Browsing by Subject "Method of Moments"
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Item Open Access Application of biconjugate gradient stabilized method with spectral acceleration for propagation over terrain profiles(Bilkent University, 2003) Babaoğlu, BarışUsing the Method of Moments (MoM) for the computation of electromagnetic radiation / surface scattering problems is a very popular approach since obtained results are accurate and reliable. But the memory requirement in the MoM to solve discretized integral equations and the long computational time of O(N3 ) operation count (where N is the number of the surface unknowns) make the method less favorable when electrically large geometries are of interest. This limitation can be overcome by using BiConjugate Gradient Stabilized (BiCGSTAB) method, a non-stationary iterative technique that was developed to solve general asymmetric/non-Hermitian systems with an operational cost of O(N2 ) per iteration. Furthermore, the computational time can be improved by the spectral acceleration (SA) algorithm which can be applied in any iterative technique. In this thesis, Spectrally Accelerated BiCGSTAB (SA-BiCGSTAB) method is processed over systems that have huge number of unknowns resulting a computational cost and memory requirement of O(N) per iteration. Applications are presented on electrically large rough terrain profiles. The accuracy of the method is compared with MoM, conventional BiCGSTAB method and Spectrally Accelerated Forward-Backward Method (SA-FBM) where available.Item Open Access Application of characteristic basis function method for scattering from and propagation over terrain profiles(Bilkent University, 2009) Yağbasan, AtacanA computationally efficient hybrid method, that combines the characteristic basis function method and the physical optics as well as the forward backward method, is applied for the solution of integral equations used to investigate the electromagnetic scattering from and propagation over large scale rough terrain problems. The method utilizes high-level basis functions defined on macro-domains (named as blocks) namely characteristic basis functions that are constructed by aggregating low-level basis functions (i.e., conventional sub-domain basis functions). In the construction of the abovementioned characteristic basis functions, forward backward method as well as the physical optics approach (when applicable) are used. The conventional characteristic basis function method originally developed by Prakash et al. is slightly modified to handle large terrain problems, and is further embellished by accelerating it and by reducing its storage requirements via the use of an extrapolation procedure. Numerical results for the induced currents, total fields and path loss are presented and compared with either measured or previously published reference solutions to assess the efficiency and the accuracy of the method. Besides, certain parametric studies and convergence tests have been carried out.Item Open Access Application of spectral acceleration forward-backward method for propagation over terrain(Bilkent University, 2003) Tunç, Celal AlpMobile radio planning requires the accurate prediction of electromagnetic eld strengths over large terrain pro les. However, numerical methods, like MoM, become not suitable for electrically large surfaces, because of the O(N3) computational cost due to the large number of surface unknowns N. The Forward- Backward Method (FBM) is a stationary iterative technique for solving linear equation systems resulting from electromagnetic rough surface scattering problems and provides accurate results within very few iterations, causing a computational cost of O(N2). The Spectral Acceleration technique reduces the computational cost and memory requirements of the FBM to O(N), so that the Spectrally Accelerated Forward-Backward Method (FBSA) can be applied over very large terrain pro les. Empirical models with re ection and multiple di raction (RMD) corrections are commonly used to predict the eld strengths over terrain pro les. In this work, applications of the FBM and FBSA are presented over electrically large terrain pro les. Also, using FBSA as a reference solution, the most common empirical models with RMD correction methods are examined to nd out the best propagation models.Item Open Access The estimators of random coefficient models(Bilkent University, 1999) Gündüz, Yasemin BalThis thesis concentrates on the estimators of Random Coefficient models. A Bayesian estimator with non-standard posterior density implementing Griddy Gibbs Sampler technique for Hildreth-Houck type Random Coefficient Model is introduced and it is compared with a range of existing estimators for Random Coefficient models. Monte Carlo experiments are used for comparing this estimator with Swamy and Tinsley (1980), Method of Moments and Zaman (1998) Modified Maximum Likelihood estimators on the basis of biases, Mean Square Errors and efficiencies of parameter estimates. The results show that performances of estimators are affected by sample size, balance of design matrix and variance structure of stochastic regression coefficients. In most of the cases estimates for variance parameter of regression coefficients are seriously biased for all estimators expect the Bayesian Griddy Gibbs estimator. The Bayesian Griddy Gibbs and Method of Moments estimators show better performance compared with others, the best one changes in line with some observable and unobservable criteria. In empirical work, using both methods in estimation and selecting the estimates with minimum out of sample forecast Mean Square Error might be recommended. Asymptotically Maximum likelihood estimator is unbiased and achieves Cramer Rao Lower Bound; therefore it can not be improved upon. The finite sample properties of Modified Maximum Likelihood estimator are studied with a separate Monte Carlo study and it is shown that except very high sample sizes relative to the dimension of the problem there is substantial room for improvement of the Modified Maximum Likelihood estimator in finite samples.Item Open Access Method of moments analysis of microstrip antennas in cylindrically stratified media using closed-form Green's functions(Bilkent University, 2012) Karan, ŞakirNumerical methods based on Method of Moments (MoM) have been widely used for the design and analysis of planar microstrip antennas/arrays and printed circuits for various applications for many years. On the other hand, although the design and analysis of similar antennas/arrays and printed circuits on cylindrical structures are of great interest for many military, civil and commercial applications, their MoM-based analysis suffers from the efficiency and accuracy problems related with the evaluation of the Green’s function representations which constitute the kernel of the regarding integral equations. In this dissertation, novel closed-form Green’s function (CFGF) representations for cylindrically stratified media, which can be used as the kernel of an electric field integral equation (EFIE) are developed. The developed CFGF representations are used in a hybrid MoM/Green’s function solution procedure. In the course of obtaining the CFGF representations, first the conventional spectral domain Green’s function representations are modified so that all the Hankel (Bessel) functions are written in the form of ratio with another Hankel (Bessel) function. Furthermore, Debye representations for the ratio terms are used when necessary in order to avoid the possible overflow and underflow problems. Acceleration techniques that are present in the literature are implemented to further increase the efficiency and accuracy of the summation and integration. Once the acceleration techniques are performed, the resultant expressions are transformed to the space domain in the form of discrete complex images (DCIM) with the aid of the generalized pencil of function (GPOF) method and the fi- nal CFGF expressions are obtained by performing the resultant space domain integrals analytically. The novel CFGF expressions are used in conjunction with MoM for the investigation of microstrip antennas on cylindrically stratified media. The singular terms in mutual impedance calculations are treated analytically. The probe-fed excitation is modeled by implementing an attachment mode that is consistent with the current modes that are used to expand the induced current on the patches. In the course of modeling the probe-fed excitation, the probe-related components of CFGF representations are also derived for the first time in the literature and MoM formulation is given in the presence of an attachment mode. Consequently, several microstrip antennas and two antenna arrays are investigated using a hybrid MoM/Green’s function technique that use the CFGF representations developed in this dissertation. Numerical results in the form of input impedance of microstrip antennas in the presence of several layers as well as the mutual coupling between two microstrip antennas are presented and compared with the available results in the literature and the results obtained from the CST Microwave Studio.