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Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions. (English) Zbl 1402.76083

Summary: We extend the multi-level Monte Carlo (MLMC) 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 is described and applied to simulate uncertain solutions of the Euler equations and ideal magnetohydrodynamics (MHD) equations. Numerical experiments showing the robustness, efficiency and scalability of the proposed algorithm are presented.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65C05 Monte Carlo methods
65Y05 Parallel numerical computation
76W05 Magnetohydrodynamics and electrohydrodynamics

Software:

ALSVID-UQ
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Full Text: DOI Link

References:

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