Numerical Methods For High Frequency Scattering By Multiple Obstacles

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Numerical Methods for Inverse Scattering Problems

Author : Jingzhi Li
Publisher : Springer Nature
ISBN 13 : 9819937728
Total Pages : 373 pages
Book Rating : 4.8/5 (199 download)

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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.

Antenna Handbook

Author : Y.T. Lo
Publisher : Springer Science & Business Media
ISBN 13 : 146156459X
Total Pages : 2282 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Antenna Handbook by : Y.T. Lo

Download or read book Antenna Handbook written by Y.T. Lo and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 2282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Techniques based on the method of modal expansions, the Rayleigh-Stevenson expansion in inverse powers of the wavelength, and also the method of moments solution of integral equations are essentially restricted to the analysis of electromagnetic radiating structures which are small in terms of the wavelength. It therefore becomes necessary to employ approximations based on "high-frequency techniques" for performing an efficient analysis of electromagnetic radiating systems that are large in terms of the wavelength. One of the most versatile and useful high-frequency techniques is the geometrical theory of diffraction (GTD), which was developed around 1951 by J. B. Keller [1,2,3]. A class of diffracted rays are introduced systematically in the GTD via a generalization of the concepts of classical geometrical optics (GO). According to the GTD these diffracted rays exist in addition to the usual incident, reflected, and transmitted rays of GO. The diffracted rays in the GTD originate from certain "localized" regions on the surface of a radiating structure, such as at discontinuities in the geometrical and electrical properties of a surface, and at points of grazing incidence on a smooth convex surface as illustrated in Fig. 1. In particular, the diffracted rays can enter into the GO shadow as well as the lit regions. Consequently, the diffracted rays entirely account for the fields in the shadow region where the GO rays cannot exist.

Scattering, Two-Volume Set

Author : E. R. Pike
Publisher : Elsevier
ISBN 13 : 0080540732
Total Pages : 1831 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Scattering, Two-Volume Set by : E. R. Pike

Download or read book Scattering, Two-Volume Set written by E. R. Pike and published by Elsevier. This book was released on 2001-10-09 with total page 1831 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering is the collision of two objects that results in a change of trajectory and energy. For example, in particle physics, such as electrons, photons, or neutrons are "scattered off" of a target specimen, resulting in a different energy and direction. In the field of electromagnetism, scattering is the random diffusion of electromagnetic radiation from air masses is an aid in the long-range sending of radio signals over geographic obstacles such as mountains. This type of scattering, applied to the field of acoustics, is the spreading of sound in many directions due to irregularities in the transmission medium. Volume I of Scattering will be devoted to basic theoretical ideas, approximation methods, numerical techniques and mathematical modeling. Volume II will be concerned with basic experimental techniques, technological practices, and comparisons with relevant theoretical work including seismology, medical applications, meteorological phenomena and astronomy. This reference will be used by researchers and graduate students in physics, applied physics, biophysics, chemical physics, medical physics, acoustics, geosciences, optics, mathematics, and engineering. This is the first encyclopedic-range work on the topic of scattering theory in quantum mechanics, elastodynamics, acoustics, and electromagnetics. It serves as a comprehensive interdisciplinary presentation of scattering and inverse scattering theory and applications in a wide range of scientific fields, with an emphasis, and details, up-to-date developments. Scattering also places an emphasis on the problems that are still in active current research. The first interdisciplinary reference source on scattering to gather all world expertise in this technique Covers the major aspects of scattering in a common language, helping to widening the knowledge of researchers across disciplines The list of editors, associate editors and contributors reads like an international Who's Who in the interdisciplinary field of scattering

Handbook of Numerical Methods for Hyperbolic Problems

Author : Remi Abgrall
Publisher : Elsevier
ISBN 13 : 044463911X
Total Pages : 612 pages
Book Rating : 4.4/5 (446 download)

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Book Synopsis Handbook of Numerical Methods for Hyperbolic Problems by : Remi Abgrall

Download or read book Handbook of Numerical Methods for Hyperbolic Problems written by Remi Abgrall and published by Elsevier. This book was released on 2017-01-16 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and become familiar with their relative advantages and limitations. - Provides detailed, cutting-edge background explanations of existing algorithms and their analysis - Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications - Written by leading subject experts in each field, the volumes provide breadth and depth of content coverage

Multiple Scattering

Author : P. A. Martin
Publisher : Cambridge University Press
ISBN 13 : 0521865549
Total Pages : 13 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Multiple Scattering by : P. A. Martin

Download or read book Multiple Scattering written by P. A. Martin and published by Cambridge University Press. This book was released on 2006-08-03 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher description

