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Numerical Analysis Of A Singular Integral Equation Arising From Electromagnetic Interior Scattering
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Book Synopsis Numerical Analysis of a Singular Integral Equation Arising from Electromagnetic Interior Scattering by :
Download or read book Numerical Analysis of a Singular Integral Equation Arising from Electromagnetic Interior Scattering written by and published by . This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving interior scattering problems of electromagnetic waves in biological media using a volume integral equation approach gives rise naturally to an integral equation with unbounded coefficients and with strongly singular kernel. The numerical solution of an analogous 1-D integral equation of the second kind is studied and a convergence proof for the numerical solution is given.
Book Synopsis Integral Equations and Iteration Methods in Electromagnetic Scattering by : A. B. Samokhin
Download or read book Integral Equations and Iteration Methods in Electromagnetic Scattering written by A. B. Samokhin and published by Walter de Gruyter. This book was released on 2013-03-12 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Integral Equation Methods for Electromagnetic and Elastic Waves by : Weng Cho Chew
Download or read book Integral Equation Methods for Electromagnetic and Elastic Waves written by Weng Cho Chew and published by Morgan & Claypool Publishers. This book was released on 2009 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods. Table of Contents: Introduction to Computational Electromagnetics / Linear Vector Space, Reciprocity, and Energy Conservation / Introduction to Integral Equations / Integral Equations for Penetrable Objects / Low-Frequency Problems in Integral Equations / Dyadic Green's Function for Layered Media and Integral Equations / Fast Inhomogeneous Plane Wave Algorithm for Layered Media / Electromagnetic Wave versus Elastic Wave / Glossary of Acronyms
Book Synopsis Novel Single Source Integral Equation for Analysis of Electromagnetic Scattering by Penetrable Objects by : Farhad Sheikh Hosseini Lori
Download or read book Novel Single Source Integral Equation for Analysis of Electromagnetic Scattering by Penetrable Objects written by Farhad Sheikh Hosseini Lori and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents a novel single source surface electric field integral equation (EFIE) for the full-wave scattering problems by homogeneous dielectric objects and magneto-quasi-static characterization of the multiconductor transmission lines (MTLs) to determine inductance and resistance. Both the low and higher order method of moments (MoM) schemes are developed for numerical solution of this novel equation. The required theorems and derivations are given in detail. Numerical validations of this equation are conducted for various formulations such as scalar and vector 2D scattering problems, full-wave 3D scattering problems, and the problems of current flow in the 2D conductors of complex cross-sections. Error controllability of the numerically computed fields confirms that the proposed equation is rigorous in nature and may be an advantageous alternative to the other known single and double source surface integral equations (SIEs). The proposed single source integral equation (SSIE) features only electric type Green's functions, which distinguishes it from the previously know SSIE formulations. As such the new equation can be formulated in the form free of derivatives acting on the kernels. The new SSIE also features only one unknown surface function instead of two unknown functions as featured in the traditional SIEs. Unlike previously known single source surface integral equations derived through restricting of the single source field representation with surface equivalence principle, the new equation is obtained by constraining of the such representation with the volume equivalence principle. As a result, the new equation features integral operators that translate the fields from the surface of the scatterer to its volume and then back to its surface, lending it the name of Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE).
Book Synopsis Singularity Treatment and High Order RWG Basis Functions for Integral Equations of Electromagnetic Scattering by : Yijun Yu
Download or read book Singularity Treatment and High Order RWG Basis Functions for Integral Equations of Electromagnetic Scattering written by Yijun Yu and published by . This book was released on 2001 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: Various numerical techniques have been developed to carry out the electromagnetic field simulation. In this dissertation, we consider a mixed potential (vector and scalar potentials) integral equation for electromagnetic scattering and study its numerical methods. At first we give and prove the approximation properties of traditional RWG basis functions proposed by S. M. Rao, D. R. Wilton, and A. W. Glisson, and high order basis functions newly developed by W. Cai, which show the advantages of high order basis functions in theory. Then we present a novel numerical method for treating singularities of the dyadic Green's functions used in the mixed potential formulation of electromagnetic scattering. Lastly, we compute the electromagnetic scattering of a curved conductor surface with an incident wave E[superscript]inc by using different order basis functions on flat and curved triangles with the proposed treatment of singularities, and provide different numerical tests and simulations to address various issues of implementing the high order basis function and the treatment of singular integrals.
