A Fast Numerical Solution of Scattering by a Cylinder: Spectral Method for the Boundary Integral Equations

It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converge slowly for high frequency waves. In this paper, a fast numerical solution is presented for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single- and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, it is shown that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented. © 1994, Acoustical Society of America

Notes on solving Maxwell equations, part 2, Green's function for stratified media

In the previous report (part 1), the problem and its governing equations are described and is discarded in this report. The finite element method in part 1, or any other method for that matter, determines the fields in and close to the scatterer (near-field) that is used to construct the fields in the far-field. The goal of part 2 is to find far-field expressions formulated as total fields or the Radar Cross Section (RCS) of the scattered fields. The far-field is calculated from the scatterer problem in the contrast formulation. The scatterer then acts as a radiating object with a known source J. Using Green's function theory, the far-field solution is just the convolution of that source with the fundamental solution G to the Maxwell equation. Without loss of generality, the expressions are formulated in total fields E and H. Again, the time convention for the time-harmonic term exp(-i¿t) is used, but in contrary to part 1, the quantities are in full dimensions, following closely the notation used by Chew, Balanis and others

A Study of a Reimaging System for Correcting Large-Scale Phase Errors in Reflector Antennas

This thesis investigates a new approach for dealing with the adverse effects of large-scale deformations in the main reflector of large Cassegrain antennas. In this method, the incident aperture distribution is imaged onto a tertiary focal plane. This is accomplished by using an optical imaging system consisting of a lens mounted behind the Cassegrain focus of the antenna. The lens forms a real image of the product of the incident aperture distribution and the pupil function of the antenna. The pupil function describes the profile of the main reflector of the antenna. If the incident aperture distribution is a plane wave, a real image of the pupil function of the main reflector will be produced at the focal plane of the image lens. Any imperfections in the main reflector will be imaged onto the tertiary focal plane but over a smaller area as defined by the magnification of the system. In principle, an active correcting element placed into the tertiary focal plane could compensate for these errors, thus preserving the maximum efficiency of the antenna. Experimental verification of this principle was carried out in the lab using a dielectric lens 152.4mm in diameter. Phase perturbations were simulated by placing dielectric shims in the incident aperture plane. The phase of these shims in most cases was measured to within 10 degrees in the image plane. This degree of accuracy is found to be quite adequate for correcting large-scale errors in the main reflector of the antenna

Fast integral methods for conformal antenna and array modeling in conjunction with hybrid finite element formulations

Fast integral methods are used to improve the efficiency of hybrid finite element formulations for conformal antenna and array modeling. We consider here cavity-backed configurations recessed in planar and curved ground planes as well as infinite periodic structures with boundary integral (BI) terminations on the top and bottom bounding surfaces. Volume tessellation is based on triangular prismatic elements which are well suited for layered structures and still give the required modeling flexibility for irregular antenna and array elements. For planar BI terminations of finite and infinite arrays the adaptive integral method is used to achieve O(NlogN) computational complexity in evaluating the matrix-vector products within the iterative solver. In the case of curved mesh truncations for finite arrays the fast multipole method is applied to obtain O(N1.5) complexity for the evaluation of the matrix-vector products. Advantages and disadvantages of these methods as they relate to different applications are discussed, and numerical results are provided

Computational aspects of electromagnetic NDE phenomena

The development of theoretical models that characterize various physical phenomena is extremely crucial in all engineering disciplines. In nondestructive evaluation (NDE), theoretical models are used extensively to understand the physics of material/energy interaction, optimize experimental design parameters and solve the inverse problem of defect characterization. This dissertation describes methods for developing computational models for electromagnetic NDE applications. Two broad classes of issues that are addressed in this dissertation are related to (i) problem formulation and (ii) implementation of computers;The two main approaches for solving physical problems in NDE are the differential and integral equations. The relative advantages and disadvantages of the two approaches are illustrated and models are developed to simulate electromagnetic scattering from objects or inhomogeneities embedded in multilayered media which is applicable in many NDE problems. The low storage advantage of the differential approach and the finite solution domain feature of the integral approach are exploited. Hybrid techniques and other efficient modeling techniques are presented to minimize the storage requirements for both approaches;The second issue of computational models is the computational resources required for implementation. Implementations on conventional sequential computers, parallel architecture machines and more recent neural computers are presented. An example which requires the use of massive parallel computing is given where a probability of detection model is built for eddy current testing of 3D objects. The POD model based on the finite element formulation is implemented on an NCUBE parallel computer. The linear system of equations is solved using direct and iterative methods. The implementations are designed to minimize the interprocessor communication and optimize the number of simultaneous model runs to obtain a maximum effective speedup;Another form of parallel computing is the more recent neurocomputer which depends on building an artificial neural network composed of numerous simple neurons. Two classes of neural networks have been used to solve electromagnetic NDE inverse problems. The first approach depends on a direct solution of the governing integral equation and is done using a Hopfield type neural network. Design of the network structure and parameters is presented. The second approach depends on developing a mathematical transform between the input and output space of the problem. A multilayered perceptron type neural network is invoked for this implementation. The network is augmented to build an incremental learning network which is motivated by the dynamic and modular features of the human brain

An introduction to acoustics

This is an extended and revised edition of IWDE 92-06

Source radiation analysis based on spatial transformation of acoustic fields

Source radiation analysis frequently involves characterization or identification of sound sources and fields. In order to effectively perform source radiation analysis, an integrated acoustical imaging system including software and hardware was developed based on spatial transformation. This system utilizes measurements of the complex sound field over a two-dimensional hologram surface with the one-microphone sequential sampling method. Four spatial transformation techniques, i.e. direct convolution, two-dimensional fast Fourier transform, Gauss-Hermite decomposition, and singular value decomposition, were implemented to project the hologram data to desired locations in the three-dimensional space. In addition, four new approaches based on feedback iteration concepts, with the variations of optimization and constraints, were developed to deal particularly with the ill-posed nature encountered in the backward reconstruction of source images;The theoretical background, numerical or experimental investigations, and applicational considerations of the previously mentioned aspects are thoroughly discussed in the dissertation. The conclusions detail the significance of the research results and the future prospects for radiation analysis based on spatial transformation. The technical aspects of the experimental implementation such as a computerized data acquisition system are also included in the appendix