Parareal computation of stochastic differential equations with time-scale separation: a numerical convergence study

摘要: The parareal algorithm is known to allow for a significant reduction in wall clock time accurate numerical solutions by parallelising across the dimension. We present and test micro-macro version of parareal, which fine propagator based on (high-dimensional, slow-fast) stochastic microscopic model, coarse low-dimensional approximate effective dynamics at slow scales. At level, we use an ensemble Monte Carlo particles, whereas uses (deterministic) Fokker-Planck equation degrees freedom. required coupling between macroscopic representations system introduces several design options, specifically how generate probability distribution consistent with perform coarse-level updating meaningful manner. numerically study these options affect efficiency number situations. choice operator strongly impacts result, superior performance if addition subtraction quantile function (inverse cumulative distribution) used. How states are generated has less pronounced impact, provided suitable prior state