Coupling of Vector and Scalar Boundary Element Methods

The vector boundary element method is a tool applied to solve electromagnetic problems in a media for which eddy currents must be taken into account. It's also known as the boundary element method for eddy current problems. The use of this method brings certain difficulties, one of which is the problem of zero wave number in the subdomains adjacent to the domain where the eddy currents should be considered. To mitigate the computational difficulty, we use the coupling with the scalar potential. The scalar boundary element method for the Laplace equation is in use for the corresponding adjacent subdomains with zero wave number and the associated scalar potential. In this paper, we present the system of variational equations written in a weak form and based on the Steklov-Poincare operators formulated for both scalar and vector boundary element methods. This coupling is supported with a simple test problem considering a conducting cube and a time-harmonic source of electromagnetic field.