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The Multi-Level Monte Carlo finite volumes (MLMC-FVM) algorithm was shown to be a robust and fast solver for uncertainty quan-tification in the solutions of multi-dimensional systems of stochastic conservation laws. A novel load balancing procedure is used to ensure scal-ability of the MLMC algorithm on massively parallel hardware. We describe this(More)
We extend the Multi-Level Monte Carlo (MLMC) algorithm of [19] in order to quantify uncertainty in the solutions of multi-dimensional hyper-bolic 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(More)
A mathematical formulation of conservation and of balance laws with random input data, specifically with random initial conditions, random source terms and random flux functions, is reviewed. The concept of random entropy solution is specified. For scalar conservation laws in multi-dimensions, recent results on the existence and on the uniqueness of random(More)
2014 Acknowledgments During my work as a PhD student and in preparation of this thesis, I was supported by numerous persons. In particular, I am thankful to Patrick Jenny and Daniel Meyer for their supervision, to Hamdi Tchelepi for being my co-examiner, to Tokareva for helpful discussions and to Jennifer Bartmess for proofreading. Abstract We consider(More)
We quantify uncertainties in the location and magnitude of extreme pressure spots revealed from large scale multi-phase flow simulations of cloud cavitation collapse. We examine clouds containing 500 cavities and quantify uncertainties related to their initial spatial arrangement. The resulting 2000-dimensional space is sampled using a non-intrusive and(More)
We consider stochastic multi-dimensional linear hyperbolic systems of conservation laws. We prove existence and uniqueness of a random weak solution, provide estimates for the regularity of the solution in terms of regularities of input data, and show existence of statistical moments. Bounds for mean square error vs. expected work are proved for the(More)
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