Electromagnetic Scattering

Author : Piergiorgio Uslenghi
Publisher : Elsevier
ISBN 13 : 0323142435
Total Pages : 812 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Electromagnetic Scattering by : Piergiorgio Uslenghi

Download or read book Electromagnetic Scattering written by Piergiorgio Uslenghi and published by Elsevier. This book was released on 2012-12-02 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electromagnetic Scattering is a collection of studies that aims to discuss methods, state of the art, applications, and future research in electromagnetic scattering. The book covers topics related to the subject, which includes low-frequency electromagnetic scattering; the uniform asymptomatic theory of electromagnetic edge diffraction; analyses of problems involving high frequency diffraction and imperfect half planes; and multiple scattering of waves by periodic and random distribution. Also covered in this book are topics such as theories of scattering from wire grid and mesh structures; the electromagnetic inverse problem; computational methods for transmission of waves; and developments in the use of complex singularities in the electromagnetic theory. Engineers and physicists who are interested in the study, developments, and applications of electromagnetic scattering will find the text informative and helpful.

Scattering By Obstacles And Potentials

Author : Alexander G Ramm
Publisher : World Scientific
ISBN 13 : 9813220988
Total Pages : 621 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Scattering By Obstacles And Potentials by : Alexander G Ramm

Download or read book Scattering By Obstacles And Potentials written by Alexander G Ramm and published by World Scientific. This book was released on 2017-11-23 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is important as it contains results many of which are not available in the literature, except in the author's papers. Among other things, it gives uniqueness theorems for inverse scattering problems when the data are non-over-determined, numerical method for solving inverse scattering problems, a method (MRC) for solving direct scattering problem.

Numerical Analysis of Multiscale Problems

Author : Ivan G. Graham
Publisher : Springer Science & Business Media
ISBN 13 : 3642220614
Total Pages : 376 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Numerical Analysis of Multiscale Problems by : Ivan G. Graham

Download or read book Numerical Analysis of Multiscale Problems written by Ivan G. Graham and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.

The Nystrom Method in Electromagnetics

Author : Mei Song Tong
Publisher : John Wiley & Sons
ISBN 13 : 1119284880
Total Pages : 528 pages
Book Rating : 4.1/5 (192 download)

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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 2020-06-29 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.

Highly Oscillatory Problems

Author : Bjorn Engquist
Publisher : Cambridge University Press
ISBN 13 : 0521134439
Total Pages : 254 pages
Book Rating : 4.5/5 (211 download)

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Book Synopsis Highly Oscillatory Problems by : Bjorn Engquist

Download or read book Highly Oscillatory Problems written by Bjorn Engquist and published by Cambridge University Press. This book was released on 2009-07-02 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Review papers from experts in areas of active research into highly oscillatory problems, with an emphasis on computation.

Integral Equation Methods in Scattering Theory

Author : David Colton
Publisher : SIAM
ISBN 13 : 1611973155
Total Pages : 286 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Integral Equation Methods in Scattering Theory by : David Colton

Download or read book Integral Equation Methods in Scattering Theory written by David Colton and published by SIAM. This book was released on 2013-11-15 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.

Partition of Unity Methods

Author : St¿phane Bordas
Publisher : John Wiley & Sons
ISBN 13 : 0470667087
Total Pages : 373 pages
Book Rating : 4.4/5 (76 download)

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Book Synopsis Partition of Unity Methods by : St¿phane Bordas

Download or read book Partition of Unity Methods written by St¿phane Bordas and published by John Wiley & Sons. This book was released on 2023-10-16 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: PARTITION OF UNITY METHODS Master the latest tool in computational mechanics with this brand-new resource from distinguished leaders in the field While it is the number one tool for computer aided design and engineering, the finite element method (FEM) has difficulties with discontinuities, singularities, and moving boundaries. Partition of unity methods addresses these challenges and is now increasingly implemented in commercially available software. Partition of Unity Methods delivers a detailed overview of its fundamentals, in particular the extended finite element method for applications in solving moving boundary problems. The distinguished academics and authors introduce the XFEM as a natural extension of the traditional finite element method (FEM), through straightforward one-dimensional examples which form the basis for the subsequent introduction of higher dimensional problems. This book allows readers to fully understand and utilize XFEM just as it becomes ever more crucial to industry practice. Partition of Unity Methods explores all essential topics on this key new technology, including: Coverage of the difficulties faced by the finite element method and the impetus behind the development of XFEM The basics of the finite element method, with discussions of finite element formulation of linear elasticity and the calculation of the force vector An introduction to the fundamentals of enrichment A revisitation of the partition of unity enrichment A description of the geometry of enrichment features, with discussions of level sets for stationary interfaces Application of XFEM to bio-film, gradient theories, and three dimensional crack propagation Perfect for researchers and postdoctoral candidates working in the field of computational mechanics, Partition of Unity Methods also has a place in the libraries of senior undergraduate and graduate students working in the field. Finite element and CFD analysts and developers in private industry will also greatly benefit from this book.

