An improvement for 3-D Magnetostatic Field Calculation using Two Scalar Potentials with BEM

Abstract

In the case of applying BEM to the 3-D magnetostatic field calculation, the two scalar potentials method introduced by J. Simkin and C. W. Trowbridge, is effective, because it needs fewer unknowns than the vector potential method and brings less calculation error than one potential method. But in the two scalar potentials method we must calculate line integrals on the boundary for making interface conditions between the inhomogeneous regions. In order to improve this disadvantage, we propose a new technique in which the interface conditions can be obtained without this line integrals and consequently we could shorten the calculation time.
In BEM, it is the most significant problem that the nearly singularity of surface integrals appears in calculating the coefficient matrices and potentials at internal points. Especially when the internal point becomes closer to the boundary, the nearly singularity of the integrands becomes severer and numerical calculation of this integrals becomes more difficult. Therefore, we apply Takeda's analytical integral formula to the two scalar potentials method, and have confirmed its validity in accuracy and calculation time.