Improved Efficiency of Multilevel Monte Carlo for Stochastic PDE through Strong Pairwise Coupling

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Detail(s)

Original languageEnglish
Article number62
Journal / PublicationJournal of Scientific Computing
Volume93
Issue number3
Online published20 Oct 2022
Publication statusPublished - 1 Dec 2022
Externally publishedYes

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Abstract

Multilevel Monte Carlo (MLMC) has become an important methodology in applied mathematics for reducing the computational cost of weak approximations. For many problems, it is well-known that strong pairwise coupling of numerical solutions in the multilevel hierarchy is needed to obtain efficiency gains. In this work, we show that strong pairwise coupling indeed is also important when MLMC is applied to stochastic partial differential equations (SPDE) of reaction-diffusion type, as it can improve the rate of convergence and thus improve tractability. For the MLMC method with strong pairwise coupling that was developed and studied numerically on filtering problems in (Chernov in Num Math 147:71-125, 2021), we prove that the rate of computational efficiency is higher than for existing methods. We also provide numerical comparisons with alternative coupling ideas on linear and nonlinear SPDE to illustrate the importance of this feature. © 2022, The Author(s).

Research Area(s)

  • Exponential Euler method, Multilevel Monte Carlo method, Stochastic partial differential equations, Weak approximations

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