TANGENTIAL VECTOR FINITE-ELEMENTS FOR ELECTROMAGNETIC-FIELD COMPUTATION

The finite element solution of the vector wave equation often results in non-physical behavior known as spurious modes. It is shown that the occurrence of spurious modes is due to the improper modeling of the nullspace of the curl operator. One approach to eliminating spurious modes is the use of tangential vector finite elements. With tangential vector finite elements, only the tangential components of the vector field are made continuous across the element boundaries. The use of this type of element has the following advantages: (1) The physical continuity requirements of the electric and magnetic fields are satisfied; (2) The interfacial boundary conditions are automatically obtained through the natural boundary conditions built into the variational principle; and (3) Dirichlet boundary conditions are easily set along curved boundaries. Edge-elements are the simplest example of tangential vector finite elements. However, edge-elements provide only the lowest-order of accuracy in numerical computations since in this approach the tangential component of the field is assumed to be constant along each edge of the element. In this paper, the configurations of the tangential vector finite elements which are of higher-order approximations on two-dimensional triangular elements as well as on three-dimensional tetrahedral elements are presented. The vector-valued basis functions are written explicitly, and the interpolatory meanings of the unknowns are also derived.