Consideration on numerical instability of Dirichlet gauge BEM

Many authors have been discussing numerical simulation methods of transient electromagnetic fields based on scalar and vector potentials and have shown that the Dirichlet type boundary conditions can be imposed on the potentials. Based on the gauge selection, some numerical simulations (BEM analysis) have been done. However, the numerical simulations often encountered numerical instabilities. To clarify the stable condition, this paper discusses numerical instabilities of the BE analysis of transient electromagnetic fields. Then, it is pointed out that there are two kinds of numerical instabilities, short and long range instabilities