|
Showing 1 - 3 of
3 matches in All Departments
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.
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.
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 this book. 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.* In order to achieve
clarification of presentation, focus on the inverse scattering
problem for scalar homogeneous media.
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
|