A spectral representation solution for electromagnetic scattering from complex structures

Significant effort has been directed towards improving computational efficiency in calculating radiated or scattered fields from a complex structure over a broad frequency band. The formulation and solution of boundary integral equation methods in commercial and scientific software has seen considerable attention; methods presented in the literature are often abstract, “curve-fits” or lacking a sound foundation in the underlying physics of the problem. Anomalous results are often characterized incorrectly, or require user expertise for analysis, a clear disadvantage in a computer-aided design tool. This dissertation documents an investigation into the motivating theory, limitations and integration into SuperNEC of a technique for the analytical, continuous, wideband description of the response of a complex conducting body to an electromagnetic excitation. The method, referred to by the author as Transfer Function Estimation (TFE) has its foundations in the Singularity Expansion Method (SEM). For scattering and radiation from a perfect electric conductor, the Electric-Field Integral Equation (EFIE) and Magnetic-Field Integral Equation (MFIE) formulations in their Stratton-Chu form are used. Solution by spectral representation methods including the Singular Value Decomposition (SVD), the Singular Value Expansion (SVE), the Singular Function Method (SFM), Singularity Expansion Method (SEM), the Eigenmode Expansion Method (EEM) and Model-Based Parameter Estimation (MBPE) are evaluated for applicability to the perfect electric conductor. The relationships between them and applicability to the scattering problem are reviewed. A common theoretical basis is derived. The EFIE and MFIE are known to have challenges due to ill-posedness and uniqueness considerations. Known preconditioners present possible solutions. The Modified EFIE (MEFIE) and Modified Combined Integral Equation (MCFIE) preconditioner is shown to be consistent with the fundamental derivations of the SEM. Prony’s method applied to the SEM poleresidue approximation enables a flexible implementation of a reduced-order method to be defined, for integration into SuperNEC. The computational expense inherent to the calculation of the impedance matrix in SuperNEC is substantially reduced by a physically-motivated approximation based on the TFE method. iv Using an adaptive approach and relative error measures, SuperNEC iteratively calculates the best continuous-function approximation to the response of a conducting body over a frequency band of interest. The responses of structures with different degrees of resonant behaviour were evaluated: these included an attack helicopter, a log-periodic dipole array and a simple dipole. Remarkable agreement was achieved

An integrated modal approach to surface and volume scattering in ocean acoustic waveguides

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution January 1996Acoustic propagation in the ocean can be strongly affected by small random variations in ocean properties, including rough surfaces and volume fluctuations in the ocean or seabed. Such inhomogeneities scatter part of the incident acoustic field, stripping energy from the coherent part of the field. This scattered energy, or reverberation, propagates further in the modes of the ocean waveguide. The distribution of energy among modes is changed and the coherence of the acoustic field is reduced. This thesis introduces several models which describe scattering of low-frequency sound. First, the rough surface scattering theory of Kuperman and Schmidt is reformulated in terms of normal modes. Scattering from rough fluid-fluid interfaces and rough elastic halfspaces is modeled, and statistics of the acoustic field are calculated. Numerical results show the modal formulation agrees well with Kuperman and Schmidt's model, while reducing computation times by several orders of magnitude for the scenarios considered. Next, a perturbation theory describing scattering from sound speed and density fluctuations in acoustic media is developed. The theory is used to find the scattered field generated by volume fluctuations in sediment bottoms. Modal attenuations due to sediment volume scattering are calculated, and agreement is demonstrated with previous work. The surface and volume scattering theories are implemented in a unified modal reverberation code and used to study bottom scattering in shallow water. Numerical examples are used to demonstrate the relationship between volume and surface scattering. Energy distribution among scattered field modes is found to be a complicated function of the scattering mechanism, the scatterer statistics, and the acoustic environment. In particular, the bottom properties strongly influence the coherence of the acoustic field. Examples show that excitation of fluid-elastic interface waves is a potentially important scattering path. Cross-modal coherences are calculated and used to study the loss of signal coherence with range. Finally, earlier work on scattering from the Arctic ice sheet is extended. Simulations of long-range transmissions are compared with data from the April 1994 trans-Arctic propagation test. The results show modal attenuations and group speeds can be predicted reasonably well, indicating that acoustic monitoring of Arctic climate is feasible.I am extremely grateful for the financial support of the Office of Naval Research, under contracts N00014-92-J -1282 and N00014-95-1-0307

