Doctor of Philosophy / Department of Mathematics / Alexander G. Ramm / In this thesis, the author presents several numerical methods for solving scalar and electromagnetic wave scattering problems. These methods are taken from the papers of Professor Alexander Ramm and the author, see [1] and [2]. In Chapter 1, scalar wave scattering by many small particles of arbitrary shapes with impedance boundary condition is studied. The problem is solved asymptotically and numerically under the assumptions a << d << λ, where k = 2π/λ is the wave number, λ is the wave length, a is the characteristic size of the particles, and d is the smallest distance between neighboring particles. A fast algorithm for solving this wave scattering problem by billions of particles is presented. The algorithm comprises the derivation of the (ORI) linear system and makes use of Conjugate Orthogonal Conjugate Gradient method and Fast Fourier Transform. Numerical solutions of the scalar wave scattering problem with 1, 4, 7, and 10 billions of small impedance particles are achieved for the first time. In these numerical examples, the problem of creating a material with negative refraction coefficient is also described and a recipe for creating materials with a desired refraction coefficient is tested. In Chapter 2, electromagnetic (EM) wave scattering problem by one and many small perfectly conducting bodies is studied. A numerical method for solving this problem is presented. For the case of one body, the problem is solved for a body of arbitrary shape, using the corresponding boundary integral equation. For the case of many bodies, the problem is solved asymptotically under the physical assumptions a << d << λ, where a is the characteristic size of the bodies, d is the minimal distance between neighboring bodies, λ = 2π/k is the wave length and k is the wave number. Numerical results for the cases of one and many small bodies are presented. Error analysis for the numerical method are also provided.

Made available in DSpace on 2014-12-17T14:55:56Z (GMT). No. of bitstreams: 1 AdrianoGS.pdf: 778842 bytes, checksum: bec8b3adf6e4043d40c60a7d9b9c6b70 (MD5) Previous issue date: 2006-06-12 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Recently, an amazing development has been observed in telecommunication systems. Two good examples of this development are observed in mobile communication and aerospace systems. This impressive development is related to the increasing need for receiving and transmitting communication signals. Particularly, this development has required the study of new antennas and filters. This work presents a fullwave analysis of reflectarrays. The considered structures are composed by arrays of rectangular conducting patches printed on multilayer dieletric substrates, that are mounted on a ground plane. The analysis is developed in the spectral domain, using an equivalent transmission line method in combination with Galerkin method. Results for the reflection coefficient of these structures are presented and compared to those available in the literature. A good agreement was observed. Particularly, the developed analysis uses the transmission lines theory in combination with the incident potentials and the field continuity equations, at the structures interfaces, for obtaining the scattered field components expressions as function of the patch surface currents and of the incident field. Galerkin method is used to determine the unknown coefficients in the boundary value problem. Curves for the reflection coefficient of several reflectarray geometries are presented as function of frequency and of the structural parameters / Os constantes avan?os das telecomunica??es tornam-se cada vez mais evidentes nas ?ltimas d?cadas. As tecnologias de comunica??es m?veis e da ind?stria aeroespacial s?o um bom exemplo desta evolu??o. Isto ocorreu devido ao aumento do fluxo de dados a serem transmitidos. Para suprir essa demanda, novas tecnologias v?m surgindo na constru??o de antenas e na filtragem dos sinais de RF. Este trabalho apresenta uma an?lise de onda completa de estrutura de arranjos refletores (reflectarray). A estrutura analisada ? composta por um arranjo de patches condutores retangulares depositados sobre um substrato com duas camadas de materiais iso/anisotr?picos, que por sua vez est?o montadas sobre um plano de terra. A an?lise foi efetuada no dom?nio espectral, sendo utilizado o m?todo da linha de transmiss?o equivalente em combina??o com o m?todo de Galerkin. Como resultado foram obtidos os coeficientes de reflex?o (amplitude e fase) correspondentes para as estruturas analisadas. Para valida??o desses resultados foi realizada uma compara??o com os resultados dispon?veis na literatura. Especificamente, a an?lise desenvolvida usa a teoria de linha de transmiss?o em conjunto com os potenciais incidentes e com a imposi??o da continuidade dos campos nas interfaces de contorno, para a obten??o das express?es das componentes dos campos espalhados em fun??o das densidades de corrente do patch e dos campos incidentes. O m?todo de Galerkin ? utilizado na determina??o num?rica dos coeficientes pesos desconhecidos. Desta forma, s?o determinados os coeficientes de reflex?o (amplitude e fase) das estruturas consideradas