Book Synopsis Inverse Acoustic and Electromagnetic Scattering Theory by : David Colton
Download or read book Inverse Acoustic and Electromagnetic Scattering Theory written by David Colton and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has now been almost ten years since our first book on scattering theory ap peared [32]. At that time we claimed that "in recent years the development of integral equation methods for the direct scattering problem seems to be nearing completion, whereas the use of such an approach to study the inverse scattering problem has progressed to an extent that a 'state of the art' survey appears highly desirable". Since we wrote these words, the inverse scattering problem for acoustic and electromagnetic waves has grown from being a few theoreti cal considerations with limited numerical implementations to a weH developed mathematical theory with tested numerical algorithms. This maturing of the field of inverse scattering theory has been based on the realization that such problems are in general not only nonlinear but also improperly posed in the sense that the solution does not depend continuously on the measured data. This was emphasized in [32] and treated with the ideas and tools available at that time. Now, almost ten years later, these initial ideas have developed to the extent that a monograph summarizing the mathematical basis of the field seems appropriate. This book is oUf attempt to write such a monograph. The inverse scattering problem for acoustic and electromagnetic waves can broadly be divided into two classes, the inverse obstacle problem and the inverse medium problem.
Book Synopsis Low Frequency Acoustic and Electromagnetic Scattering by : S. I. Hariharan
Download or read book Low Frequency Acoustic and Electromagnetic Scattering written by S. I. Hariharan and published by . This book was released on 1983 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This paper deals with two classes of problems arising from acoustics and electromagnetics scattering in the low frequency situations. The first class of problem is solving Helmholtz equation with Dirichlet boundary conditions on an arbitrary two-dimensional body while the second one is an interior-exterior interface problem with Helmholtz equation in the exterior. Low frequency analysis show that there are two intermediate problems which solve the above problems accurate to 0(k^2 log k) where k is the frequency. These solutions greatly differ from the zero frequency approximations. For the Dirichlet problem numerical examples are shown to verify our theoretical estimates" -- abstract.
Book Synopsis Electromagnetic Scattering by Numerical Methods Applicable for Large Structures by :
Download or read book Electromagnetic Scattering by Numerical Methods Applicable for Large Structures written by and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Electromagnetic Scattering by Numerical Methods Applicable for Large Structures by :
Download or read book Electromagnetic Scattering by Numerical Methods Applicable for Large Structures written by and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this research is to develop numerical methods for general and efficient solutions to the linear systems obtained using the integral equations arising from electromagnetic scattering problems involving electrically large structures. In the process, the prior art in this area is reviewed. Then, the integral equations and their solutions by the method of moments (MoM) are derived. The progressive numerical method (PNM) and the projection iterative method (PIM) are analysed, including formulations, operation counts, stopping criteria, and their connection. In practice, the PNM is successful in calculation of two-dimensional scattering problems. The iterative PNM and a special case of the PNM, the modified spatial decomposition technique (SDT), are applied to the problems and compared with the PNM. Examples show that the PNM can depress internal resonances. The PIM is implemented in the two-dimensional TE case and convergent solutions are obtained. In order to overcome the difficulties with three-dimensional scattering problems, the PIM is implemented to solve the matrix equation obtained by MoM. Convergent results are observed in all examples being calculated for two- and three-dimensional objects. The PIM's iteration process can be accelerated by appropriate relaxation factors. The dependence of optimum relaxation factors on various parameters are investigated. Approximate results of large objects are obtained by the PIM with much less computation effort than the direct method. By allowing certain smaller elements in a coefficient matrix to be zero, the PIM can be further sped up, while still getting good far field results. This technique was found to be object dependent, providing better results for spheres than other objects.
Book Synopsis An Introduction to Inverse Scattering and Inverse Spectral Problems by : Khosrow Chadan
Download or read book An Introduction to Inverse Scattering and Inverse Spectral Problems written by Khosrow Chadan and published by SIAM. This book was released on 1997-01-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems.
