Finite-element modelling of high-frequency electromagnetic problems with material discontinuities

Abstract

A weighted residual formulation, suitable for finite-element application, is given for the general high-frequency time-harmonic electromagnetic problem presented by a lossy anisotropic inhomogeneous boundary driven linear system. Either of the dual field vectors H or E may be chosen as the working variable. New light is thrown on the difficulties arising in finite-element analysis when components of the working variable are discontinuous owing to sharp jumps in material properties. The latter are shown to represent ‘natural’ boundaries not specifically requiring any constraint. The modification of the formulation applying to the eigenproblem of an axially uniform waveguide is presented. The equivalence of the Galerkin option of the formulation used in the paper and the corresponding variational approach is discussed. Some finite-element numerical results relating to the analytically soluble problem of a waveguide with an axial discontinuity in material property are presented, confirming the predictions made and demonstrating the practical possibility of solving high-frequency problems by the finite-element method successively with dual working variables.