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arXiv · 2510.26427

On a semi-discrete model of Maxwell's equations in three and two dimensions

Volodymyr Sushch
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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. 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.

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Volodymyr Sushch. 2025-10-30. On a semi-discrete model of Maxwell's equations in three and two dimensions. https://doi.org/10.3390/sym17122123

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