A domain decomposition method for stochastic evolution equations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910298096533504 |
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| author | Buckwar, Evelyn Djurdjevac, Ana Eisenmann, Monika |
| author_facet | Buckwar, Evelyn Djurdjevac, Ana Eisenmann, Monika |
| contents | In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of efficient and practical time-stepping methods for SPDEs.
Operator splitting schemes are a powerful tool for deterministic and stochastic differential equations. An example is given by domain decomposition schemes, where we split the domain into sub-domains. Instead of solving one expensive problem on the entire domain, we deal with cheaper problems on the sub-domains. This is particularly useful in modern computer architectures, as the sub-problems may often be solved in parallel. While splitting methods have already been used to study domain decomposition methods for deterministic PDEs, this is a new approach for SPDEs.
We provide an abstract convergence analysis of a splitting scheme for stochastic evolution equations and state a domain decomposition scheme as an application of the setting. The theoretical results are verified through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07291 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A domain decomposition method for stochastic evolution equations Buckwar, Evelyn Djurdjevac, Ana Eisenmann, Monika Numerical Analysis Probability 65C30, 90C15, 65M55 In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of efficient and practical time-stepping methods for SPDEs. Operator splitting schemes are a powerful tool for deterministic and stochastic differential equations. An example is given by domain decomposition schemes, where we split the domain into sub-domains. Instead of solving one expensive problem on the entire domain, we deal with cheaper problems on the sub-domains. This is particularly useful in modern computer architectures, as the sub-problems may often be solved in parallel. While splitting methods have already been used to study domain decomposition methods for deterministic PDEs, this is a new approach for SPDEs. We provide an abstract convergence analysis of a splitting scheme for stochastic evolution equations and state a domain decomposition scheme as an application of the setting. The theoretical results are verified through numerical experiments. |
| title | A domain decomposition method for stochastic evolution equations |
| topic | Numerical Analysis Probability 65C30, 90C15, 65M55 |
| url | https://arxiv.org/abs/2401.07291 |