Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Fast Numerical Methods For High Frequency Wave Scattering
Download Fast Numerical Methods For High Frequency Wave Scattering full books in PDF, epub, and Kindle. Read online Fast Numerical Methods For High Frequency Wave Scattering ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Fast Numerical Methods for High Frequency Wave Scattering by : Khoa Dang Tran
Download or read book Fast Numerical Methods for High Frequency Wave Scattering written by Khoa Dang Tran and published by . This book was released on 2012 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer simulation of wave propagation is an active research area as wave phenomena are prevalent in many applications. Examples include wireless communication, radar cross section, underwater acoustics, and seismology. For high frequency waves, this is a challenging multiscale problem, where the small scale is given by the wavelength while the large scale corresponds to the overall size of the computational domain. Research into wave equation modeling can be divided into two regimes: time domain and frequency domain. In each regime, there are two further popular research directions for the numerical simulation of the scattered wave. One relies on direct discretization of the wave equation as a hyperbolic partial differential equation in the full physical domain. The other direction aims at solving an equivalent integral equation on the surface of the scatterer. In this dissertation, we present three new techniques for the frequency domain, boundary integral equations.
Author :National Aeronautics and Space Administration (NASA) Publisher :Createspace Independent Publishing Platform ISBN 13 :9781721999552 Total Pages :38 pages Book Rating :4.9/5 (995 download)
Book Synopsis A Fast Numerical Solution of Scattering by a Cylinder by : National Aeronautics and Space Administration (NASA)
Download or read book A Fast Numerical Solution of Scattering by a Cylinder written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-28 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 converges slowly for high frequency waves. In this paper, we present a fast number solution 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, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented. Hu, Fang Q. Unspecified Center NAS1-19480; RTOP 505-90-52-01...
Book Synopsis A Fast Numerical Solution of Scattering by a Cylinder: Spectral Method for the Boundary Integral Equations by : Fang Q. Hu
Download or read book A Fast Numerical Solution of Scattering by a Cylinder: Spectral Method for the Boundary Integral Equations written by Fang Q. Hu and published by . This book was released on 1994 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topics in Computational Wave Propagation by : Mark Ainsworth
Download or read book Topics in Computational Wave Propagation written by Mark Ainsworth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: These ten detailed and authoritative survey articles on numerical methods for direct and inverse wave propagation problems are written by leading experts. Researchers and practitioners in computational wave propagation, from postgraduate level onwards, will find the breadth and depth of coverage of recent developments a valuable resource. The articles describe a wide range of topics on the application and analysis of methods for time and frequency domain PDE and boundary integral formulations of wave propagation problems. Electromagnetic, seismic and acoustic equations are considered. Recent developments in methods and analysis ranging from finite differences to hp-adaptive finite elements, including high-accuracy and fast methods are described with extensive references.
Book Synopsis Asymptotic and Numerical Methods for High-frequency Scattering Problems by : Tatiana Kim
Download or read book Asymptotic and Numerical Methods for High-frequency Scattering Problems written by Tatiana Kim and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the development, analysis and implementation of efficient and accurate numerical methods for solving high-frequency acoustic scattering problems. Classical boundary or finite element methods that are based on approximating the solution by polynomials can be effective for small and moderate frequencies. However, as the frequency increases, the solution to the scattering problem becomes more oscillatory and classical numerical methods cope very badly with high oscillation. For example, for two-dimensional scattering problems, classical numerical methods require their number of degrees of freedom to grow at least linearly with frequency to capture the oscillatory behaviour of the solution accurately. Therefore, at large frequencies, classical numerical methods become essentially numerically intractable. In order to overcome the limitations of classical methods, one can seek to incorporate the known asymptotic behaviour of the solution in the numerical method. This involves using asymptotic theory to determine the oscillatory part of the solution and then using classical numerical methods to approximate the slowly varying remainder. Such methods are often referred to as hybrid numerical-asymptotic methods. Determining the high frequency asymptotics of acoustic scattering problems is a classic problem in applied mathematics, with methods such as geometrical optics or the geometrical theory of diffraction providing asymptotic expansions of the solutions. Considerable amount of research has been directed towards both constructing these asymptotic expansions and proving error bounds for truncated asymptotic series of the solution, notably by Buslaev [23], Morawetz and Ludwig [78], and Melrose and Taylor [75], among others. Often, the oscillatory component of the solution can be determined explicitly from these asymptotic expansions. This can then be used in designing ecient hybrid methods. Furthermore, from the asymptotic expansions, frequency-dependent bounds on the slowly-varying remainder and its derivatives can be obtained (in some cases these follow directly from classical results, in other cases some additional work is required). The frequency-dependent bounds are the key results used in the frequency-explicit numerical error analysis of the approximation of the slowly-varying remainder. This thesis presents a rigorous justification of one of the key result using only elementary techniques. Hybrid numerical-asymptotic methods have been shown in theory to be substantially more efficient than classical numerical methods alone. For example, [40] presented a hybrid numerical-asymptotic method in the