<abstract xmlns="http://www.w3.org/1999/xhtml"><p>MultiLevel Monte Carlo (MLMC) attracts great interest for numerical simulations of Stochastic Partial Differential Equations (SPDEs), due to its superiority over the standard Monte Carlo (MC) approach. MLMC combines in a proper manner many cheap fast simulations with few slow and expensive ones, the variance is reduced, and a significant speed up is achieved. Simulations with MC/MLMC consist of three main components: generating random fields, solving deterministic problem and reduction of the variance. Each part is subject to a different degree of parallelism. Compared to the classical MC, MLMC introduces “levels” on which the sampling is done. These levels have different computational cost, thus, efficiently utilizing the parallel resources becomes a non-trivial problem. The main focus of this paper is the parallelization of the MLMC Algorithm.</p></abstract>

MultiLevel Monte Carlo (MLMC) attracts great interest for numerical simulations of Stochastic Partial Differential Equations (SPDEs), due to its superiority over the standard Monte Carlo (MC) approach. MLMC combines in a proper manner many cheap fast simulations with few slow and expensive ones, the variance is reduced, and a significant speed up is achieved. Simulations with MC/MLMC consist of three main components: generating random fields, solving deterministic problem and reduction of the variance. Each part is subject to a different degree of parallelism. Compared to the classical MC, MLMC introduces “levels” on which the sampling is done. These levels have different computational cost, thus, efficiently utilizing the parallel resources becomes a non-trivial problem. The main focus of this paper is the parallelization of the MLMC Algorithm.

On Dynamic Parallelization of Multilevel Monte Carlo Algorithm

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On Dynamic Parallelization of Multilevel Monte Carlo Algorithm"}

MultiLevel Monte Carlo (MLMC) attracts great interest for numerical simulations of Stochastic Partial Differential Equations (SPDEs), due to its superiority...

On Dynamic Parallelization of Multilevel Monte Carlo Algorithm

Published Online: Dec 31, 2020

Page range: 116 - 125

Received: Sep 25, 2020

Accepted: Nov 04, 2020

DOI: https://doi.org/10.2478/cait-2020-0066

Keywords
SPDE, MLMC, UQ, Parallelization, Flow in random porous media

© 2020 Nikolay Shegunov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On Dynamic Parallelization of Multilevel Monte Carlo Algorithm

Published Online: Dec 31, 2020

Page range: 116 - 125

Received: Sep 25, 2020

Accepted: Nov 04, 2020

DOI: https://doi.org/10.2478/cait-2020-0066

KeywordsSPDE, MLMC, UQ, Parallelization, Flow in random porous media

© 2020 Nikolay Shegunov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
SPDE, MLMC, UQ, Parallelization, Flow in random porous media