Houssem Haddar's Books

Inverse Scattering Theory and Transmission Eigenvalues

By: Fioralba Cakoni,David Colton,Houssem Haddar

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Inverse Scattering Theory and Transmission Eigenvalues

By: Fioralba Cakoni,David Colton,Houssem Haddar

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.?

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Page Count

200

Publisher

SIAM

Published Date

ISBN 10

1611974461

ISBN 13

9781611974461

Computational Electromagnetism

Cetraro, Italy 2014

By: Houssem Haddar,Ralf Hiptmair,Peter Monk,Rodolfo Rodríguez

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Computational Electromagnetism

Cetraro, Italy 2014

By: Houssem Haddar,Ralf Hiptmair,Peter Monk,Rodolfo Rodríguez

Presenting topics that have not previously been contained in a single volume, this book offers an up-to-date review of computational methods in electromagnetism, with a focus on recent results in the numerical simulation of real-life electromagnetic problems and on theoretical results that are useful in devising and analyzing approximation algorithms. Based on four courses delivered in Cetraro in June 2014, the material covered includes the spatial discretization of Maxwell’s equations in a bounded domain, the numerical approximation of the eddy current model in harmonic regime, the time domain integral equation method (with an emphasis on the electric-field integral equation) and an overview of qualitative methods for inverse electromagnetic scattering problems. Assuming some knowledge of the variational formulation of PDEs and of finite element/boundary element methods, the book is suitable for PhD students and researchers interested in numerical approximation of partial differential equations and scientific computing.

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Page Count

249

Publisher

Springer

Published Date

ISBN 10

3319193066

ISBN 13

9783319193069

Inverse Scattering Theory and Transmission Eigenvalues

By: Fioralba Cakoni,David Colton,Houssem Haddar

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Inverse Scattering Theory and Transmission Eigenvalues

By: Fioralba Cakoni,David Colton,Houssem Haddar

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.

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200

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SIAM

Published Date

ISBN 10

1611974453

ISBN 13

9781611974454

Inverse Scattering Theory and Transmission Eigenvalues

Second Edition

By: Fioralba Cakoni,David Colton,Houssem Haddar

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Inverse Scattering Theory and Transmission Eigenvalues

Second Edition

By: Fioralba Cakoni,David Colton,Houssem Haddar

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.

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Page Count

259

Publisher

SIAM

Published Date

ISBN 10

1611977428

ISBN 13

9781611977424

Computational Electromagnetism

Cetraro, Italy 2014

By: Houssem Haddar,Ralf Hiptmair,Peter Monk,Rodolfo Rodríguez

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Computational Electromagnetism

Cetraro, Italy 2014

By: Houssem Haddar,Ralf Hiptmair,Peter Monk,Rodolfo Rodríguez

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

249

Publisher

Springer

Published Date

ISBN 10

3319193066

ISBN 13

9783319193069

Book's by Houssem Haddar

Inverse Scattering Theory and Transmission Eigenvalues

Inverse Scattering Theory and Transmission Eigenvalues

Computational Electromagnetism

Computational Electromagnetism

Inverse Scattering Theory and Transmission Eigenvalues

Inverse Scattering Theory and Transmission Eigenvalues

Inverse Scattering Theory and Transmission Eigenvalues

Inverse Scattering Theory and Transmission Eigenvalues

Computational Electromagnetism

Computational Electromagnetism

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