context of boundary integral equations (BIEs) for solving the problem of high-frequency scattering by smooth, convex obstacles in two dimensions. It was proved in [40] that in order to maintain the accuracy as the frequency increases, the hybrid BIE method requires the number of degrees of freedom to grow slightly faster than k1=9, where k is a parameter proportional to the frequency. This is a substantial improvement from the classical boundary integral methods that require O(k) number of degrees of freedom to achieve the same accuracy for this problem. Despite this slow growth in the number of degrees of freedom, hybrid numerical-asymptotic methods lead to stiffness matrices with entries that are highly-oscillatory singular integrals that can not be computed exactly. Thus, without efficient and accurate numerical treatment of these integrals, the hybrid numerical-asymptotic methods, regardless of their attractive theoretical accuracy, can not be efficiently implemented in practice. In order to resolve this difficulty, this thesis develops a methodology for approximating the integrals arising from hybrid methods in the context of BIEs. The integrals are transformed under a change of variables into integrals amenable to Filon-type quadratures. Filon-type quadratures are designed to cope well with high oscillations in the integrands. Then, graded meshes are used to capture the singularities accurately. Along with k-explicit error bounds for the integration methods, this thesis derives k-explicit error bounds for the hybrid BIE methods that incorporate the error of the inexact approximation of the entries of the stiffness matrix. The error bounds suggest that, with an appropriate choice of parameters of Filon quadrature and mesh grading, the overall error of the hybrid method does not deteriorate due to inexact approximation of the stiffness matrix, therefore preserving its attractive theoretical convergence properties.
Book Synopsis Wave and Scattering Methods for Numerical Simulation by : Stefan Bilbao
Download or read book Wave and Scattering Methods for Numerical Simulation written by Stefan Bilbao and published by John Wiley & Sons. This book was released on 2004-10-22 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering-based numerical methods are increasingly applied to the numerical simulation of distributed time-dependent physical systems. These methods, which possess excellent stability and stability verification properties, have appeared in various guises as the transmission line matrix (TLM) method, multidimensional wave digital (MDWD) filtering and digital waveguide (DWN) methods. This text provides a unified framework for all of these techniques and addresses the question of how they are related to more standard numerical simulation techniques. Covering circuit/scattering models in electromagnetics, transmission line modelling, elastic dynamics, as well as time-varying and nonlinear systems, this book highlights the general applicability of this technique across a variety of disciplines, as well as the inter-relationships between simulation techniques and digital filter design. provides a comprehensive overview of scattering-based numerical integration methods. reviews the basics of classical electrical network theory, wave digital filters, and digital waveguide networks. discusses applications for time-varying and nonlinear systems. includes an extensive bibliography containing over 250 references. Mixing theory and application with numerical simulation results, this book will be suitable for both experts and readers with a limited background in signal processing and numerical techniques.
Book Synopsis Numerical Methods for High Frequency Scattering by Multiple Obstacles by : Andrew Gibbs
Download or read book Numerical Methods for High Frequency Scattering by Multiple Obstacles written by Andrew Gibbs and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for High Frequency Scattering by Multiple Obstacles by : Andrew James Gibbs
Download or read book Numerical Methods for High Frequency Scattering by Multiple Obstacles written by Andrew James Gibbs and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Nystrom Method in Electromagnetics by : Mei Song Tong
Download or read book The Nystrom Method in Electromagnetics written by Mei Song Tong and published by John Wiley & Sons. This book was released on 2020-07-06 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, step-by-step reference to the Nyström Method for solving Electromagnetic problems using integral equations Computational electromagnetics studies the numerical methods or techniques that solve electromagnetic problems by computer programming. Currently, there are mainly three numerical methods for electromagnetic problems: the finite-difference time-domain (FDTD), finite element method (FEM), and integral equation methods (IEMs). In the IEMs, the method of moments (MoM) is the most widely used method, but much attention is being paid to the Nyström method as another IEM, because it possesses some unique merits which the MoM lacks. This book focuses on that method—providing information on everything that students and professionals working in the field need to know. Written by the top researchers in electromagnetics, this complete reference book is a consolidation of advances made in the use of the Nyström method for solving electromagnetic integral equations. It begins by introducing the fundamentals of the electromagnetic theory and computational electromagnetics, before proceeding to illustrate the advantages unique to the Nyström method through rigorous worked out examples and equations. Key topics include quadrature rules, singularity treatment techniques, applications to conducting and penetrable media, multiphysics electromagnetic problems, time-domain integral equations, inverse scattering problems and incorporation with multilevel fast multiple algorithm. Systematically introduces the fundamental principles, equations, and advantages of the Nyström method for solving electromagnetic problems Features the unique benefits of using the Nyström method through numerical comparisons with other numerical and analytical methods Covers a broad range of application examples that will point the way for future research The Nystrom Method in Electromagnetics is ideal for graduate students, senior undergraduates, and researchers studying engineering electromagnetics, computational methods, and applied mathematics. Practicing engineers and other industry professionals working in engineering electromagnetics and engineering mathematics will also find it to be incredibly helpful.
