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Title: Higher-order (LT/QN) vector finite elements for waveguide analysis
Abstract: The finite element (FE) formulation for waveguide discontinuity analysis is reviewed and extended to multiple, arbitrarily-oriented ports. Several higher-order vector elements - specifically hierarchal linear tangential/quadratic normal (LT/QN) - are compared, and the extensions required to incorporate LT/QN elements in the formulation are presented. The improved accuracy afforded by LT/QN elements compared to constant tangential/linear normal (CT/LN) elements is investigated by considering energy conservation in an empty waveguide. Results obtained using both CT/LN and LT/QN elements are also shown for a problem of engineering interest: an E-plane bend. Results for the LT/QN elements compare especially well to approximate analytical results using quite coarse meshes. The paper concludes with a discussion of the use of iterative solvers and possible convergence problems encountered when using higher-order elements.
Author(s): David B Davidson
File Type: Journal Paper
Issue:Volume: 17      Number: 1      Year: 2002
Download Link:Click here to download PDF     File Size: 152 KB

Title: Higher Order Spatial Operators for the Finite Integration Theory
Abstract: The Finite Integration Technique (FIT) according to T. Weiland is an efficient and universal method for solving a large scale of problems in computational electrodynamics. Up to now the conventional formulation itself has had an accuracy order of two with respect to the spatial discretization. In this paper an innovative extension to fourth or even higher order is presented. The convergence of the presented scheme is demonstrated by a general dispersion equation and stability issues are discussed. An approach for a stable spatial interface connecting regions of higher order with the standard FIT scheme is proposed.
Author(s): Holger Spachmann, Rolf Schuhmann, Thomas Weiland
File Type: Journal Paper
Issue:Volume: 17      Number: 1      Year: 2002
Download Link:Click here to download PDF     File Size: 2009 KB

Title: A FDTD HYBRID "M3d24 -YEE" SCHEME WITH SUBGRIDDING FOR SOLVING LARGE ELECTROMAGNETIC PROBLEMS
Abstract: A hybrid scheme consisting of a modified second order in time- fourth order in space finite-difference time-domain (FDTD) scheme "M3d24 " and the Yee algorithm, with subgridding is introduced to overcome the errors of applying the 4th order in space FDTD at the interfaces of perfect electric conductors (PEC) or dielectric scatterers. This hybrid scheme is based on applying the Yee algorithm in the vicinity of the scatterer using a high resolution grid (number of points per wavelength), and the M3d24 scheme in the other regions using a low resolution grid in order to reduce the required computer storage for large problems, while still good accuracy. The results of this hybrid scheme are shown to agree well with the results of the Yee algorithm using a high resolution grid, for problems of plane wave scattering from PEC cubes, spheres.
Author(s): Hany AbdEl-Raouf, Esam El-Diwani, Abd El-Hadi Ammar, Fatma El-Hefnawi
File Type: Journal Paper
Issue:Volume: 17      Number: 1      Year: 2002
Download Link:Click here to download PDF     File Size: 322 KB

Title: Modified Fresnel Coefficients for Huygens' Sources in FDTD
Abstract: Scattering of electromagnetic fields from objects on or beneath the ground can be analyzed with the Finite-Difference Time-Domain (FDTD) method. The equivalence principle can be utilized for generation of incident plane waves where the Fresnel reflection and refraction coefficients are multiplied by the pulse spectrum in the frequency domain and the result is transformed into the time-domain. Errors will appear in the Huygens' sources due to numerical dispersion where the main errors come from the use of analytical reflection and refraction coefficients. Their influence on the accuracy is generally negligible for applications where the scattered field from the object is greater than the numerical errors introduced. However, if weak scattering events are considered, such as for objects buried in ground, the dispersion errors can be of the same order of magnitude as the scattered field. In this paper we derive the modified Fresnel coefficients for a homogeneous lossy ground which are consistent with the FDTD algorithm and can be used in the Huygens' sources for suppressing numerical errors. It is shown that the modified Fresnel coefficients reduces the noise level for an empty FDTD volume with 30 to 60 dB. As an application example, the far-zone scattering of a buried dipole is considered.
Author(s): Torleif Martin, Lars Pettersson
File Type: Journal Paper
Issue:Volume: 17      Number: 1      Year: 2002
Download Link:Click here to download PDF     File Size: 351 KB

Title: A Comparative Study of Expansion Functions Using the Boundary Residual Method on a Linear Dipole - Part I: Entire-Domain Functions
Abstract: the Boundary Residual Method, which is a specialization of the Least Squares Method, is described. A significant benefit of the approach is that error in the residual satisfaction of the boundary condition is explicitly reported. Use of error values facilitates better monitoring of solution convergence as expansion functions are added to the underlying model. Furthermore, better discrimination between competing models is possible when errors are known. These concepts are explored and applied to dipoles of various lengths with key findings reported.
Author(s): Malcolm M. Bibby
File Type: Journal Paper
Issue:Volume: 17      Number: 1      Year: 2002
Download Link:Click here to download PDF     File Size: 244 KB