Made available in DSpace on 2014-12-17T14:56:21Z (GMT). No. of bitstreams: 1 AdrianoGS.pdf: 947514 bytes, checksum: 6261ee06e26f3e814492d948462a3233 (MD5) Previous issue date: 2006-06-12 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Recently, an amazing development has been observed in telecommunication systems. Two good examples of this development are observed in mobile communication and aerospace systems. This impressive development is related to the increasing need for receiving and transmitting communication signals. Particularly, this development has required the study of new antennas and filters. This work presents a fullwave analysis of reflectarrays. The considered structures are composed by arrays of rectangular conducting patches printed on multilayer dieletric substrates, that are mounted on a ground plane. The analysis is developed in the spectral domain, using an equivalent transmission line method in combination with Galerkin method. Results for the reflection coefficient of these structures are presented and compared to those available in the literature. A good agreement was observed. Particularly, the developed analysis uses the transmission lines theory in combination with the incident potentials and the field continuity equations, at the structures interfaces, for obtaining the scattered field components expressions as function of the patch surface currents and of the incident field. Galerkin method is used to determine the unknown coefficients in the boundary value problem. Curves for the reflection coefficient of several reflectarray geometries are presented as function of frequency and of the structural parameters / Os constantes avan?os das telecomunica??es tornamse cada vez mais evidentes nas ?ltimas d?cadas. As tecnologias de comunica??es m?veis e da ind?stria aeroespacial s?o um bom exemplo desta evolu??o. Isto ocorreu devido ao aumento do fluxo de dados a serem transmitidos. Para suprir essa demanda, novas tecnologias v?m surgindo na constru??o de antenas e na filtragem dos sinais de RF. Este trabalho apresenta uma an?lise de onda completa de estrutura de arranjos refletores (reflectarray). A estrutura analisada ? composta por um arranjo de patches condutores retangulares depositados sobre um substrato com duas camadas de materiais iso/anisotr?picos, que por sua vez est?o montadas sobre um plano de terra. A an?lise foi efetuada no dom?nio espectral, sendo utilizado o m?todo da linha de transmiss?o equivalente em combina??o com o m?todo de Galerkin. Como resultado foram obtidos os coeficientes de reflex?o (amplitude e fase) correspondentes para as estruturas analisadas. Para valida??o desses resultados foi realizada uma compara??o com os resultados dispon?veis na literatura. Especificamente, a an?lise desenvolvida usa a teoria de linha de transmiss?o em conjunto com os potenciais incidentes e com a imposi??o da continuidade dos campos nas interfaces de contorno, para a obten??o das express?es das componentes dos campos espalhados em fun??o das densidades de corrente do patch e dos campos incidentes. O m?todo de Galerkin ? utilizado na determina??o num?rica dos coeficientes pesos desconhecidos. Desta forma, s?o determinados os coeficientes de reflex?o (amplitude e fase) das estruturas consideradas

The reduction of noise generated by new and existing engineering products is of increasing importance commercially, socially and environmentally. Commercially, the noise emission of vehicles, such as cars and aircraft, may often be considered a selling point and the effects of noise pollution on human health and the environment has led to legislation restricting the noise emissions of many engineering products. Noise prediction schemes are important tools to help us understand and develop a means of controlling noise. Acoustic problems present numerous challenges to traditional CFD-type numerical methods rendering all but the most trivial problems unsuitable. Difficulties relate to the length scale discrepancies which arise due to the relatively tiny pressure and density fluctuations of an acoustic wave propagating over large distancesto the point of interest; the result being large computational domains to capture wave behaviour accurately between source and observer. Noise prediction may be performed using a hybrid Computational Aero-Acoustics (CAA) scheme, an approach to noise prediction which alleviates many issues associated with exclusively numerical or analytical approaches. Hybrid schemes often rely on knowledge of a Green’s function, representing the scattering of the geometry, to propagate source fluctuations to the far-field. Presently, these functions only exist in analytical form for relatively simple geometries. This research develops principles for the robust calculation of Green’s functions for general situations. In order to achieve this, three techniques to computeGreen’s functions for the Helmholtz equation within an extended class of 2D geometries are developed, evaluated and compared. Where appropriate, their extension to 3D is described. Guidance is provided on the selection of a suitable numerical method in practice given knowledge of the geometry of interest. Through inclusion of the numerical methods for the construction of Green’s functions presented here, the applicability of existing hybrid schemes will be significantly extended. Thus, it is expected that noise predictions may be performed on a more general range of geometries while exploiting the computational efficiency of hybrid prediction schemes.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第20513号 / 情博第641号 / 新制||情||111(附属図書館) / 京都大学大学院情報学研究科複雑系科学専攻 / (主査)教授 西村 直志, 教授 磯 祐介, 准教授 吉川 仁 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

No description available.