Book Synopsis High-order Wave Tracking Strategy for Solving High-frequency Scattering Problems by : Inga Girshfeld
Download or read book High-order Wave Tracking Strategy for Solving High-frequency Scattering Problems written by Inga Girshfeld and published by . This book was released on 2021 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave equations effectively model physical phenomena, applying but not limited to earthquake engineering, geophysical exploration, medical imaging, nondestructive testing, underwater acoustics, electromagnetics, etc. Extensively studied for over a century, the mathematics of wave propagation problems are relatively well-understood, but their computation poses substantial issues, especially for high-frequency regime [3]. Traditional FEM techniques require fine discretization or high order elements, resulting in the pollution effect [1] and numerical instabilities. Over the last few decades, significant efforts have been dedicated toward developing alternative techniques, including a least-squares method, plane wave discontinuous Galerkin methods, etc. Helmholtz problems, which describe time harmonic wave propagation, are well understood mathematically [3], but difficult to solve numerically in the high-frequency regime [1]. Moreover, practical applications of the Helmholtz equation demand solving systems with more than ten million complex unknowns in the mid-frequency range. Thus, reducing the computational cost and the complexity of implementation while preserving the level of accuracy and expanding the frequency regime would have far-reaching effects in the area of real-world application as well as in the computationally important infrastructure. We propose a numerical method to efficiently solve the Helmholtz problem in the high-frequency wave regime by implementing oscillating basis functions, along with a wave tracking strategy to align the basis functions with the direction of the propagating field. Thus, we are able to reduce the number of basis functions which grants access to the high-frequency regime. We use an adaptive local wave tracking strategy that implements a least-squares method. On each element of the mesh, shape functions are rotated until one aligns with the direction of the propagated wave, determined by solving a nonlinear minimization problem using Newton's method. This method is an extended effort from [2], where the distinguishing difference is the choice of basis functions. Moreover, the computation of Jacobians and Hessians that arise in the iterations of Newton's method is based on the exact characterization of the Fréchet derivatives of the field with respect to the propagation directions. Such a characterization is crucial for the stability, fast convergence, and computational efficiency of the Newton algorithm.
Book Synopsis Low and High Frequency Asymptotics by : Vijay K. Varadan
Download or read book Low and High Frequency Asymptotics written by Vijay K. Varadan and published by . This book was released on 1986 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects by : Erdogan Alkan
Download or read book Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects written by Erdogan Alkan and published by Springer Nature. This book was released on 2022-05-31 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid (DG-FDFD) approach for general bianisotropic materials. The validity of the derived formulations for different scattering problems has been shown by comparing the obtained results to exact and other solutions obtained using different numerical methods. Table of Contents: Introduction / Chiral Media / Basics of the Finite-Difference Frequency-Domain (FDFD) Method / The Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Bianisotropic Medium / Scattering FromThree Dimensional Chiral Structures / ImprovingTime and Memory Efficiencies of FDFD Methods / Conclusions / Appendix A: Notations / Appendix B: Near to Far FieldTransformation
Book Synopsis High Frequency Electromagnetic Propagation/Scattering Codes by :
Download or read book High Frequency Electromagnetic Propagation/Scattering Codes written by and published by . This book was released on 2005 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of our effort was to develop computational methods for constructing high-frequency asymptotic solutions in scattering on perfectly conducting objects. The emphasis of the first stage of our work was to describe high frequency phenomena in terms of numerically implemented evolution of wave-fronts associated with the propagating waves. The wave-front evolution algorithm is implemented for the leading high frequency mechanisms including: free-space propagation, reflection on smooth surfaces, wave-front splitting at the shadow boundary, generation and propagation of edge diffracted wave-fronts, and surface wave propagation. The second stage of our work was directed towards developing novel fast rigorous (direct or iterative) solution methods based on construction of economical parameterization of high frequency solutions in terms of basis functions defined on large supports. The wave-front evolution technique developed in the first stage provides a numerical prescription for the selection and determination the parameters of the postulated analytical representation of such basis functions. The numerical prescription together with numerical tools constructed during this effort will constitute an important element of the planned future, high frequency solution technique employing basis functions defined on large supports.