A rigorous analysis of cascaded step discontinuities in open waveguides

SIGLEAvailable from British Library Document Supply Centre- DSC:DX174172 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Finite element and boundary element analysis of electromagnetic NDE phenomena

The endeavor to produce quality products coupled with a drive to minimize failure in major industries such as aerospace, power and transportation is the driving force behind studies of electromagnetic nondestructive evaluation (NDE) methods. Popular domain and integral methods used for the purpose of modeling electromagnetic NDE phenomena include the finite element and boundary element methods. However no single numerical modeling technique has emerged as the optimal choice for all electromagnetic NDE processes. In a computer aided design environment, where the choice of an optimum modeling technique is critical, an evaluation of the various aspects of different numerical approaches is extremely helpful;In this dissertation, a comparison is made of the relative advantages and disadvantages of the finite element (FE) and boundary element (BE) methods as applied to the DC and AC Potential drop (DCPD and ACPD) methods for characterizing fatigue cracks. The comparison covers aspects of robustness, computer resource requirements and ease of numerically implementing the methods. Two dimensional FE and BE models are used to model an infinitely thin fatigue crack using the ACPD method, and a two and three dimensional FE and BE model is used to study the compact tension and single edge notch specimen using the DCPD method. Calibration curves and field plots in the specimen are compared to experimental and analytical data. The FE and BE methods are complementary numerical techniques and are combined to exploit their individual merits in the latter part of this dissertation. A three dimensional hybrid formulation to model eddy current NDE is then developed which discretizes the interior with finite elements and the exterior with boundary elements. The three dimensional model is applied to an absolute eddy current coil over a finite block. A feasibility study to confirm the validity of the formulation is undertaken by comparing the numerical results for probe lift-off and coil impedance measurements with published data;This comparative study outlined above indicates that when the solution is required at discrete points, as in the potential drop methods, or the model needs to handle infinite boundaries, as in eddy current NDE, the boundary element model is more suitable. Since it is based 011 the Green\u27s function, the BE method is limited to linear problems. Finite element analysis gives full field solutions, making it ideal for studying energy/defect interactions. The hybrid FE/BE formulation handles non-linearity and infinite boundaries naturally, thus utilizing the best of both worlds

Method of the Riemann-Hilbert Problem for the Solution of the Helmholtz Equation in a Semi-infinite Strip

In this dissertation, a new method is developed to study BVPs of the modified Helmholtz and Helmholtz equations in a semi-infinite strip subject to the Poincare type, impedance and higher order boundary conditions. The main machinery used here is the theory of Riemann Hilbert problems, the residue theory of complex variables and the theory of integral transforms. A special kind of interconnected Laplace transforms are introduced whose parameters are related through branch of a multi-valued function. In the chapter 1 a brief review of the unified transform method used to solve BVPs of linear and non-linear integrable PDEs in convex polygons is given. Then unified transform method is applied to the BVP of the modified Helmholtz equation in a semi-infinite strip subject to the Poincare type and impedance boundary conditions. In the case of BVP of the modified Helmholtz equation in a semi-infinite strip subject to the impedance boundary conditions, two scalar RHPs are derived, then the closed form solutions of the given BVP are derived. The difficulty in application of the unified transform method to BVP of the Helmholtz equation in a semi infinite strip is discussed later on. The chapter 2 contains application of the finite integral transform (FIT) method to study the BVP for the Helmholtz equation in a semi-infinite strip subject to the Poincare type and impedance boundary conditions. In the case of the impedance boundary conditions, a series representation of the solution of the BVP for the Helmholtz equation in a semi-infinite strip is derived. The Burniston-Siewert method to find integral representations of a certain transcendental equation is presented. The roots of this equation are required for both methods, the FIT method and the RHP based method. To implement the Burniston-Siewert method, we solve a scalar RHP on several segments of the real axis. In chapter 3, we have applied the new method to study the Poincare type and impedance BVPs for the Helmholtz equation in a semi-infinite strip. In the case of the Poincare type boundary conditions an order two vector RHP is derived. In general, it is not possible to find closed form solution of an order two vector RHP. In the case of the impedance boundary conditions two scalar RHPs are derived whose closed form solutions are found. Then the series representation for solution of the BVP of the Helmholtz equation in a semi-infinite strip subject to the impedance boundary conditions, is recovered using the inverse transform operator, and the residue theory of complex variables. The numerical results are presented for various values of the parameters involved. It is observed that the FIT method and the new method generate exactly the same solution of the BVP of the Helmholtz equation in a semi-infinite strip subject to the impedance boundary conditions. In chapter 4, we have applied the new method to study the acoustic scattering from a semi-infinite strip subject to higher order boundary conditions. Two scalar RHPs are derived whose closed form solutions are found. A unique solution of the problem is obtained

