On a semi-discrete model of Maxwell's equations in three and two dimensions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918316759580672 |
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| author | Sushch, Volodymyr |
| author_facet | Sushch, Volodymyr |
| contents | In this paper, we develop a geometric, structure-preserving semi-discrete formulation of Maxwell's equations in both three- and two-dimensional settings within the framework of discrete exterior calculus. This approach preserves the intrinsic geometric and topological structures of the continuous theory while providing a consistent spatial discretization. We analyze the essential properties of the proposed semi-discrete model and compare them with those of the classical Maxwell's equations. As a special case, the model is illustrated on a combinatorial two-dimensional torus, where the semi-discrete Maxwell's equations take the form of a system of first-order linear ordinary differential equations. An explicit expression for the general solution of this system is also derived. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26427 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a semi-discrete model of Maxwell's equations in three and two dimensions Sushch, Volodymyr Mathematical Physics Numerical Analysis Analysis of PDEs 39A12, 39A70, 35Q61 In this paper, we develop a geometric, structure-preserving semi-discrete formulation of Maxwell's equations in both three- and two-dimensional settings within the framework of discrete exterior calculus. This approach preserves the intrinsic geometric and topological structures of the continuous theory while providing a consistent spatial discretization. We analyze the essential properties of the proposed semi-discrete model and compare them with those of the classical Maxwell's equations. As a special case, the model is illustrated on a combinatorial two-dimensional torus, where the semi-discrete Maxwell's equations take the form of a system of first-order linear ordinary differential equations. An explicit expression for the general solution of this system is also derived. |
| title | On a semi-discrete model of Maxwell's equations in three and two dimensions |
| topic | Mathematical Physics Numerical Analysis Analysis of PDEs 39A12, 39A70, 35Q61 |
| url | https://arxiv.org/abs/2510.26427 |