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arXiv · 2604.13921

A higher-order dual cell method for time-domain Maxwell equations

Lorenzo Codecasa·Bernard Kapidani·Joachim Schöberl·Markus Wess
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Abstract

We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and generalises a previously developed two-dimensional high-order formulation. The electric and magnetic fields are discretised on mutually dual barycentric grids using curl-conforming polynomial spaces constructed via tensor-product Gauss--Radau interpolation. The resulting semi-discrete formulation yields block-diagonal mass matrices and sparse discrete curl operators, enabling explicit time integration while preserving a discrete energy identity. Special attention is devoted to the construction of compatible approximation spaces on the three-dimensional primal and dual meshes, the reference-to-physical element mappings, and the preservation of tangential continuity. We show that the method achieves arbitrary-order convergence, avoids spurious modes, and maintains optimal sparsity properties. Numerical experiments confirm spectral correctness, high-order accuracy, and computational efficiency on unstructured tetrahedral meshes.

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Lorenzo Codecasa, Bernard Kapidani, Joachim Schöberl, Markus Wess. 2026-04-15. A higher-order dual cell method for time-domain Maxwell equations. https://arxiv.org/abs/2604.13921

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