FieldTNN-based machine learning method for Maxwell eigenvalue problems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929603698753536 |
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| author | Jiang, Jiantao Wang, Yanli Wang, Yifan Xie, Hehu |
| author_facet | Jiang, Jiantao Wang, Yanli Wang, Yifan Xie, Hehu |
| contents | The aim of this paper is to introduce a FieldTNN-based machine learning method for solving the Maxwell eigenvalue problem in both 2D and 3D domains, including both tensor and non-tensor computational regions. First, we extend the existing TNN-based approach to address the Maxwell eigenvalue problem, a fundamental challenge in electromagnetic field theory. Second, we tackle non-tensor computational domains, which represents a novel and significant contribution of this work. Third, we incorporate the divergence-free condition into the optimization process, allowing for the automatic filtering of spurious eigenpairs. Numerical examples are presented to demonstrate the efficiency and accuracy of our algorithm, underscoring its potential for broader applications in computational electromagnetics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15828 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | FieldTNN-based machine learning method for Maxwell eigenvalue problems Jiang, Jiantao Wang, Yanli Wang, Yifan Xie, Hehu Numerical Analysis 35A15, 35Q60, 65N25, 68T07 The aim of this paper is to introduce a FieldTNN-based machine learning method for solving the Maxwell eigenvalue problem in both 2D and 3D domains, including both tensor and non-tensor computational regions. First, we extend the existing TNN-based approach to address the Maxwell eigenvalue problem, a fundamental challenge in electromagnetic field theory. Second, we tackle non-tensor computational domains, which represents a novel and significant contribution of this work. Third, we incorporate the divergence-free condition into the optimization process, allowing for the automatic filtering of spurious eigenpairs. Numerical examples are presented to demonstrate the efficiency and accuracy of our algorithm, underscoring its potential for broader applications in computational electromagnetics. |
| title | FieldTNN-based machine learning method for Maxwell eigenvalue problems |
| topic | Numerical Analysis 35A15, 35Q60, 65N25, 68T07 |
| url | https://arxiv.org/abs/2411.15828 |