Title: A Comparative Study of Expansion Functions Using the Boundary Residual Method on a Linear Dipole - Part II: Sub-Domain Functions
Abstract: The Boundary Residual Method is used to compare the performance of a range of sub-domain expansion functions in three different settings. It is found that as the complexity of the structure/system being studied increases the importance of the order of the expansion function decreases - at least for uniform excitation. These results point out the need for more research into the behaviour and performance of these, and other, expansion functions.
Author(s): Malcolm M. Bibby
File Type: Journal Paper
Issue:Volume: 17      Number: 1      Year: 2002
Download Link:Click here to download PDF     File Size: 312 KB

Title: Methods for the Evaluation of Regular, Weakly Singular and Strongly SingularSurface Reaction Integrals Arising in Method of Moments
Abstract: The accurate and fast evaluation of surface reaction integrals for Method of Moments computations is presented. Starting at the classification of the integrals into regular and weakly, strongly and nearly singular integrals, appropriate methods are presented that handle each. A Gauss-Legendre quadrature rule evaluates regular integrals. For singular integrals, the singularity is lifted or weakened by an extraction of the singularity, a transform to polar coordinates or a domain transform. The resulting regular integral is in turn solved by a quadrature rule. The different methods are finally applied to an example, and the resulting accuracy tested against the analytical result. The presented methods are general enough to be used as integration methods for integrands with various degrees of singularity and is not limited to Method of Moments.
Author(s): Alexander Herschlein, Juergen v. Hagen, Werner Wiesbeck
File Type: Journal Paper
Issue:Volume: 17      Number: 1      Year: 2002
Download Link:Click here to download PDF     File Size: 340 KB

Title: Accuracy of currents produced by the locally-corrected Nystrom method and the method of moments when used with higher-order representations
Abstract: The locally-corrected Nyström method is described, and the accuracy of the currents produced by it and the method of moments are compared. Results suggest that when the underlying representation has the same order, the methods are comparable in accuracy. Additional results are presented to illustrate the Nyström approach, and advantages and disadvantages of the method are reported.
Author(s): Andrew F. peterson
File Type: Journal Paper
Issue:Volume: 17      Number: 1      Year: 2002
Download Link:Click here to download PDF     File Size: 184 KB

Title: High-Order Nystrom Method for Computing Waveguide Modes
Abstract: We report a novel method for accurately computing the modes of an arbitrarily-shaped hollow waveguide. Our method uses a point-based (Nystrom) discretization of an integral operator over the waveguide aperture to compute the modes.
Author(s): J. J. Ottusch, S. M. Wandzura
File Type: Journal Paper
Issue:Volume: 17      Number: 1      Year: 2002
Download Link:Click here to download PDF     File Size: 2246 KB

Title: CIRCLE-FIT SUMMATION ACCELERATION OF PERIODIC GREEN’S FUNCTIONS
Abstract: The circle-fit algorithm is shown to be an attractive alternative to the spectral domain form of the two-dimensional periodic Green’s function when the radiated fields are evaluated in the plane of the array. As the name implies, the circle-fit algorithm predicts the summation limit by fitting circles to the converging spiral of spatial domain partial sums in the complex plane. Several numerical examples comparing the raw spatial, spectral, and circle-fit accelerated spatial sums demonstrate the algorithm's computational savings. While other series extrapolation methods are shown to be more efficient, the circle-fit algorithm has the advantage of providing insight into how the Green’s function converges.
Author(s): Peter J. Collins
File Type: Journal Paper
Issue:Volume: 17      Number: 1      Year: 2002
Download Link:Click here to download PDF     File Size: 185 KB

Title: The Stabilized Biconjugate Gradient Fast Fourier Transform Method for Electromagnetic Scattering
Abstract: An iterative method, the stabilized biconjugate gradient (BiCGSTAB) method, combined with the fast Fourier transform (FFT) for solving electromagnetic scattering problems is developed for the 3-D volume electric field integral equation. It converges significantly faster than the conventional conjugate gradient (CG) and biconjugate gradient (BiCG) fast Fourier transform methods. With this BCGS-FFT method, we can solve a large-scale volume integral equation with $20$ million unknowns on a single CPU workstation.
Author(s): Xue Min Xu, Qing Huo Liu,, Zhong Qing Zhang
File Type: Journal Paper
Issue:Volume: 17      Number: 1      Year: 2002
Download Link:Click here to download PDF     File Size: 235 KB

Title: Introduction of an Adaptive Modeling Technique for the Simulation of RF Structures Requiring the Coupling of Maxwell’s, Mechanical, and Solid-State Equations
Abstract: As RF technologies mature designing complex RF systems is becoming an increasingly difficult task. Modern systems include components that cannot be modeled with traditional simulators. This paper introduces a modeling technique for use in RF systems that combines Maxwell’s, mechanical, and solid-state equations. The resulting simulator can be used to simulate microelectromechanical structures (MEMS) and semiconductor devices. The motion coupling technique is applied to a MEMS parallel plate capacitor for demonstration purposes.
Author(s): N.Bushyager, B.McGarvey, E.M.Tentzeris
File Type: Journal Paper
Issue:Volume: 17      Number: 1      Year: 2002
Download Link:Click here to download PDF     File Size: 456 KB