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Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions

by S. Mishra and Ch. Schwab and J. Sukys

(Report number 2011-02)

Abstract
We extend the Multi-Level Monte Carlo (MLMC) algorithm of [19] in order to quantify uncertainty in the solutions of multi-dimensional hyperbolic systems of conservation laws with uncertain initial data. The algorithm is presented and several issues arising in the massively parallel numerical implementation are addressed. In particular, we present a novel load balancing procedure that ensures scalability of the MLMC algorithm on massively parallel hardware. A new code ALSVID-UQ is described and applied to simulate uncertain solutions of the Euler equations and ideal MHD equations. Numerical experiments showing the robustness, effciency and scalability of the proposed algorithm are presented.

Keywords:

@Techreport{MSS11_104,
  author = {S. Mishra and Ch. Schwab and J. Sukys},
  title = {Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-02.pdf },
  year = {2011}
}

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