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Convergence of the Micro-Macro Parareal Method for a Linear Scale-Separated Ornstein-Uhlenbeck SDE

Boekbijdrage - Boekhoofdstuk Conferentiebijdrage

Time-parallel methods can reduce the wall clock time required for the accurate numerical solution of differential equations by parallelizing across the time-dimension. In this paper, we present and test the convergence behavior of a multiscale, micro-macro version of a Parareal method for stochastic differential equations (SDEs). In our method, the fine propagator of the SDE is based on a high-dimensional slow-fast microscopic model; the coarse propagator is based on a model-reduced version of the latter, that captures the low-dimensional, effective dynamics at the slow time scales. We investigate how the model error of the approximate model influences the convergence of the micro-macro Parareal algorithm and we support our analysis with numerical experiments.
Boek: Domain Decomposition Methods in Science and Engineering XXVII
Pagina's: 69 - 76
Jaar van publicatie:2023