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Inverse Acoustic And Electromagnetic Scattering Theory

Author: David Colton
Publisher: Springer Science & Business Media
ISBN: 3662028352
Size: 77.83 MB
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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.

Numerische N Herungsverfahren F R Elliptische Randwertprobleme

Author: Olaf Steinbach
Publisher: Springer-Verlag
ISBN: 3322800547
Size: 63.22 MB
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Für die näherungsweise Lösung von Randwertproblemen zweiter Ordnung wird eine einheitliche Theorie der Finiten Elemente Methode und der Randelementmethode präsentiert. Neben der Stabilitäts- und Fehleranalysis wird vor allem auf effiziente Lösungsverfahren eingegangen. Für die Diskretisierung der auftretenden Randintegraloperatoren werden schnelle Randelementmethoden (Wavelets, Multipol, algebraische Techniken) mit der Darstellung durch partielle Integration verknüpft. Durch die Kopplung von FEM und BEM mittels Gebietszerlegungsmethoden können gekoppelte Randwertprobleme in komplexen Strukturen behandelt werden. Numerische Beispiele illustrieren die theoretischen Aussagen.

An Introduction To Mathematics Of Emerging Biomedical Imaging

Author: Habib Ammari
Publisher: Springer Science & Business Media
ISBN: 3540795537
Size: 39.97 MB
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Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics. This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so. The volume is suitable for a graduate-level course in applied mathematics and helps prepare the reader for a deeper understanding of research areas in biomedical imaging.

Inside Out

Author: Gunther Uhlmann
Publisher: Cambridge University Press
ISBN: 9780521824699
Size: 80.87 MB
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Inverse problems arise in practical situations such as medical imaging, geophysical exploration, and non-destructive evaluation where measurements made on the exterior of a body are used to determine properties of the inaccessible interior. There have been substantial developments in the mathematical theory of inverse problems, and applications have expanded greatly. In this volume, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in modern inverse problems, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms. Each article covers a particular topic or topics with an emphasis on accessibility and integration with the whole volume. Thus the collection can be at the same time stimulating to researchers and accessible to graduate students.

Inverse Scattering Theory And Transmission Eigenvalues

Author: Fioralba Cakoni
Publisher: SIAM
ISBN: 1611974453
Size: 34.57 MB
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Inverse scattering theory is a major theme of applied mathematics, and it has 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 particular problems in the development of efficient inversion algorithms. Although linearized models continue to play an important role in many applications, an increased need to focus on problems in which multiple scattering effects cannot be ignored has led to a central role for nonlinearity, and the possibility of collecting large amounts of data over limited regions of space means that the ill-posed nature of the inverse scattering problem has become a problem of central importance. Initial efforts to address the nonlinear and the ill-posed nature of the inverse scattering problem focused on nonlinear optimization methods. While efficient in many situations, strong a priori information is necessary for their implementation. This problem led to a qualitative approach to inverse scattering theory in which the amount of a priori information is drastically reduced, although at the expense of only obtaining limited information about the values of the constitutive parameters. This qualitative approach (the linear sampling method, the factorization method, the theory of transmission eigenvalues, etc.) is the theme of Inverse Scattering Theory and Transmission Eigenvalues. The authors begin with a basic introduction to the theory, then proceed to more recent developments, including a detailed discussion of the transmission eigenvalue problem; present the new generalized linear sampling method in addition to the well-known linear sampling and factorization methods; and in order to achieve clarification of presentation, focus on the inverse scattering problem for scalar homogeneous media.

Integral Equation Methods In Scattering Theory

Author: David Colton
Publisher: SIAM
ISBN: 1611973155
Size: 45.41 MB
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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 HÓlder 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 HÓlder 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.

Point Sources And Multipoles In Inverse Scattering Theory

Author: Roland Potthast
Publisher: CRC Press
ISBN: 1420035487
Size: 73.75 MB
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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 applications, from medical imaging and radar to remote sensing and seismic exploration. Point Sources and Multipoles in Inverse Scattering Theory provides a survey of recent developments in inverse acoustic and electromagnetic scattering theory. Focusing on methods developed over the last six years by Colton, Kirsch, and the author, this treatment uses point sources combined with several far-reaching techniques to obtain qualitative reconstruction methods. The author addresses questions of uniqueness, stability, and reconstructions for both two-and three-dimensional problems. With interest in extracting information about an object through scattered waves at an all-time high, Point Sources and Multipoles in Inverse Scattering Theory provides a valuable source of information from both the mathematical and applications perspectives. It offers insight into the general recovery of information from incomplete data and has direct, practical relevance to work on image reconstruction.

Erm Dungsrisse

Author: Hans Albert Richard
Publisher: Springer-Verlag
ISBN: 3834886637
Size: 64.93 MB
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Das Fachbuch Ermüdungsrisse beschäftigt sich mit der Auslegung von Bauteilen nach Festigkeitskriterien sowie der Analyse von Schäden durch Risswachstum bei Belastung mit konstanter Amplitude und bei Betriebsbelastung. Die Ermittlung und Darstellung bruchmechanischer Werkstoffkennwerte und -kennfunktionen wird behandelt. Selbsterklärende Abbildungen zu charakteristischen Anwendungsbeispielen aus der Praxis visualisieren überzeugend die dargestellten Sachverhalte.