Three-Dimensional Boundary Element Method Using A Time-Dependent Fundamental Solution

The boundary element method is applied to analyze the three-dimensional diffusion equation for the eddy current problems. The diffusion equation is known as the governing equation of the heat conduction problems. The boundary element method using scalar variables and the time-dependent fundamental solution have been applied to solve these scalar potential problems and similar problems with one component of vector variables. This paper deals with the boundary element method using vector variables for mangetic field analysis. The formulation of this method is based on the vector Green's theorem and the time-dependent fundamental solution. For the analysis of the three-dimensional eddy current distribution, the magnetic vector potential, the current vector potential and the magnetic flux density are used as an unknown vector variable, respectively. The methods for each of the above unknown vector variables are applied to the permeation problem on the magnetic field. It is indicated that our method is available in transient magnetic field analysis. We also point out the necessity of a consistent choice of time step and spatial discretization.