Finite-Element Method

The finite-element method (FEM) is a full-wave numerical method that discretizes the variational of a functional. The evolution of this method within the scope of electromagnetics traces back to the solving of two classes of problems, namely, the eigenmode problems and the deterministic problems. If we try to use some examples to illustrate the most typical and the most complete techniques with the most complete solution, the eigenmode problem of a dielectrically loaded waveguide and the wave propagation in a three-dimensional (3D) discontinuous waveguide are good candidates representing the eigenmode and the closed-domain solutions, respectively. As for the open-domain scattering problem and radiating problems, the authors consider the essential and key parts are presented in solving the 3D scattering problems. For this reason, we will illustrate the theoretical basics, the critical solving techniques and the typical skills involved in FEM through solving of the above three specific problems. At the end of this chapter, we will also briefly review the FEM solution for some other problems.