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

Neil Kumar Chada, H. Hoel, Ajay Jasra, G. E. Zouraris

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.
Original languageEnglish (US)
JournalJournal of Scientific Computing
Volume93
Issue number3
DOIs
StatePublished - Oct 20 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-10-31
Acknowledgements: Open access funding provided by University of Oslo (incl Oslo University Hospital) Research reported in this publication received support from the Alexander von Humboldt Foundation. NKC and AJ are sponsored by KAUST baseline funding and HH acknowledges support by University of Oslo and RWTH Aachen University.

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Theoretical Computer Science
  • Software
  • General Engineering

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