Resolution of coupled Helmholtz equation in the inhomogeneous coaxial waveguides by the finite element method

This paper presents the application of the Finite Element Method FEM to the resolution of system Helmholtz coupled equations that has been obtained in the coaxial waveguides containing magnetic anisotropic materials with loss. This application is based on variational method which necessitates the construction of functional stationary written in the form of integral equation and dependent on the electromagnetic fields. After being minimized, this functional leads to algebraic equation system to which we can apply many numerical resolution algorithms. The electromagnetic study of the waveguide led us to a system of Helmholtz coupled equations which is difficult to be solved analytically. Our software code allows us to determine the electromagnetic field distribution in all points of the coaxial waveguide. The result has been validated when the coaxial waveguide was entirely loaded with air. This software has later been applied when the waveguide was partially filled with a magnetic anisotropic material with loss (epsilon(r), mu(r)).