On Dynamic Parallelization of Multilevel Monte Carlo Algorithm

摘要

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