Unified Transform for Boundary Value Problems

Author : Athanasios S. Fokas
Publisher : SIAM
ISBN 13 : 1611973821
Total Pages : 290 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Unified Transform for Boundary Value Problems by : Athanasios S. Fokas

Download or read book Unified Transform for Boundary Value Problems written by Athanasios S. Fokas and published by SIAM. This book was released on 2015-01-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs. The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.

Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials

Author : Mezhlum A. Sumbatyan
Publisher : Springer
ISBN 13 : 3030174700
Total Pages : 261 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials by : Mezhlum A. Sumbatyan

Download or read book Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials written by Mezhlum A. Sumbatyan and published by Springer. This book was released on 2019-05-17 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses theoretical and experimental methods for exploring microstructured metamaterials, with a special focus on wave dynamics, mechanics, and related physical properties. The authors use various mathematical and physical approaches to examine the mechanical properties inherent to particular types of metamaterials. These include: • Boundary value problems in reduced strain gradient elasticity for composite fiber-reinforced metamaterials • Self-organization of molecules in ferroelectric thin films • Combined models for surface layers of nanostructures • Computer simulation at the micro- and nanoscale • Surface effects with anisotropic properties and imperfect temperature contacts • Inhomogeneous anisotropic metamaterials with uncoupled and coupled surfaces or interfaces • Special interface finite elements and other numerical and analytical methods for composite structures

Scientific and Technical Aerospace Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 836 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Inverse Problems in Wave Propagation

Author : Guy Chavent
Publisher : Springer Science & Business Media
ISBN 13 : 1461218780
Total Pages : 502 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Inverse Problems in Wave Propagation by : Guy Chavent

Download or read book Inverse Problems in Wave Propagation written by Guy Chavent and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems in wave propagation occur in geophysics, ocean acoustics, civil and environmental engineering, ultrasonic non-destructive testing, biomedical ultrasonics, radar, astrophysics, as well as other areas of science and technology. The papers in this volume cover these scientific and technical topics, together with fundamental mathematical investigations of the relation between waves and scatterers.

The Discontinuous Enrichment Method (DEM) for Multi-scale Transport Problems

Author : Irina Kalashnikova
Publisher : Stanford University
ISBN 13 :
Total Pages : 178 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis The Discontinuous Enrichment Method (DEM) for Multi-scale Transport Problems by : Irina Kalashnikova

Download or read book The Discontinuous Enrichment Method (DEM) for Multi-scale Transport Problems written by Irina Kalashnikova and published by Stanford University. This book was released on 2011 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discontinuous enrichment method (DEM) for the efficient finite element solution of advection-dominated transport problems in fluid mechanics whose solutions are known to possess multi-scale features is developed. Attention is focused specifically on the two-dimensional (2D) advection-diffusion equation, the usual scalar model for the Navier-Stokes equations. Following the basic DEM methodology [1], the usual Galerkin polynomial approximation is locally enriched by the free-space solutions to the governing homogeneous partial differential equation (PDE). For the constant-coefficient advection-diffusion equation, several families of free-space solutions are derived. These include a family of exponential functions that exhibit a steep gradient in some flow direction, and a family of discontinuous polynomials. A parametrization of the former class of functions with respect to an angle parameter is developed, so as to enable the systematic design and implementation of DEM elements of arbitrary orders. It is shown that the original constant-coefficient methodology has a natural extension to variable-coefficient advection-diffusion problems. For variable-coefficient transport problems, the approximation properties of DEM can be improved by augmenting locally the enrichment space with a "higher-order" enrichment function that solves the governing PDE with the advection field a(x) linearized to second order. A space of Lagrange multipliers, introduced at the element interfaces to enforce a weak continuity of the solution and related to the normal derivatives of the enrichment functions, is developed. The construction of several low and higher-order DEM elements fitting this paradigm is discussed in detail. Numerical results for several constant as well as variable-coefficient advection-diffusion benchmark problems reveal that these DEM elements outperform their standard Galerkin and stabilized Galerkin counterparts of comparable computational complexity by a large margin, especially when the flow is advection-dominated.