Higher-order multiscale method and its convergence analysis for nonlinear thermo-electric coupling problems of composite structures
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| Format: | Preprint |
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2025
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| _version_ | 1866929684750532608 |
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| author | Dong, Hao Yang, Zongze Nie, Yufeng |
| author_facet | Dong, Hao Yang, Zongze Nie, Yufeng |
| contents | This paper proposes a higher-order multiscale computational method for nonlinear thermo-electric coupling problems of composite structures, which possess temperature-dependent material properties and nonlinear Joule heating. The innovative contributions of this work are the novel multiscale formulation with the higher-order correction terms for periodic composite structures and the global error estimation with an explicit rate for higher-order multiscale solutions. By employing the multiscale asymptotic approach and the Taylor series technique, the higher-order multiscale method is established for time-dependent nonlinear thermo-electric coupling problems, which can keep the local balance of heat flux and electric charge for high-accuracy multiscale simulation. Furthermore, an efficient numerical algorithm with off-line and on-line stages is presented in detail, and corresponding convergent analysis is also obtained. Two- and three-dimensional numerical experiments are conducted to showcase the competitive advantages of the proposed method for simulating the time-dependent nonlinear thermo-electric coupling problems in composite structures, not only exceptional numerical accuracy, but also less computational cost. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_13425 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-order multiscale method and its convergence analysis for nonlinear thermo-electric coupling problems of composite structures Dong, Hao Yang, Zongze Nie, Yufeng Numerical Analysis 35B27, 80M40, 65M60, 65M15 This paper proposes a higher-order multiscale computational method for nonlinear thermo-electric coupling problems of composite structures, which possess temperature-dependent material properties and nonlinear Joule heating. The innovative contributions of this work are the novel multiscale formulation with the higher-order correction terms for periodic composite structures and the global error estimation with an explicit rate for higher-order multiscale solutions. By employing the multiscale asymptotic approach and the Taylor series technique, the higher-order multiscale method is established for time-dependent nonlinear thermo-electric coupling problems, which can keep the local balance of heat flux and electric charge for high-accuracy multiscale simulation. Furthermore, an efficient numerical algorithm with off-line and on-line stages is presented in detail, and corresponding convergent analysis is also obtained. Two- and three-dimensional numerical experiments are conducted to showcase the competitive advantages of the proposed method for simulating the time-dependent nonlinear thermo-electric coupling problems in composite structures, not only exceptional numerical accuracy, but also less computational cost. |
| title | Higher-order multiscale method and its convergence analysis for nonlinear thermo-electric coupling problems of composite structures |
| topic | Numerical Analysis 35B27, 80M40, 65M60, 65M15 |
| url | https://arxiv.org/abs/2501.13425 |