Characteristic Basis Function Method for Solving Electromagnetic Scattering Problems over Rough Terrain Profiles

Cataloged from PDF version of article.A computationally efficient algorithm, which combines the characteristic basis function method (CBFM), the physical optics (PO) approach (when applicable) with the forward backward method (FBM), is applied for the investigation of electromagnetic scattering from—and propagation over—large-scale rough terrain problems. The algorithm utilizes high-level basis functions defined on macro-domains (blocks), called the characteristic basis functions (CBFs) that are constructed by aggregating low-level basis functions (i.e., conventional sub-domain basis functions). The FBM as well as the PO approach (when applicable) are used to construct the aforementioned CBFs. The conventional CBFM is slightly modified to handle large-terrain problems, and is further embellished by accelerating it, as well as reducing its storage requirements, via the use of an extrapolation procedure. Numerical results for the total fields, as well as for the path loss are presented and compared with either measured or previously published reference solutions to assess the efficiency and accuracy of the algorithm

Accelerated integral equation techniques for solving EM wave propagation and scattering problems

This dissertation focuses on the development of the robust, efficient and accurate numerical methods of EM wave propagation and scattering from urban, rural areas and random rough surfaces. There are four main contributions of this dissertation. - The Improved Tabulated Interaction Method (ITIM) is proposed to compute EM wave propagation over lossy terrain profiles using a coupled surface integral equation formulation. The ITIM uses a common set of basis functions in conjunction with a simple matching technique to compress the original system to a reduced system containing considerably smaller number of unknowns and therefore provide a very efficient and accurate method. - Initial efforts in using the full-wave method to compute EM wave propagation over urban areas. The un-accelerated full-wave method has a massive computational burden. In order to reduce the computational complexity, Generalized Forward Backward Method (GFBM) is applied (note that the conventional Forward Backward Method diverges in this scenario). - The Improved Forward Backward Method with Spectral Acceleration (FBM-SA) is proposed to solve the problem of 2D wave scattering from random lossy rough surfaces. - An efficient and accurate iterative method is proposed for computing the 3D wave scattering from 2D dielectric random rough surfaces. The proposed method referred to as the Block Forward Backward Method improves the convergence of the 3D FBM, makes it converge for the case of 2D dielectric surfaces. In addition the Spectral Acceleration is also modified and combined with the BFBM to reduce the computational complexity of the proposed method

Application of spectral acceleration forward-backward method for propagation over terrain

Cataloged from PDF version of article.Mobile 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.Tunç, Celal AlpM.S

Fast Numerical Algorithms for 3-D Scattering from PEC and Dielectric Random Rough Surfaces in Microwave Remote Sensing

abstract: We present fast and robust numerical algorithms for 3-D scattering from perfectly electrical conducting (PEC) and dielectric random rough surfaces in microwave remote sensing. The Coifman wavelets or Coiflets are employed to implement Galerkin’s procedure in the method of moments (MoM). Due to the high-precision one-point quadrature, the Coiflets yield fast evaluations of the most off-diagonal entries, reducing the matrix fill effort from O(N^2) to O(N). The orthogonality and Riesz basis of the Coiflets generate well conditioned impedance matrix, with rapid convergence for the conjugate gradient solver. The resulting impedance matrix is further sparsified by the matrix-formed standard fast wavelet transform (SFWT). By properly selecting multiresolution levels of the total transformation matrix, the solution precision can be enhanced while matrix sparsity and memory consumption have not been noticeably sacrificed. The unified fast scattering algorithm for dielectric random rough surfaces can asymptotically reduce to the PEC case when the loss tangent grows extremely large. Numerical results demonstrate that the reduced PEC model does not suffer from ill-posed problems. Compared with previous publications and laboratory measurements, good agreement is observed.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Application of characteristic basis function method for scattering from and propagation over terrain profiles

