Numerical solution of eddy current problems in bounded domains using realistic boundary conditions
Numerical solution of eddy current problems in bounded domains using realistic boundary conditions
复制标题
使用实际边界条件对有界域中的涡流问题进行数值求解
DOI：
10.1016/j.cma.2004.05.016
复制
发表时间：
2005
影响因子：
7.2
通讯作者：
P. Salgado
中科院分区：
文献类型：
--
作者：
A. Bermúdez;R. Rodríguez;P. Salgado
本文的目的是分析在包含导体和介电体的有界域中求解低频谐波麦克斯韦方程组的有限元方法，并利用易于测量的实际边界条件。这些方程式为所谓的涡流提供了一个模型。这个问题是用磁场来表示的。该公式在四面体网格上采用nsamdastlec边缘有限元进行离散化。当在介质域中显式地对元件施加无旋度条件时，容易得到误差估计。然后引入多值磁标量势来施加此无旋度条件。这个公式的离散对应物可以大大节省计算工作量。还考虑了与拓扑有关的问题，更准确地说，考虑了具有非单连通介电域的可能性。最后，将该方法应用于两个三维模型问题的求解：已知解析解的试验和冶金电弧炉电磁场的计算。
The aim of this paper is to analyze a finite element method to solve the low-frequency harmonic Maxwell equations in a bounded domain containing conductors and dielectrics, and using realistic boundary conditions in that they can be easily measured. These equations provide a model for the so-called eddy currents. The problem is formulated in terms of the magnetic field. This formulation is discretized by using Nédélec edge finite elements on a tetrahedral mesh. Error estimates are easily obtained when the curl-free condition is imposed explicitly on the elements in the dielectric domain. A multivalued magnetic scalar potential is introduced then to impose this curl-free condition. The discrete counterpart of this formulation leads to an important saving in computational effort. Problems related to the topology are also considered, more precisely, the possibility of having a non-simply connected dielectric domain is taken into account. Finally, the method is applied to solve two three-dimensional model problems: a test with a known analytical solution and the computation of the electromagnetic field in a metallurgical arc furnace.