Abstract
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. The proposed 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 representative example, the framework is applied to a combinatorial two-dimensional torus, where the semi-discrete Maxwell system reduces to a set of first-order linear ordinary differential equations. An explicit expression for the general solution of this system is also derived.
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Publication Info
- Year
- 2025
- Type
- article
- Volume
- 17
- Issue
- 12
- Pages
- 2123-2123
- Citations
- 0
- Access
- Closed
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Cite This
Volodymyr Sushch
(2025).
On a Semi-Discrete Model of Maxwell’s Equations in Three and Two Dimensions.
Symmetry
, 17
(12)
, 2123-2123.
https://doi.org/10.3390/sym17122123
Identifiers
- DOI
- 10.3390/sym17122123