A combined vector method of finite and boundary elements for simulating electromagnetic filed propagation considering an eddy current model
This work is devoted to the application of the Finite Element Method (FEM) coupled with the Boundary Element Method (BEM) for the purpose of electromagnetic field simulation using an eddy current model. Therefore the combined derived variational problem is numerically compared with the analytical solution in this paper. The paper also shows the convergence of the numerical solution to the corresponding analytical values for the specific points of the computational domain. The method of deriving a coupled problem is described relative to the electric field strength. The essence of this method is partitioning of the computational domain into parts and each part must be simulated by either FEM or BEM techniques. In addition, the continuity of tangential vector field components of electric field strength in a strong form and magnetic field strength in a weak form is also taken into account by formulating the equations of the coupled approach. The coupled approach may be beneficial when one does not construct a volume mesh for the environment domain. In the case of eddy currents being involved in the computation, the vector FEM elements must be used and an eddy current equation with the rot-rot operator must be solved. This paper presents an example of such coupling y using the Steklof-Poincare operator for which a weak form of the corresponding equation is derived to obtain the coupled method. Using the presented approach one may simulate, for instance, a wireless transmission of electro-magnetic energy with sources having non-linear properties.