Download or read book The Factorization Method for Inverse Scattering from Periodic Inhomogeneous Media written by Kai Sandfort and published by KIT Scientific Publishing. This book was released on 2014-10-16 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the identification of the shape of penetrable periodic media by means of scattered time-harmonic waves. Mathematically, this is about the determination of the support of a function which occurs in the governing equations. Our theoretical analysis shows that this problem can be strictly solved for acoustic as well as for electromagnetic radiation by the so-called Factorization Method. We apply this method to reconstruct a couple of media from numerically simulated field data.
Download or read book The Factorization Method for Inverse Scattering from Periodic Inhomogeneous Media written by Kai Sandfort and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Scattering from Chiral Media written by Sven Heumann and published by Sudwestdeutscher Verlag Fur Hochschulschriften AG. This book was released on 2012 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chirality - handedness - is everywhere. Snail shells run clockwise or anti-clockwise. Optical activity caused by chiral molecules was discovered at the beginning of the 19th century when studying light passing through liquid solutions of sugar. The development of artificial chiral materials attracts the attention of research in the field of inverse scattering problems. This work deals with several aspects of inverse scattering for inhomogeneous chiral materials: A chiral object - the scatterer - is situated in vacuum and illuminated by an electromagnetic wave. This wave is scattered. The direct problem is to compute the scattered wave for a given incident wave and a given chiral object. The inverse problem is to determine the scatterer from information about the scattered field. The Factorization Method is generalized to inverse scattering problems for Maxwell's equations in combination with the Drude-Born-Fedorov constitutive relations as well as for the 2D vector Helmholtz equation. It provides a necessary and sufficient criterion to determine the characteristic function of the scatterer and overcomes the disadvantages of other solving methods.
Download or read book Maxwell s Equations in Periodic Structures written by Gang Bao and published by Springer Nature. This book was released on 2021-11-22 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses recent developments in mathematical analysis and computational methods for solving direct and inverse problems for Maxwell’s equations in periodic structures. The fundamental importance of the fields is clear, since they are related to technology with significant applications in optics and electromagnetics. The book provides both introductory materials and in-depth discussion to the areas in diffractive optics that offer rich and challenging mathematical problems. It is also intended to convey up-to-date results to students and researchers in applied and computational mathematics, and engineering disciplines as well.
Download or read book The Factorization Method for Inverse Problems written by Andreas Kirsch and published by OUP Oxford. This book was released on 2007-12-13 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The factorization method is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. Aimed at students and researchers in Applied Mathematics, Physics and Engineering, this text introduces the reader to this promising approach for solving important classes of inverse problems. The wide applicability of this method is discussed by choosing typical examples, such as inverse scattering problems for the scalar Helmholtz equation, a scattering problem for Maxwell's equation, and a problem in impedance and optical tomography. The last section of the book compares the Factorization Method to established sampling methods (the Linear Sampling Method, the Singular Source Method, and the Probe Method).
Download or read book The Factorization Method in Inverse Scattering from Periodic Structures written by Tilo Arens and published by . This book was released on 2002 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Topics In Scattering And Biomedical Engineering Proceedings Of The 8th International Workshop On Mathematical Methods In Scattering Theory And Biomedical Engineering written by Dimitrios I Fotiadis and published by World Scientific. This book was released on 2008-05-20 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of proceedings consists of the papers presented during the 8th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering, held in Lefkada, Greece, on 27-29 September 2007.The book contains papers on scattering theory and biomedical engineering — two rapidly evolving fields which have a considerable impact on today's research. All the papers are state-of-the-art, have been carefully reviewed before publication and the authors are well-known in the scientific community. In addition, some papers focus more on applied mathematics, which is the solid ground for development and innovative research in scattering and biomedical engineering.
Download or read book Advanced Topics in Scattering and Biomedical Engineering written by Dimitrios Ioannou Fotiadis and published by World Scientific. This book was released on 2008 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of proceedings consists of the papers presented during the 8th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering, held in Lefkada, Greece, on 27-29 September 2007. The book contains papers on scattering theory and biomedical engineering - two rapidly evolving fields which have a considerable impact on today's research. All the papers are state-of-the-art, have been carefully reviewed before publication and the authors are well-known in the scientific community. In addition, some papers focus more on applied mathematics, which is the solid ground for development and innovative research in scattering and biomedical engineering.
Download or read book Inverse Scattering Theory and Transmission Eigenvalues written by Fioralba Cakoni and published by SIAM. This book was released on 2022-12-07 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.
Download or read book The Factorization Method for Inverse Scattering from Chiral Media written by Sven Heumann and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Point Sources and Multipoles in Inverse Scattering Theory written by Roland Potthast and published by CRC Press. This book was released on 2001-05-30 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last twenty years, the growing availability of computing power has had an enormous impact on the classical fields of direct and inverse scattering. The study of inverse scattering, in particular, has developed rapidly with the ability to perform computational simulations of scattering processes and led to remarkable advances in a range of
Download or read book The factorization method for inverse elastic scattering from periodic structures written by Guanghui Hu and published by . This book was released on 2013 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Direct and Inverse Scattering Transmission Problem for Periodic Inhomogeneous Media written by Beata Strycharz-Szemberg and published by . This book was released on 1996 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
Download or read book Numerical Fourier Analysis written by Gerlind Plonka and published by Springer. This book was released on 2019-02-05 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods. It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums. The code of most of the presented algorithms is available in the authors’ public domain software packages. Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms.
Download or read book Inverse Scattering for a Penetrable Cavity and the Transmission Eigenvalue Problem written by Shixu Meng and published by . This book was released on 2016 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we consider the scattering of point sources inside a cavity surrounded by an inhomogeneous medium and its inverse problem of determining the boundary of the cavity from measurements of the scattered field inside the cavity. We apply the linear sampling method and factorization method to numerically reconstruct the boundary of the cavity. We prove that the linear sampling method works when the wave number is not an exterior transmission eigenvalue. We prove that the exterior transmission eigenvalues form a discrete set. We then consider both the exterior transmission eigenvalue problem and the interior transmission eigenvalue problem for a spherically stratified media and study the inverse spectral problem for the exterior transmission eigenvalue problem. Finally we consider the interior transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that changes sign inside its support. We prove that the set of transmission eigenvalues is nonempty discrete, infinite and without finite accumulation points.
Download or read book Optimization and Regularization for Computational Inverse Problems and Applications written by Yanfei Wang and published by Springer Science & Business Media. This book was released on 2011-06-29 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Optimization and Regularization for Computational Inverse Problems and Applications" focuses on advances in inversion theory and recent developments with practical applications, particularly emphasizing the combination of optimization and regularization for solving inverse problems. This book covers both the methods, including standard regularization theory, Fejer processes for linear and nonlinear problems, the balancing principle, extrapolated regularization, nonstandard regularization, nonlinear gradient method, the nonmonotone gradient method, subspace method and Lie group method; and the practical applications, such as the reconstruction problem for inverse scattering, molecular spectra data processing, quantitative remote sensing inversion, seismic inversion using the Lie group method, and the gravitational lensing problem. Scientists, researchers and engineers, as well as graduate students engaged in applied mathematics, engineering, geophysics, medical science, image processing, remote sensing and atmospheric science will benefit from this book. Dr. Yanfei Wang is a Professor at the Institute of Geology and Geophysics, Chinese Academy of Sciences, China. Dr. Sc. Anatoly G. Yagola is a Professor and Assistant Dean of the Physical Faculty, Lomonosov Moscow State University, Russia. Dr. Changchun Yang is a Professor and Vice Director of the Institute of Geology and Geophysics, Chinese Academy of Sciences, China.