In this work the scattering of an incident plane wave propagating along a plane perpendicular to the xy-plane is studied. The wave is scattered from an infinitely long cylindrical object of arbitrary cross-section. Due to the arbitrary geometry of the obstacle, a finite differences numerical method is employed to approximate the solution of the scattering problems. The wave equation is expressed in terms of generalized curvilinear coordinates. Boundary conforming grids are generated using elliptic grid generators. Then, a explicit marching in time scheme is implemented over these grids. It is found that as time grows the numerical solution converges to a wave with harmonic time dependence. The amplitude of these waves is analyzed and graphed over generalized grids for different geometries. An important physical measure of the energy scattered, the differential scattering cross section, is also obtained. In particular, the method is applied to a circular cylindrical obstacle. For this case, the analytical solution can also be obtained by traditional spectral techniques. The method is validated by comparing this exact solution with the numerical approximation obtained from the application of it.

This thesis concerns the numerical simulation of creeping rays and their contribution to high frequency scattering problems. Creeping rays are a type of diffracted rays which are generated at the shadow line of the scatterer and propagate along geodesic paths on the scatterer surface. On a perfectly conducting convex body, they attenuate along their propagation path by tangentially shedding diffracted rays and losing energy. On a concave scatterer, they propagate on the surface and importantly, in the absence of dissipation, experience no attenuation. The study of creeping rays is important in many high frequency problems, such as design of sophisticated and conformal antennas, antenna coupling problems, radar cross section (RCS) computations and control of scattering properties of metallic structures coated with dielectric materials. First, assuming the scatterer surface can be represented by a single parameterization, we propose a new Eulerian formulation for the ray propagation problem by deriving a set of escape partial differential equations in a three-dimensional phase space. The equations are solved on a fixed computational grid using a version of fast marching algorithm. The solution to the equations contain information about all possible creeping rays. This information includes the phase and amplitude of the ray field, which are extracted by a fast post-processing. The advantage of this formulation over the standard Eulerian formulation is that we can compute multivalued solutions corresponding to crossing rays. Moreover, we are able to control the accuracy everywhere on the scatterer surface and suppress the problems with the traditional Lagrangian formulation. To compute all possible creeping rays corresponding to all shadow lines, the algorithm is of computational order O(N3 log N), with N3 being the total number of grid points in the computational phase space domain. This is expensive for computing the wave field for only one shadow line, but if the solutions are sought for many shadow lines (for many illumination angles), the phase space method is more efficient than the standard methods such as ray tracing and methods based on the eikonal equation. Next, we present a modification of the single-patch phase space method to a multiple-patch scheme in order to handle realistic problems containing scatterers with complicated geometries. In such problems, the surface is split into multiple patches where each patch has a well-defined parameterization. The escape equations are solved in each patch, individually. The creeping rays on the scatterer are then computed by connecting all individual solutions through a fast post-processing. We consider an application to mono-static radar cross section problems where creeping rays from all illumination angles must be computed. The numerical results of the fast phase space method are presented. / QC 20101119

Attention has been focused on electromagnetic chirality and its potential applications to microwave, millimeter wave and optical wave devices. In this work, wave propagation through a chiral periodic structure with arbitrary shape is investigated. Although perturbation theory and coupled-mode theory have been used to analyze chiral periodic structure, those are approximate methods and can only be used for low frequency applications. In this work, the rigorous mode-matching method is used to solve the problem. Staircase approximation is introduced to change the curved structure to a multilayer structure. The field solutions in the uniform air regions and unbounded air-chiral periodic array have been derived. Finite element method is used to solve the eigenvalues and eigenfunctions in the periodic chiral slabs. Mode-matching method is used at the boundaries to calculate the scattering characteristics. Numerical results are displayed to explain the underlying physical properties of the chiral periodic structure. The Wood's anomalies at high frequencies have been investigated and explained by the excitation of leaky waves guided along the periodic layer. The influence of frequency, chirality parameter, incident angle, curve shape and period are discussed. It has been found that the chiral periodic structure can be used as both a frequency selective device and a mode conversion device. First, the derivation and numeric calculation were done with the principal plane incidence. Then, the discussion was extended to the more general case of oblique incidence by the coordinate transformation.

No / A novel technique for the laboratory characterization of the frequency-dependent acoustic surface admittance of partly saturated samples of sands is presented. The technique is based on a standard laboratory de-watering apparatus coupled with a standard acoustic impedance tube. The dependence of the surface admittance on the degree of water saturation is investigated for two samples of sand with widely different flow resistivities. It is shown that a relatively small change (e.g., from 0% to 11% by volume) in the degree of water saturation can result in a much larger change (e.g., twofold) in the acoustic surface admittance. An empirical relationship is found between the peaks observed in the real part of admittance spectra for the low flow resistivity sand and the degree of water saturation. The data are compared with predictions of two widely used ground impedance models: a semiempirical single parameter model and a two parameter model. A modified two-parameter version of a single-parameter model is found to give comparable fit to the two-parameter model. However, neither model provides an accurate fit.