly stringent CFL condition on the time step on coarser levels significantly reduces the advantages of the multilevel approach. To overcome that bottleneck we propose to combine the multilevel approach of MLMC with local time-stepping. By adapting the time step to the locally refined elements on each level, the efficiency of MLMC methods is restored even in the presence of complex geometry without sacrificing the explicitness and inherent parallelism. In a careful cost comparison, we quantify the reduction in computational cost for local refinement either inside a small fixed region or towards a reentrant corner.
机译：因为他们的健壮性、效率、和非侵入性,可能是蒙特卡罗方法最受欢迎的方法的不确定性量化计算的预期值大量的兴趣。(MLMC)方法显著减少通过分布抽样计算成本在离散的层次结构分配大多数样品粗网格。与时间有关的问题,空间粗化通常需要增加时间步。然而,几何约束可能阻碍均匀粗化从而迫使一些元素保持小的在所有的水平。使用时域,将时间的一步由最小的元素在每个级别的数值稳定性。严格的CFL条件在时间步粗糙的水平显著降低多级方法的优势。克服这一瓶颈我们建议结合MLMC与当地的多层次的方法利用。本地提炼元素在每个层面上,MLMC方法即使在恢复的效率复杂几何的存在牺牲的明确性和固有的并行性。量化的减少计算成本局部细化内部固定地区或向一个可重入的角落。

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