Efficient Long-Time Simulations of Multiscale Systems via High-Order Numerical Homogenization
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911173644910592 |
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| author | Chen, Bojin Jin, Zeyu Li, Ruo |
| author_facet | Chen, Bojin Jin, Zeyu Li, Ruo |
| contents | By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose an efficient algorithm able to carry out simulations up to a long time which was prohibitive before. The new algorithm is a multigrid-in-time method which combines coarse-grid high-order approximations with fine-grid low-order evaluations. The high efficiency is attained by minimizing the computational cost while the approximation accuracy is guaranteed. A priori error estimates are rigorously established and validated by numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient Long-Time Simulations of Multiscale Systems via High-Order Numerical Homogenization Chen, Bojin Jin, Zeyu Li, Ruo Numerical Analysis 65L11, 65L04, 34E13 By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose an efficient algorithm able to carry out simulations up to a long time which was prohibitive before. The new algorithm is a multigrid-in-time method which combines coarse-grid high-order approximations with fine-grid low-order evaluations. The high efficiency is attained by minimizing the computational cost while the approximation accuracy is guaranteed. A priori error estimates are rigorously established and validated by numerical examples. |
| title | Efficient Long-Time Simulations of Multiscale Systems via High-Order Numerical Homogenization |
| topic | Numerical Analysis 65L11, 65L04, 34E13 |
| url | https://arxiv.org/abs/2509.20108 |