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Science of Bilkent University, 2009.Thesis (Master's) -- Bilkent University, 2009.Includes bibliographical references leaves 69-73.A 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.Yağbasan, AtacanM.S

Application of biconjugate gradient stabilized method with spectral acceleration for propagation over terrain profiles

Cataloged from PDF version of article.Using 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.Babaoğlu, BarışM.S

Application of iterative techniques for electromagnetic scattering from dielectric random and reentrant rough surfaces

Cataloged from PDF version of article.Stationary [e.g., forward–backward method (FBM)] and nonstationary [e.g., conjugate gradient squared, quasi-minimal residual, and biconjugate gradient stabilized (Bi-CGSTAB)] iterative techniques are applied to the solution of electromagnetic wave scattering from dielectric random rough surfaces with arbitrary complex dielectric constants. The convergence issues as well as the efficiency and accuracy of all the approaches considered in this paper are investigated by comparing obtained scattering (in the form of normalized radar cross section) and surface field values with the numerically exact solution, computed by employing the conventional method of moments. It has been observed that similar to perfectly and imperfectly conducting rough surface cases, the stationary iterative FBM converges faster when applied to geometries yielding best conditioned systems but exhibits convergence difficulties for general geometries due to its inherit limitations. However, nonstationary techniques are, in general, more robust when applied to arbitrarily general dielectric random rough surfaces, which yield more ill-conditioned systems. Therefore, they might prove to be more suitable for general scattering problems. Besides, as opposed to the perfectly and imperfectly conducting rough surface cases, the Bi-CGSTAB method and FBM show two interesting behaviors for dielectric rough surface pro- files: 1) FBM generally converges for reentrant surfaces when the vertical polarization is considered and 2) the Bi-CGSTAB method has a peculiar convergence problem for horizontal polarization. Unlike the other nonstationary iterative techniques used in this paper, where a Jacobi preconditioner is used, convergent results are obtained by using a block-diagonal preconditioner

Accelerated iterative solvers for the solution of electromagnetic scattering and wave propagation propagation problems

The aim of this work is to contribute to the development of accelerated iterative methods for the solution of electromagnetic scattering and wave propagation problems. In spite of recent advances in computer science, there are great demands for efficient and accurate techniques for the analysis of electromagnetic problems. This is due to the increase of the electrical size of electromagnetic problems and a large amount of design and analytical work dependent on simulation tools. This dissertation concentrates on the use of iterative techniques, which are expedited by appropriate acceleration methods, to accurately solve electromagnetic problems. There are four main contributions attributed to this dissertation. The first two contributions focus on the development of stationary iterative methods while the other two focus on the use of Krylov iterative methods. The contributions are summarised as follows: • The modified multilevel fast multipole method is proposed to accelerate the performance of stationary iterative solvers. The proposed method is combined with the buffered block forward backward method and the overlapping domain decomposition method for the solution of perfectly conducting three dimensional scattering problems. The proposed method is more efficient than the standard multilevel fast multipole method when applied to stationary iterative solvers. • The modified improvement step is proposed to improve the convergence rate of stationary iterative solvers. The proposed method is applied for the solution of random rough surface scattering problems. Simulation results suggest that the proposed algorithm requires significantly fewer iterations to achieve a desired accuracy as compared to the conventional improvement step. • The comparison between the volume integral equation and the surface integral equation is presented for the solution of two dimensional indoor wave propagation problems. The linear systems resulting from the discretisation of the integral equations are solved using Krylov iterative solvers. Both approaches are expedited by appropriate acceleration techniques, the fast Fourier transform for the volumetric approach and the fast far field approximation for the surface approach. The volumetric approach demonstrates a better convergence rate than the surface approach. • A novel algorithm is proposed to compute wideband results of three dimensional forward scattering problems. The proposed algorithm is a combination of Krylov iterative solvers, the fast Fourier transform and the asymptotic waveform evaluation technique. The proposed method is more efficient to compute the wideband results than the conventional method which separately computes the results at individual frequency points