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Adaptive load balancing for massively parallel multi-level Monte Carlo solvers

by J. Sukys

(Report number 2013-21)

Abstract
The Multi-Level Monte Carlo (MLMC) algorithm was shown to be a robust and fast solver for uncertainty quantification in the solutions of multi-dimensional systems of stochastic conservation laws. A novel static load balancing procedure is already developed to ensure scalability of the MLMC algorithm on massively parallel hardware up to 40 000 cores. However, for random fluxes or random initial data with large variances, the time step of the explicit time stepping scheme becomes also random due to the random CFL stability restriction. Such sample path dependent complexity of the underlying deterministic solver renders the aforementioned static load balancing very inefficient. We introduce an improved, adaptive load balancing procedure which is based on two key ingredients: 1) pre-computation of the time step size for each realization, 2) distribution of the obtained loads using the greedy algorithm to workers (core groups) with non-identical speed of execution. Numerical experiments in multi-dimensions showing strong scaling of our implementation are presented.

Keywords: Uncertainty quantification, conservation laws, multi-level Monte Carlo, FVM, load balancing, greedy algorithms, linear scaling.

@Techreport{S13_518,
  author = {J. Sukys},
  title = {Adaptive load balancing for massively parallel multi-level Monte Carlo solvers},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2013-21},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2013/2013-21.pdf },
  year = {2013}
}

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