Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism
Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism
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DOI：
10.1049/ip-a-1:19880077
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发表时间：
1988-11
期刊：
影响因子：
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通讯作者：
A. Bossavit
中科院分区：
文献类型：
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作者：
A. Bossavit
已经认识到，通过有限元方法对磁场进行数值计算可能需要新类型的单元，其自由度不是网格节点处的场值，而是其他与场相关的量，例如沿网格边缘的循环。如果用微分形式而不是矢量场来表示基本方程，就可以得到使用这些特殊的“混合”元素的基本原理。本文对这一观点作了初步的介绍，提出了Whitney格式(所指的混合有限元)，并在此基础上提出了两种涡流数值计算方法(DUAL，某种意义上的)。
It has been recognised that numerical computations of magnetic fields by the finite-element method may require new types of elements, whose degrees of freedom are not field values at mesh nodes, but other field-related quantities like e.g. circulations along edges of the mesh. A rationale for the use of these special ‘mixed’ elements can be obtained if one cxpresses basic equations in terms of differential forms, instead of vector fields. The paper gives an elementary introduction to this point of view, presents Whitney forms (the mixed finite elements alluded to), and sketches two numerical methods (dual, in some sense), for eddy-current studies, based on these elements.