Analysis of Magnetic Fields Induced by Line Currents using Coupling of FEM and Analytical Solution

The line current problem(2-dimensional space : point source) is not easy to analyze the magnetic field using the standard finite element method(FEM), such as overhead trolley line or transmission line. To supplement such a defect this paper is proposed the coupling scheme of analytical solution and FEM. In analysis of the magnetic field using the standard FEM. If the current region is a relatively small compared to the whole region. Therefore the current region must be finely divided using a large number of elements. And the large number of elements increase the number of unknown variables and the use of computer memories. In this paper, an analytical solution is suggested to supplement this weak points. When source is line current and the part of interest is far from line current, the analytical solution can be coupling with FEM at the boundary. Analytical solution can be described by the multiplication of two functions. One is power function of radius, the other is a trigonometric function of angle in the cylindrical coordinate system. There are integral constants of two types which can be established by fourier series expansion. Also fourier series is represented as the factor to apply the continuity of the magnetic vector potential and magnetic field intensity with tangential component at the boundary. To verify the proposed algorithm, we chose simplified model existing magnetic material in FE region. The results are compared with standard FE solution. And it is good agreed by increasing harmonic order.

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