Efficient computation of Maxwell eigenmodes in axisymmetric cavities using hierarchical vector finite elements

Computation of Maxwell eigenmodes in an axisymmetric cavity using hierarchical vector finite elements is presented. The use of curl conforming vector basis functions, which span the null space of the curl operator, leads to the appearance of spurious modes with zero eigenvalues. Such spurious modes lead to electric flux solution with non‐zero divergence. Constraining the solution space in the variational statement for the eigenvalue problem by weakly enforcing the flux to be divergence‐free leads to the elimination of such modes. Discrete equivalent of such a constraint equation is developed for axisymmetric problems solved using hierarchical vector and scalar basis functions of orders complete to p=2. The discrete constraint equation, developed individually for Fourier modes m=0 and m≥1, is efficiently integrated with a subspace iteration‐based eigenvalue solution technique such as the Lanczos/Arnoldi method. The resulting solution technique is free of spurious modes added with an advantage of seeking a solution of a positive definite matrix during each iteration of the eigenvalue solver. Convergence in solution is demonstrated for orders up to p=2, while the proposed technique can be extended to basis functions of arbitrary order. Copyright © 2009 John Wiley & Sons, Ltd.     

Removal of spurious DC modes in edge element solutions for modeling three-dimensional resonators

When using edge element basis functions for the solution of eigenmodes of the vector wave equation, "dc spurious modes" are introduced. The eigenvalues of these modes are zero and their corresponding eigenvectors are in the space of the curl operator. These modes arise due to the irrotational vector space spanned by the edge element basis functions and lead to nonzero divergence of the electric flux. We introduce a novel method to eliminate the occurrence of such solutions using "divergence-free" constraint equations. The constraint equations are imposed efficiently by tree-cotree partitioning of the finite-element mesh and does not require any basis functions other than the edge elements. The constraint equations can be directly incorporated into any Krylov-subspace-based eigenvalue solver, such as the Lanczos/Arnoldi algorithm used widely for the solution of generalized sparse eigenvalue problems.     

On the numerical errors in the 2D FE/FDTD algorithm for different hybridization schemes

Numerical experiments are carried out to study the accuracy of the two-dimensional Finite-Element/Finite-Difference Time-Domain (FE/FDTD) hybrid algorithm with three different hybridization schemes. The physical space is split into two domains viz., the finite difference (FD) and finite element (FE) domains. In the FD domain, a uniform Cartesian grid is used and in the FE domain, triangular elements with edge vector basis functions are used. Newmark-/spl beta/ scheme is used for temporal discretization in the FE domain. The unphysical reflections introduced by the FE domain for the different schemes are compared by computing the 2-D radar cross section of the FE domain surrounded by the FD domain. Computed results of scattering by a PEC circular cylinder for TE/sub z/ incidence using the three schemes and the traditional FDTD algorithm are presented.     

Numerical modeling of ultrawide-band dielectric horn antennas using FDTD

A detailed characterization of the input impedance of ultrawide-band (UWB) dielectric horn antennas is presented using the finite-difference time-domain (FDTD) technique. The FDTD model is first validated by computing the characteristic impedance of two conical plate transmission lines (including planar bow-tie antennas) and comparing the results to analytical solutions. The FDTD model is next used to calculate the surge impedance of dielectric horn antennas using the conical plates as launchers. Design curves of the surge impedance for different choices of geometries and dielectric loadings are provided. The modeled antennas are particularly attractive for applications such as UWB ground penetrating radars (GPR) applications.