Some realizations of a discrete Hodge operator: a reinterpretation of finite element techniques [for EM field analysis]

Tarhasaari T.; Kettunen L.

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Some realizations of a discrete Hodge operator: a reinterpretation of finite element techniques [for EM field analysis]

机译：离散Hodge算子的一些实现：有限元技术的重新解释[用于EM场分析]

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In this paper, some structures which underlie the numerical treatment of second-order boundary value problems are studied using magnetostatics as an example. The authors show that the construction of a discrete Hodge is a central problem. In this light, they interpret finite element techniques as a realization of the discrete Hodge operator in the Whitney complex. This enables one to view the Galerkin method as a way to set up circuit equations, the metric of space being encoded in the values of branch impedances.

机译：本文以静磁学为例，研究了构成二阶边值问题数值处理基础的一些结构。作者表明，离散式Hodge的构造是一个中心问题。有鉴于此，他们将有限元技术解释为惠特尼复杂系统中离散Hodge算子的实现。这样一来，人们就可以将Galerkin方法视为一种建立电路方程式的方法，其中空间度量被编码为分支阻抗的值。

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《IEEE Transactions on Magnetics》 |1999年第3期|P.1494-1497|共4页
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Tarhasaari T.; Kettunen L.;
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Some realizations of a discrete Hodge operator: a reinterpretation of finite element techniques [for EM field analysis]

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