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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)
Two layer Savage-Hutter type shallow water PDEs model flows such as tsunamis generated by rockslides. On account of heterogeneities in the composition of the granular matter, these models contain uncertain parameters like the ratio of densities of layers, Coulomb and interlayer friction. These parameters are modeled statistically and quantifying the(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)
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)