Book Synopsis A Fixed-time Numerical Method for High Frequency Scattering Problems by : Khoa D. Tran
Download or read book A Fixed-time Numerical Method for High Frequency Scattering Problems written by Khoa D. Tran and published by . This book was released on 2005 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects by : Erdogan Alkan
Download or read book Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects written by Erdogan Alkan and published by Morgan & Claypool Publishers. This book was released on 2013-01-01 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid (DG-FDFD) approach for general bianisotropic materials. The validity of the derived formulations for different scattering problems has been shown by comparing the obtained results to exact and other solutions obtained using different numerical methods. Table of Contents: Introduction / Chiral Media / Basics of the Finite-Difference Frequency-Domain (FDFD) Method / The Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Bianisotropic Medium / Scattering FromThree Dimensional Chiral Structures / ImprovingTime and Memory Efficiencies of FDFD Methods / Conclusions / Appendix A: Notations / Appendix B: Near to Far FieldTransformation
Book Synopsis Fast Methods for Inverse Wave Scattering Problems by : Jung Hoon Lee (Ph. D.)
Download or read book Fast Methods for Inverse Wave Scattering Problems written by Jung Hoon Lee (Ph. D.) and published by . This book was released on 2008 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse wave scattering problems arise in many applications including computerized/diffraction tomography, seismology, diffraction/holographic grating design, object identification from radar singals, and semiconductor quality control. Efficient algorithms exist for some inverse wave scattering problems in the low- and high-frequency regime or with weak scatterers. However, inverse wave scattering problems in the resonance regime with strong scatterers still pose many challenges. This thesis proposes algorithms for inverse wave scattering problems in the resonance regime with strong scatterers. These problems are part of, for instance, grating design, object identification, and semiconductor quality control. The proposed methods are (a) a spectrally convergent Nyström method for periodic structures in 2-D; (b) a fast Jacobian approximation method accompanying a Nyström method; (c) a fast and accurate method for evaluating the potential integrals in the 3-D mixed-potential integral operator with the Rao-Wilton-Glisson basis function; and (d) optimization with parameterized reduced-order models. The Nyström method and the method to evaluate the potential integrals accelerate scattered field evaluations by solving integral equations efficiently. The Jacobian approximation method and optimization with parameterized reduced-order models efficiently couple algorithms to evaluate scattered fields due to a guess of the scatterer and optimization methods to improve the guess. The Nyström and the Jacobian approximation methods are used to identify the parameters characterizing a periodic dielectric grating in 2-D. The method to evaluate the potential integrals and optimization with parameterized reduced-order models are applied to the problem of identifying simple discrete geometries in 3-D.
Book Synopsis Numerical Methods for Inverse Scattering Problems by : Jingzhi Li
Download or read book Numerical Methods for Inverse Scattering Problems written by Jingzhi Li and published by Springer Nature. This book was released on 2023-09-07 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the latest developments on the numerical methods for inverse scattering problems associated with acoustic, electromagnetic, and elastic waves. Inverse scattering problems are concerned with identifying unknown or inaccessible objects by wave probing data, which makes possible many industrial and engineering applications including radar and sonar, medical imaging, nondestructive testing, remote sensing, and geophysical exploration. The mathematical study of inverse scattering problems is an active field of research. This book presents a comprehensive and unified mathematical treatment of various inverse scattering problems mainly from a numerical reconstruction perspective. It highlights the collaborative research outputs by the two groups of the authors yet surveys and reviews many existing results by global researchers in the literature. The book consists of three parts respectively corresponding to the studies on acoustic, electromagnetic, and elastic scattering problems. In each part, the authors start with in-depth theoretical and computational treatments of the forward scattering problems and then discuss various numerical reconstruction schemes for the associated inverse scattering problems in different scenarios of practical interest. In addition, the authors provide an overview of the existing results in the literature by other researchers. This book can serve as a handy reference for researchers or practitioners who are working on or implementing inverse scattering methods. It can also serve as a graduate textbook for research students who are interested in working on numerical algorithms for inverse scattering problems.
