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Polarization and Moment Tensors : With Applications to Inverse Problems and Effective Medium Theory
Authors: ---
ISBN: 1280943637 9786610943630 0387715665 0387715657 1441924493 Year: 2007 Publisher: New York, NY : Springer New York : Imprint: Springer,

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This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. The methods involved come from various areas of pure and applied mathematics, such as potential theory, PDEs, complex analysis, and numerical methods. The unifying thread in this book is the use of generalized polarization and moment tensors. The main approach is based on modern layer potential techniques. By augmenting the theory with interesting practical examples and numerical illustrations, the exposition brings simplicity to the advanced material. An introductory chapter covers the necessary basics. With its extensive list of references and open problems, the book should enhance accessibility to specialized literature and stimulate progress in the fields of impedance imaging and composite materials. Graduate students and researchers in applied mathematics will benefit from this book. Researchers in engineering and physics might also find this book helpful.


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Polarization and Moment Tensors : With Applications to Inverse Problems and Effective Medium Theory
Authors: ---
ISBN: 9780387715667 Year: 2007 Publisher: New York, NY Springer Science+Business Media, LLC


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Reconstruction of Small Inhomogeneities from Boundary Measurements
Authors: ---
ISBN: 3540445013 Year: 2004 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,

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This is the first book to provide a systematic exposition of promising techniques for the reconstruction of small inhomogeneities from boundary measurements. In particular, theoretical results and numerical procedures for the inverse problems for the conductivity equation, the Lamé system, as well as the Helmholtz equation are discussed in a readable and informative manner. The general approach developed in this book is based on layer potential techniques and modern asymptotic analysis of partial differential equations. The book is particularly suitable for graduate students in mathematics.


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Polarization and Moment Tensors : With Applications to Inverse Problems and Effective Medium Theory
Authors: --- ---
ISBN: 9780387715667 Year: 2007 Publisher: New York NY Springer New York

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Abstract

This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. The methods involved come from various areas of pure and applied mathematics, such as potential theory, PDEs, complex analysis, and numerical methods. The unifying thread in this book is the use of generalized polarization and moment tensors. The main approach is based on modern layer potential techniques. By augmenting the theory with interesting practical examples and numerical illustrations, the exposition brings simplicity to the advanced material. An introductory chapter covers the necessary basics. With its extensive list of references and open problems, the book should enhance accessibility to specialized literature and stimulate progress in the fields of impedance imaging and composite materials. Graduate students and researchers in applied mathematics will benefit from this book. Researchers in engineering and physics might also find this book helpful.


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Mathematical and Statistical Methods for Multistatic Imaging
Authors: --- --- --- --- --- et al.
ISBN: 9783319025858 Year: 2013 Publisher: Cham Springer International Publishing

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Mathematical and Statistical Methods for Multistatic Imaging
Authors: --- --- --- --- --- et al.
ISBN: 3319025848 3319025856 Year: 2013 Publisher: Cham : Springer International Publishing : Imprint: Springer,

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This book covers recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. The waves can be acoustic, elastic or electromagnetic. They are generated by point sources on a transmitter array and measured on a receiver array. An important problem in multistatic imaging is to quantify and understand the trade-offs between data size, computational complexity, signal-to-noise ratio, and resolution. Another fundamental problem is to have a shape representation well suited to solving target imaging problems from multistatic data. In this book the trade-off between resolution and stability when the data are noisy is addressed. Efficient imaging algorithms are provided and their resolution and stability with respect to noise in the measurements analyzed. It also shows that high-order polarization tensors provide an accurate representation of the target. Moreover, a dictionary-matching technique based on new invariants for the generalized polarization tensors is introduced. Matlab codes for the main algorithms described in this book are provided. Numerical illustrations using these codes in order to highlight the performance and show the limitations of numerical approaches for multistatic imaging are presented.

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