Time-harmonic Electromagnetic Problems Research Articles

The generalized method of lines based on the discretization technique of the pseudospectral method

In this paper, a novel semianalytical higher order numerical approach to solve electromagnetic field boundary value problems is described. This pseudospectral-based method of lines is developed by combining the pseudospectral technique and the method of lines so that it not only has a high accuracy of the semianalytical technique in the line direction, but also maintains high accuracy in the discrete direction. The pseudospectral-based discretization technique, distribution of collocation nodes, global interpolation of the differential quadrature, second-order difference matrix for various homogeneous boundary conditions, and decoupling of coupled ordinary differential equations are discussed in detail. Our numerical results demonstrate that this higher order semianalytical method can efficiently solve the boundary value problems with fewer mesh lines when compared to the conventional method of lines. It primarily shows that this method will be a competitive technique to model time-harmonic complex electromagnetic problems. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 339–342, 1999.

Wave-envelope and transformation methods for finite element solution of unbounded electromagnetic wave problems

The wave-envelope (WE) method is a technique that has been applied to acoustic problems to model the unbounded domain surrounding an acoustic source. Here it is applied to electromagnetic wave problems. A key feature of the method is that it uses a change of dependent variable to remove the wave-like qualities of the solution and thereby permits the use of arbitrarily large elements in the exterior domain. This makes it possible to apply to wave problems some of the techniques developed for magnetostatics, such as transformation methods. These methods map the very large exterior domain into a smaller region which is more easily meshed. The combined wave-envelope transformation method is applied to two time-harmonic electromagnetic wave problems: radiation of a single cylindrical wave function; and scattering of an incident plane wave by a perfectly-conducting circular cylinder. In both cases the near-zone electric field is compared to the exact solution, for a range of frequencies.

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

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.

Partial variational principle for electromagnetic field problems: theory and applications

A partial variation concept is proposed to clarify and extend the ideas and techniques used in variational electromagnetic (VEM) and variation reaction theory (VRT) of recent papers. Based on this concept, a partial variational principle (PVP) is established for handling a general linear time-harmonic interior and/or exterior electromagnetic field problem. This principle is then applied to attack the problem of waves incident on a dielectric discontinuity in a parallel-plate guide. Also included are numerical results and discussions about such waveguide discontinuity problems for illustrating the use of the proposed technique. >