A note on the application of edge-elements for modeling three-dimensional inhomogeneously-filled cavities

Abstract

The application of edge-elements for modeling three-dimensional inhomogeneouslylled cavities is presented in this paper. Explicit representations for the two element matrices, S] e and T ] e , are provided in order to facilitate the implementation of the FEM formulation. Also included are the results of a numerical experiment that investigates the rate of convergence of the computation of the dominant resonance frequency of a rectangular cavity when the edge-element formulation is employed..

Basis Functions With Divergence Constraints for the Finite Element Method

“…The relative permittivity r is 16 and the dimensions are given in figure 2.8. This is the same as one of the examples found in the paper by Lee and Mittra [50]. The discontinuity of the normal component of the electric field is implemented exactly during the assembly of the S and T matrices, as is the continuity of the tangential components and the derivative terms.…”

“…This geometry does not allow for separation of variables and an exact solution for the resonant frequencies does not exist at this point in time. This example is chosen because it has been analyzed previously by Lee and Mittra in 1992 using edge elements [50] and by Albani and Bernardi in 1974 using a finite difference method for an integral equation [49]. The paper by Albani and Bernardi also contains an experimental measurement, which is exceptionally valuable because it creates a test problem with a non-trivial geometry.…”

Finite element method solutions of field distributions in large cavities

“…The total electric field distributions inside the substrate at z = 0.8 mm for six arbitrarily chosen frequencies cf = 0.5, 2,4,5,6, and 7 GHz) are shown in Figure 8. Again, it is clear from these distributions that the hybrid and the edge-elements solutions are almost identical.…”

An FFT-Accelerated Integral-Equation Solver for Analyzing Scattering in Rectangular Cavities

“…These applications require the analysis of scattering and radiation from arbitrarily shaped 3-D structures composed of perfect electrically conducting (PEC) surfaces and penetrable volumes. Several conventional numerical methods, such as the method of moments (MOM) [6], [7], the finite-element method [8], and the finite-difference time-domain method [9] are used for simulating scattering from such structures inside cavities. These classical methods have various shortcomings, which are: 1) differential-equation-based methods [8], [9] have to include the whole cavity in the computational domain to capture scattering from the walls; thus, they become less effective when modeling electrically large cavities such as those used in testing wireless communication terminals [10]; 2) integral-equation based methods [6], [7] become less effective when modeling complex materials and irregular geometries such as those that arise in microwave power applications [11]; and 3) these methods are generally too slow to perform the numerous simulations needed for the computer-aided design and optimization of cavities [12].…”

“…Several conventional numerical methods, such as the method of moments (MOM) [6], [7], the finite-element method [8], and the finite-difference time-domain method [9] are used for simulating scattering from such structures inside cavities. These classical methods have various shortcomings, which are: 1) differential-equation-based methods [8], [9] have to include the whole cavity in the computational domain to capture scattering from the walls; thus, they become less effective when modeling electrically large cavities such as those used in testing wireless communication terminals [10]; 2) integral-equation based methods [6], [7] become less effective when modeling complex materials and irregular geometries such as those that arise in microwave power applications [11]; and 3) these methods are generally too slow to perform the numerous simulations needed for the computer-aided design and optimization of cavities [12]. Among the classical methods, the frequency-domain MOM solution of the surface-volume electric field integral equation (SV-EFIE) is a promising approach for analyzing scattering in rectangular cavities because: 1) the unknowns are constrained to only the PEC surfaces and penetrable volumes in the cavity; 2) dispersive properties of materials are modeled without any time-domain approximations; and 3) propagation in the cavity and reflections from the walls are modeled exactly/analytically by using rectangular-cavity Green functions [1], [2], [10], [13]- [15].…”