Micro-macro Parareal, from ODEs to SDEs and back again
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| Format: | Preprint |
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2024
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| _version_ | 1866917046388785152 |
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| author | Bossuyt, Ignace Vandewalle, Stefan Samaey, Giovanni |
| author_facet | Bossuyt, Ignace Vandewalle, Stefan Samaey, Giovanni |
| contents | In this paper, we are concerned with the micro-macro Parareal algorithm for the simulation of initial-value problems. In this algorithm, a coarse (fast) solver is applied sequentially over the time domain, and a fine (time-consuming) solver is applied as a corrector in parallel over smaller chunks of the time interval. Moreover, the coarse solver acts on a reduced state variable, which is coupled to the fine state variable through appropriate coupling operators. We first provide a contribution to the convergence analysis of the micro-macro Parareal method for multiscale linear ordinary differential equations (ODEs). Then, we extend a variant of the micro-macro Parareal algorithm for scalar stochastic differential equations (SDEs) to higher-dimensional SDEs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_01798 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Micro-macro Parareal, from ODEs to SDEs and back again Bossuyt, Ignace Vandewalle, Stefan Samaey, Giovanni Numerical Analysis Computation 65L11, 34E13, 65C30, 68Q10, 65C35, 60H35, In this paper, we are concerned with the micro-macro Parareal algorithm for the simulation of initial-value problems. In this algorithm, a coarse (fast) solver is applied sequentially over the time domain, and a fine (time-consuming) solver is applied as a corrector in parallel over smaller chunks of the time interval. Moreover, the coarse solver acts on a reduced state variable, which is coupled to the fine state variable through appropriate coupling operators. We first provide a contribution to the convergence analysis of the micro-macro Parareal method for multiscale linear ordinary differential equations (ODEs). Then, we extend a variant of the micro-macro Parareal algorithm for scalar stochastic differential equations (SDEs) to higher-dimensional SDEs. |
| title | Micro-macro Parareal, from ODEs to SDEs and back again |
| topic | Numerical Analysis Computation 65L11, 34E13, 65C30, 68Q10, 65C35, 60H35, |
| url | https://arxiv.org/abs/2401.01798 |