Stochastic Parareal: An Application of Probabilistic Methods to Time-Parallelization
نویسندگان
چکیده
Parareal is a well-studied algorithm for numerically integrating systems of time-dependent differential equations by parallelising the temporal domain. Given approximate initial values at each sub-interval, locates solution in fixed number iterations using predictor-corrector, stopping once tolerance met. This iterative process combines solutions located inexpensive (coarse resolution) and expensive (fine numerical integrators. In this paper, we introduce stochastic parareal aimed accelerating convergence deterministic algorithm. Instead providing predictor-corrector with deterministically set values, samples from dynamically varying probability distributions sub-interval. All are then propagated parallel integrator. The sampled yielding most continuous (smoothest) trajectory across consecutive sub-intervals fed into converging fewer than given probability. performance algorithm, implemented various distributions, illustrated on low-dimensional ordinary (ODEs). We provide evidence that when large enough, converges almost certainly maintaining accuracy. its nature, also highlight multiple simulations return distribution can represent measure uncertainty over ODE solution.
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2022
ISSN: ['1095-7197', '1064-8275']
DOI: https://doi.org/10.1137/21m1414231