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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.27654 |
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| _version_ | 1866915897464061952 |
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| author | Li, Lei Liu, Yunxiao Wan, Chenchen |
| author_facet | Li, Lei Liu, Yunxiao Wan, Chenchen |
| contents | We propose a quasi-random operator splitting method for evolution equations driven by multiple mechanisms. The method uses a low-discrepancy sequence to generate the ordering of the subflows, while requiring only one application of each subflow per time step. In particular, for a decomposition into \(p\) operators, the classical multi-operator Strang splitting requires essentially \(2p-2\) subflow evaluations per step, whereas the present method uses only \(p\). In contrast to randomized splitting, the quasi-random scheme is deterministic once the underlying sequence is fixed, so its improved accuracy is achieved in a single run rather than through averaging over many independent realizations. To analyze this method, we develop a convergence framework that exploits the discrepancy structure of the induced ordering sequence and translates it into cancellation in the accumulated local errors. For two operators, this yields an essentially second-order global error bound of order \(O(τ^{2}|\log τ|)\) for bounded linear problems. We further extend the analysis to the Allen--Cahn equation and present numerical experiments, including bounded linear systems and the Allen--Cahn equation, which confirm the predicted convergence behavior and demonstrate that the proposed method achieves near-Strang accuracy at a substantially lower computational cost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27654 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi-random splitting method for accurate and efficient multiphysics simulation Li, Lei Liu, Yunxiao Wan, Chenchen Numerical Analysis We propose a quasi-random operator splitting method for evolution equations driven by multiple mechanisms. The method uses a low-discrepancy sequence to generate the ordering of the subflows, while requiring only one application of each subflow per time step. In particular, for a decomposition into \(p\) operators, the classical multi-operator Strang splitting requires essentially \(2p-2\) subflow evaluations per step, whereas the present method uses only \(p\). In contrast to randomized splitting, the quasi-random scheme is deterministic once the underlying sequence is fixed, so its improved accuracy is achieved in a single run rather than through averaging over many independent realizations. To analyze this method, we develop a convergence framework that exploits the discrepancy structure of the induced ordering sequence and translates it into cancellation in the accumulated local errors. For two operators, this yields an essentially second-order global error bound of order \(O(τ^{2}|\log τ|)\) for bounded linear problems. We further extend the analysis to the Allen--Cahn equation and present numerical experiments, including bounded linear systems and the Allen--Cahn equation, which confirm the predicted convergence behavior and demonstrate that the proposed method achieves near-Strang accuracy at a substantially lower computational cost. |
| title | Quasi-random splitting method for accurate and efficient multiphysics simulation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.27654 |