The Physics of Rodent Ultrasonic Vocalizations

Although much work has been done on the physics of vocalizations caused by the vibrating motion of vocal folds, relatively little work has been done on the physics of ultrasonic vocalizations (USVs). There are two orders of mammals known to make these kind of vocalizations: cetaceans and rodents. Of these two the mechanism behind the rodent calls are better understood. Thus, this thesis investigates the physics of rodent USVs with the hope that findings will help elucidate the mechanisms behind cetacean USVs. Chapter 1 discusses the anatomical background of rodent vocal tracts, evolutionary pressures that shaped the development of USVs, physical modeling of vibrating vocal folds, and experimental work that discounts the possibility of vibrating vocal folds as the mechanism behind rodent USVs. Chapter 2 discusses acoustic and fluid dynamics background as well as a previously proposed physical model, known as the hole tone, for the rodent USV mechanism. Chapter 3 discusses an original data analysis of rodent USVs. This analysis exploits the presence of frequency jumps in the USVs. These frequency jumps are extracted. A machine learning model is then used to fit the frequency jumps to acoustic equations. The results of this analysis show that the hole tone model is incorrect. Chapter 4 discusses original modeling of the rodent vocal production mechanism, in which the rodent vocal tract is treated as a resonator driven by a jet of air emerging from the vocal folds. This representation of the rodent vocal tract is used to derive a set of time domain acoustic oscillator equations, which describe the transient acoustics of rodent USVs. It is found in chapter 4 that an additional driving mechanism is needed in the oscillator equations, or the acoustic oscillations will decay to a fixed point. Chapter 5 discusses several attempts at including this driving mechanism by considering the forcing that results from the formation of vortex rings in the rodent vocal tract. First, a linear frequency domain approach is attempted. However, it is found that this approach is incompatible with the time domain equations of chapter 4. Next, a nonlinear time domain approach is attempted. This approach is compatible with the time domain equations of chapter 4, and solves the decay problem that occurs without the additional driving force. Furthermore, the model is able to reproduce the 22 kHz alarm call made by rats. However, it is unable to produce the higher harmonics or the frequency jumps observed in rodent USVs. It is concluded that the model is successful in producing the fundamental frequency of the rodent vocal tract, but it seems to be neglecting a mechanism which can account for the higher harmonics and the frequency jumps

