Multilevel Monte-Carlo for measure valued solutions
For researchers in computational fluid dynamics and hyperbolic PDEs, this provides a more efficient numerical method for measure-valued solutions, though the efficiency is case-dependent.
The paper proposes a Multilevel Monte-Carlo method for computing entropy measure valued solutions of hyperbolic conservation laws, deriving optimal work-vs-error bounds and demonstrating efficiency gains over standard Monte-Carlo in numerical experiments.
We propose a Multilevel Monte-Carlo (MLMC) method for computing entropy measure valued solutions of hyperbolic conservation laws. Sharp bounds for the narrow convergence of MLMC for the entropy measure valued solutions are proposed. An optimal work-vs-error bound for the MLMC method is derived assuming only an abstract decay criterion on the variance. Finally, we display numerical experiments of cases where MLMC is, and is not, efficient when compared to Monte-Carlo.