<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

Publicado en línea: 31 dic 2020

Páginas: 116 - 125

Recibido: 25 sept 2020

Aceptado: 04 nov 2020

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

Palabras clave
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

Publicado en línea: 31 dic 2020

Páginas: 116 - 125

Recibido: 25 sept 2020

Aceptado: 04 nov 2020

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

Palabras claveSPDE, 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.

Palabras clave
SPDE, MLMC, UQ, Parallelization, Flow in random porous media