This contribution addresses the solution of eddy-current problems by means of a volume integral formulation based on the electric vector potential on a computational domain that exhibits a cyclic symmetry. Even if grids discretizing the domain are typically composed of tetrahedral or hexahedral elements, the proposed approach also works for general polyhedral meshes, such as those ones obtained by subgridding. In this article, an algorithm to compute a set of suitable cohomology generators needed when the conductors are not simply connected is introduced first. Besides being purely combinatorial, with linear-time worst case complexity and suitable with polyhedral meshes, it reuses a code that computes generators for triangular surface meshes, with obvious advantages concerning the implementation effort. Second, the formulation and the algorithm for cohomology computation are tweaked to be able to solve eddy-current problems with cyclic symmetry reserving specific attention to the construction of suitable tree–cotree decomposition for the problem gauging.

中文翻译：

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涡流体积积分公式中的循环对称性：上同调计算和测量


这一贡献通过基于表现出循环对称性的计算域上的电矢量势的体积积分公式来解决涡流问题。即使离散化域的网格通常由四面体或六面体元素组成，所提出的方法也适用于一般的多面体网格，例如通过子网格获得的网格。在本文中，首先介绍了一种计算导体非简单连接时所需的一组合适的上同调生成器的算法。除了纯粹的组合性、线性时间最坏情况复杂性以及适用于多面体网格之外，它还重用了计算三角形表面网格生成器的代码，在实现工作方面具有明显的优势。其次，对上同调计算的公式和算法进行了调整，以便能够解决具有循环对称性的涡流问题，同时特别注意为问题测量构建合适的树-共树分解。