Book Synopsis An Integral Equation Method for Electromagnetic Scattering Problems by : Arthur K. Jordan
Download or read book An Integral Equation Method for Electromagnetic Scattering Problems written by Arthur K. Jordan and published by . This book was released on 1975 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this memorandum report is to document the analysis which was performed to obtain the matrix equation which represents the electromagnetic fields scattered from axially symmetric targets. Although these results are not new, the analysis is presented in a concise, logical manner which is suitable for computer programming and which provides the foundation for the solution of diverse transient electromagnetic scattering problems by the newer methods of natural mode representations and singularity expansion techniques. The motivation for this study was to formulate in an understandable manner the necessarily complicated and tedious electromagnetic scattering calculations. Even relatively simple targets, e.g., missiles and torpedoes, require lengthy calculations. The integral equation for electromagnetic scattering from axially symmetric targets is derived. The boundary conditions for the case of metallic (perfectly conducting) and for the case of lossy dielectric targets are applied. The integral equation is reduced to matrix form by application of the method of moments. The scattering cross section is derived. A typical target geometry (sphere-cone-sphere) is used as an example. The detailed calculations are documented for reference with future computer calculations.
Book Synopsis On an integral equation arising in inverse scattering by : C. H. Yang
Download or read book On an integral equation arising in inverse scattering written by C. H. Yang and published by . This book was released on 1960 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Inverse Acoustic and Electromagnetic Scattering Theory by : David Colton
Download or read book Inverse Acoustic and Electromagnetic Scattering Theory written by David Colton and published by Springer Science & Business Media. This book was released on 1997-12-11 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. The second edition includes material on Newton’s method for the inverse obstacle problem, an elegant proof of uniqueness for the inverse medium problem, a discussion of the spectral theory of the far field operator and a method for determining the support of an inhomogeneous medium from far field data.
Book Synopsis Direct and Inverse Problems in Wave Propagation and Applications by : Ivan Graham
Download or read book Direct and Inverse Problems in Wave Propagation and Applications written by Ivan Graham and published by Walter de Gruyter. This book was released on 2013-10-14 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the third volume of three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" taking place in Linz, Austria, October 3-7, 2011. This book surveys recent developments in the analysis of wave propagation problems. The topics covered include aspects of the forward problem and problems in inverse problems, as well as applications in the earth sciences. Wave propagation problems are ubiquitous in environmental applications such as seismic analysis, acoustic and electromagnetic scattering. The design of efficient numerical methods for the forward problem, in which the scattered field is computed from known geometric configurations is very challenging due to the multiscale nature of the problems. Even more challenging are inverse problems where material parameters and configurations have to be determined from measurements in conjunction with the forward problem. This book contains review articles covering several state-of-the-art numerical methods for both forward and inverse problems. This collection of survey articles focusses on the efficient computation of wave propagation and scattering is a core problem in numerical mathematics, which is currently of great research interest and is central to many applications in energy and the environment. Two generic applications which resonate strongly with the central aims of the Radon Special Semester 2011 are forward wave propagation in heterogeneous media and seismic inversion for subsurface imaging. As an example of the first application, modelling of absorption and scattering of radiation by clouds, aerosol and precipitation is used as a tool for interpretation of (e.g.) solar, infrared and radar measurements, and as a component in larger weather/climate prediction models in numerical weather forecasting. As an example of the second application, inverse problems in wave propagation in heterogeneous media arise in the problem of imaging the subsurface below land or marine deposits. The book records the achievements of Workshop 3 "Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment". It brings together key numerical mathematicians whose interest is in the analysis and computation of wave propagation and scattering problems, and in inverse problems, together with practitioners from engineering and industry whose interest is in the applications of these core problems.
Book Synopsis On an integral equation arising in inverse scattering by : C. H. Yang
Download or read book On an integral equation arising in inverse scattering written by C. H. Yang and published by . This book was released on 1960 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On a Volume Integral Equation Used in Solving 3-D Electromagnetic Interior Scattering Problems by :
Download or read book On a Volume Integral Equation Used in Solving 3-D Electromagnetic Interior Scattering Problems written by and published by . This book was released on 1997 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: For microwave dosimetry an accurate mathematical model of interior scattering in 3-D is needed. Human body is highly inhomogeneous. A formulation of the scattering problem based on a volume integral equation and which addressed inhomogeneity in detail is derived. As a by-product, this work provides credence to a certain heuristically derived formulation.
