A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Multilevel Monte Carlo Methods
LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers
Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
Updating formulae and a pairwise algorithm for computing sample variances
Updating formulae and a pairwise algorithm for computing sample variances
Uncertainty analysis for the steady-state flows in a dual throat nozzle
Journal of Computational Physics
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Improved long-period generators based on linear recurrences modulo 2
ACM Transactions on Mathematical Software (TOMS)
Fast random number generators based on linear recurrences modulo 2: overview and comparison
WSC '05 Proceedings of the 37th conference on Winter simulation
Uncertainty quantification for systems of conservation laws
Journal of Computational Physics
Journal of Computational Physics
Multilevel Monte Carlo Path Simulation
Operations Research
Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
Computing and Visualization in Science
SIAM Journal on Numerical Analysis
Static load balancing for multi-level monte carlo finite volume solvers
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
Journal of Computational Physics
Hi-index | 31.45 |
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.