Weak and strong formulations for the time-harmonic eddy-current problem in general multi-connected domains
Weak and strong formulations for the time-harmonic eddy-current problem in general multi-connected domains
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一般多连通域中时谐涡流问题的弱和强公式
DOI：
10.1017/s0956792503005151
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发表时间：
2003
影响因子：
1.9
通讯作者：
A. Valli
中科院分区：
文献类型：
--
作者：
A. A. Rodríguez;P. Fernandes;A. Valli
本文研究了具有一般拓扑结构的导体的时谐麦克斯韦方程组的涡流问题。对于适当的弱公式，证明了唯一磁场的存在。然后推导出一个等价的强公式，其中与域的特定几何形状相关的条件是明确的。特别是，一个新的条件，必须满足的多连接导体和非导电区域之间的界面上的磁场被确定。最后，导出了非导电区电场问题的强形式，并证明了其唯一解的存在性。总之，这导致确定描述涡流问题的磁场和电场的完整方程组。并对一些常用的公式是否满足界面上的附加条件进行了检验。
The eddy-current problem for the time-harmonic Maxwell equations in domains and with conductors of general topology is considered. The existence of a unique magnetic field is proved for a suitable weak formulation. An equivalent strong formulation is then derived, where the conditions related to the specific geometry of the domain are made explicit. In particular, a new condition that must be satisfied by the magnetic field on the interface between a multiply-connected conductor and the non-conducting region is determined. Finally, the strong formulation of the problem for the electric field in the non-conducting region is derived, and the existence of a unique solution is proved. In conclusion, this leads to the determination of the complete set of equations describing the eddy-current problem in terms of the magnetic and the electric fields. Whether some commonly-used formulations satisfy the additional condition on the interface is also checked.