Paper Info
Title
Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data.
Abstract
We consider scalar hyperbolic conservation laws in spatial dimension d >= 1 with stochastic initial data. We prove existence and uniqueness of a random-entropy solution and give sufficient conditions on the initial data that ensure the existence of statistical moments of any order k of this random entropy solution. We present a class of numerical schemes of multi-level Monte Carlo Finite Volume (MLMC-FVM) type for the approximation of the ensemble average of the random entropy solutions as well as of their k-point space-time correlation functions. These schemes are shown to obey the same accuracy vs. work estimate as a single application of the finite volume solver for the corresponding deterministic problem. Numerical experiments demonstrating the efficiency of these schemes are presented. In certain cases, statistical moments of discontinuous solutions are found to be more regular than pathwise solutions.
Year
DOI
Venue
2012
10.1090/S0025-5718-2012-02574-9
MATHEMATICS OF COMPUTATION
Field
DocType
Volume
Monte Carlo method,Mathematical optimization,Tensor,Hybrid Monte Carlo,Monte Carlo integration,Finite volume method,Monte Carlo molecular modeling,Mathematics,Conservation law
Journal
81
Issue
ISSN
Citations 
280
0025-5718
24
PageRank 
References 
Authors
1.73
4
2
Name
Order
Citations
PageRank
Siddhartha Mishra117021.36
Christoph Schwab259558.38