Remote Sensing of the Ocean Environment Using Finite Element Methods

Oceans are a vast, complex world where underwater sound is the most efficient tool available to understand its detailed characteristics. However the underwater channel has a very complex geometrical and material structure and hence special techniques are required to model it. Analytical solutions are feasible only when one makes gross assumptions and approximations. Several numerical and semi-numerical techniques have been developed for estimating the sound field in the ocean channel. But no single method is capable of handling all possible environmental conditions, frequency, and ranges of interest in remote sensing problems. We explore in this chapter the scope and feasibility of finite element method in underwater remote sensing. The current study is based on a channel model with cylindrical symmetry and a time-harmonic source signal. A variational formulation is used to derive the finite element model for acoustical radiation, scattering and propagation in the ocean. A Bayliss-type radiation boundary condition is used to model the far field behaviour without the need to deal with a large solution domain. Since the ocean geometry can support several propagating, evanescent, and radiation modes, a penalty function approach is employed to impose the far field radiation condition. A distinct feature of the ocean channel is its depth-dependent sound speed. The eigensolution for this channel is required for imposing the radiation condition at the truncation boundary. We have cast this eigenproblem in a variational form and employed a Rayleigh-Ritz method to obtain an approximate eigensolution. This approach has provided a good approximation of the depth eigenmodes in a compact semi-analytic form. We have employed our finite element algorithm to model several range- and depth-dependent ocean problems. Our numerical study has established that our finite element algorithm gives accurate results with reasonable effort. In particular, our finite element approach is most appropriate for shallow water problems where the interaction of wave modes with irregular ocean bottom is quite complex. The penalty function approach employed to implement the radiation boundary condition has been found to be robust over a wide range of penalty scale factors. We have also extended this work for the case of irregular elastic sea bed. We continue to explore and further develop our finite element approach by applying it to several other ocean acoustic problems encountered in the remote sensing of ocean environment

Efficient modeling of sound source radiation in free-space and room environments

Motivated by the need to develop efficient acoustics simulations for sources in different room environments, a modeling procedure has been proposed that consists of two steps in general: (1) the modeling of the free-space radiation of the source based on measurements in a anechoic environment, and (2) the prediction of the sound field in a room environment based on that free-space information. To achieve a high modeling efficiency, i.e., to reduce the number of modeling parameters while still maintaining acceptable accuracy, a Multipole Equivalent Source Model (ESM) with undetermined source locations has been developed for the free-space sound field prediction. In contrast with traditional ESM’s, or acoustical holography methods in general, the model developed in the present work possesses two efficiency improvements: (1) the use of the series of monopoles, dipoles, quadrupoles, etc. as equivalents sources (since in predicting the sound field, the multipole series can be simply represented as closely located monopoles) and (2) the flexibility of using spatially separated sources with undetermined locations. In the inverse parameter estimation process of this method, the calculation of the source strengths is linear while the source locations are determined by a nonlinear optimization procedure. It is shown, by an experimental validation, that the prediction using this method can be accurate for almost the whole audio frequency range. To model the sound field at high frequencies specifically, different types of methods using local-basis functions were developed. At high frequencies, the spatial variation of the sound field is usually large and thus the number of measurements points in space is likely not to be enough to model a relatively complicated source if a traditional equivalent source model is used, and the under-sampling errors from all regions will accumulate to affect the predictions in any particular region. However, if localized basis functions are used to represent the sound field, the under-sampling errors from different regions do not affect each other. Two types of local-basis method are developed in this work: one based on piece-wise polynomial interpolation (which is limited to having only a single source) and the other based on least squares (which can be applied to multiple sources and even to interior problems). Simulation results have shown that these local-basis methods, at very high frequencies, can achieve good overall prediction accuracy with only a loss of some details in the spatial variation of the sound field. In the room acoustics modeling section, the Equivalent Source Method is modified and implemented which, compared with the geometric acoustics models, gives a prediction based on a more rigorous mathematical foundation and, compared with Boundary Element methods, reduces the computational intensity. In this proposed room acoustics ESM, the free-space source radiation is assumed known, and the room component sound field is determined by an ESM. Differing from the free-space ESMs, this room acoustics ESM (1) contains additional equivalent sources representing the incoming waves, and (2) uses impedance boundary conditions on the surfaces instead of the measured sound field, to estimate the source strengths. It is validated by simulations (in both 2D and 3D spaces) and then by experiments that the proposed room acoustics ESM can be used as a reduced order modeling technique in simulating the sound field in a room. It is also shown that the prediction accuracy and the computational load can be flexibly balanced, if Multipole ESMs are used, by selecting an appropriate maximum source order