Research reports

Years: 2025 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

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}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).