Browsing by Subject "Transmission line matrix methods"

Now showing 1 - 8 of 8

Open Access
Analytical evaluation of the MoM matrix elements
(Institute of Electrical and Electronics Engineers, 1996-04) Alatan, L.; Aksun, M. I.; Mahadevan, K.; Birand, M. T.
Derivation of the closed-form Green's functions has eliminated the computationally expensive evaluation of the Sommerfeld integrals to obtain the Green's functions in the spatial domain. Therefore, using the closed-form Green's functions in conjunction with the method of moments (MoM) has unproved the computational efficiency of the technique significantly. Further improvement can be achieved on the calculation of the matrix elements involved in the MoM, usually double integrals for planar geometries, by eliminating the numerical integration. The contribution of this paper is to present the analytical evaluation of the matrix elements when the closed-form Green's functions are used, and to demonstrate the amount of improvement in computation time. © 1996 IEEE.
Open Access
Efficient methods for electromagnetic characterization of 2-D geometries in stratified media
(IEEE, 1998) Çalışkan, Fatma; Aksun, M. İrşadi; Gürel, Levent
Numerically efficient method of moments (MoM) algorithms are developed for and applied to 2-D geometries in multilayer media. These are, namely, the spatial-domain MoM in conjunction with the closed-form Green's functions, the spectral-domain MoM using the generalized pencil of functions (GPOF) algorithm and FFT algorithm to evaluate the MoM matrix entries. These approaches are mainly to improve the computational efficiency of the evaluation of the MoM matrix entries. Among these, the spectral-domain MoM using the GPOF algorithm is the most efficient approach for printed multilayer geometries. The assessment of the efficiency of this method is performed on several problems, by comparing the matrix fill times for these three approaches.
Open Access
Electromagnetic scattering solution of conducting strips in layered media using the fast multipole method
(Institute of Electrical and Electronics Engineers, 1996-08) Gürel, Levent; Aksun, M. I.
The fast multipole method (FMM) is applied to the solution of the electromagnetic scattering problems in layered media for the first time. This is achieved by using closed-form expressions for the spatial-domain Green's functions for layered media. Until now, the FMM has been limited to the homogeneous-medium problems. An integral equation based on the two-dimensional scalar Helmholtz equation is solved to compute the electromagnetic scattering from sample geometries of conducting strips in layered media in order to demonstrate the accuracy and the efficiency of the new method.
Open Access
Fast and accurate solutions of large-scale scattering problems with parallel multilevel fast multipole algorithm
(IEEE, 2007) Ergül, Özgür; Gürel, Levent
Fast and accurate solution of large-scale scattering problems obtained by integral-equation formulations for conducting surfaces is considered in this paper. By employing a parallel implementation of the multilevel fast multipole algorithm (MLFMA) on relatively inexpensive platforms. Specifically, the solution of a scattering problem with 33,791,232 unknowns, which is even larger than the 20-million unknown problem reported recently. Indeed, this 33-million-unknown problem is the largest integral-equation problem solved in computational electromagnetics.
Open Access
On the errors arising in surface integral equations due to the discretization of the identity operator
(IEEE, 2009) Ergül, Özgür; Gürel, Levent
Surface integral equations (SIEs) are commonly used to formulate scattering and radiation problems involving three-dimensional metallic and homogeneous dielectric objects with arbitrary shapes. For numerical solutions, equivalent electric and/or magnetic currents defined on surfaces are discretized and expanded in a series of basis functions. Then, the boundary conditions are tested on surfaces via a set of testing functions. Solutions of the resulting dense matrix equations provide the expansion coefficients of the equivalent currents, which can be used to compute the scattered or radiated electromagnetic fields. This study consists of two parts. In the first part, the authors show that the identity operator is truly a major error source in normal and mixed formulations that are discretized with low-order functions, e.g., Rao-Wilton-Glisson (RWG) functions. In the second part, the authors investigate the incompatibility of SIE formulations in the context of iterative solutions. The authors show that a compatibility test can be used to determine the breakpoint, where the accuracy of the solution is saturated and cannot be enhanced any more.
Open Access
Preconditioned MLFMA solution of multiple dielectric-metallic composite objects with the electric and magnetic current combined-field integral equation (JMCFIE)
(IEEE, 2009-06) Ergül, Özgür; Gürel, Levent
We consider fast and accurate solutions of scattering problems involving multiple dielectric and composite dielectric-metallic structures with three-dimensional arbitrary shapes. Problems are formulated rigorously with the electric and magnetic current combined-field integral equation (JMCFIE), which produces well-conditioned matrix equations. Equivalent electric and magnetic surface currents are discretized by using the Rao-Wilton-Glisson (RWG) functions defined on planar triangles. Matrix equations obtained with JMCFIE are solved iteratively by employing a Krylov subspace algorithm, where the required matrix- vector multiplications are performed efficiently with the multilevel fast multipole algorithm (MLFMA). We also present a four-partition block-diagonal preconditioner (4PBDP), which provides efficient solutions of JMCFIE by reducing the number of iterations significantly. The resulting implementation based on JMCFIE, MLFMA, and 4PBDP is tested on large electromagnetics problems.
Open Access
A robust approach for the derivation of closed-form Green's functions
(Institute of Electrical and Electronics Engineers, 1996-05) Aksun, M. I.
Spatial-domain Green's functions for multilayer, planar geometries are cast into closed forms with two-level approximation of the spectral-domain representation of the Green's functions. This approach is very robust and much faster compared to the original one-level approximation. Moreover, it does not require the investigation of the spectral-domain behavior of the Green's functions in advance to decide on the parameters of the approximation technique, and it can be applied to any component of the dyadic Green's function with the same ease.
Open Access
Transient analysis of nonlinear circuits by combining asymptotic waveform evaluation with volterra series
(Institute of Electrical and Electronics Engineers, 1995-08) Celik, M.; Atalar, Abdullah; Tan, M. A.
A new method is proposed for the transient analysis of circuits with large number of linear lumped elements and lossy coupled transmission lines, and with few mildly nonlinear terminations. The method combines the Volterra-series technique with Asymptotic Waveform Evaluation approach and corresponds to recursive analysis of a linear equivalent circuit.