Consideration on the Dirichlet-gauge boundary element method from topological point of view

The authors have discussed the numerical simulation method for transient electromagnetic fields using the boundary element method which is based on scalar and vector potentials. To use the BEM which is based on potentials to transient electromagnetic fields, a special gauge transformation has been performed to get an appropriate boundary condition for potentials. This paper discusses a restriction on the topological configuration of the considered region, that is necessitated by the use of the gauge transformation. The discussion is done using the four-dimensional space-time formulation. It is shown that the BEM which is based on potentials is almost free from a topological restriction on the considered region.