Title: Influence of Vector Variables to the Computational Accuracies of Boundary Element Method for Electrostatic and Magnetostatic Problems
Abstract: The applicability of boundary element method has been shown by its applications to scalar potential problems. However, unified formulations for the boundary element method using vector variables and relations between unknown vector variables and the accuracy of the solutions have not been discussed. In this paper, the unified formulation, how to select unknowns and their influence to the accuracy of the solutions in magnetostatics and electrostatics were investigated, and the following results were obtained.When electric field is assumed as unknown in electrostatic problems, or magnetic flux density or vector potential is assumed as unknown in magnetostatic problems, the formulation for the boundary element method using vector variables can be performed. In magnetostatic problems, the equations for the method using a vector potential were shown, and their suitability was verified. Furthermore, in the method using the vector potential as unknown, there is a tendency for computational error of magnetic flux density to larger than the method using magnetic flux density as unknown, and computational error for the numerical integration of magnetic flux density may become large near the boundary surfaces because of its strong singularity.