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Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions
(2011)SAM Research ReportWe 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 ...Report -
Multi-level Monte Carlo finite volume methods for shallow water equations with uncertain topography in multi-dimensions
(2011)SAM Research ReportThe initial data and bottom topography, used as inputs in shallow water models, are prone to uncertainty due to measurement errors. We model this uncertainty statistically in terms of random shallow water equations. We extend the Multi-Level Monte Carlo (MLMC) algorithm to numerically approximate the random shallow water equations efficiently. The MLMC algorithm is suitably modified to deal with uncertain (and possibly uncorrelated) data ...Report -
Static load balancing for multi-level Monte Carlo finite volume solvers
(2011)SAM Research ReportThe Multi-Level Monte Carlo finite volumes (MLMC-FVM) 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 load balancing procedure is used to ensure scalability of the MLMC algorithm on massively parallel hardware. We describe this procedure together with other arising challenges in great detail. Finally, numerical experiments ...Report