2025/01/31 by Ignace Bossuyt, Bossuyt, Ignace, Giovanni Samaey +3
Engineering · #34E13 #60H35 #65C30 #65L11 #68Q10 #FOS: Mathematics #Heat Transfer and Optimization #Heat and Mass Transfer in Porous Media #Nanofluid Flow and Heat Transfer #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2501.19210
openalex publication_date 2025/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. This is an extended and corrected version of [Domain Decomposition Methods in Science and Engineering XXVII. DD 2022, vol 149 (2024), pp. 69-76, Bossuyt, I., Vandewalle, S., Samaey, G.].