Fioralba Cakoni, David Colton, and Peter Monk
CBMS-NSF Regional Conference Series in Applied Mathematics 80
The linear sampling method is the oldest and most developed of the qualitative methods in inverse scattering theory. It is based on solving a linear integral equation and then using the equation’s solution as an indicator function for the determination of the support of the scattering object. This book describes the linear sampling method for a variety of electromagnetic scattering problems. It presents uniqueness theorems and the derivation of various inequalities on the material properties of the scattering object from a knowledge of the far field pattern of the scattered wave. Also covered are
• the approximation properties of Herglotz wave functions;
• the behavior of solutions to the interior transmission problem, a novel interior boundary value problem; and
• numerical examples of the inversion scheme.
This book is intended for mathematicians and engineers performing research in inverse electromagnetic scattering theory. It is also appropriate for an advanced graduate course on inverse problems.
About the Authors
Fioralba Cakoni is a professor in the Department of Mathematical Sciences at the University of Delaware. She is coauthor, with David Colton, of Qualitative Methods in Inverse Scattering Theory (Springer, 2006).
David Colton is a professor in the Department of Mathematical Sciences at the University of Delaware, where he was appointed Unidel Professor in 1996. He is coauthor of the aforementioned book with Fioralba Cakoni and of Inverse Acoustic and Electromagnetic Scattering Theory (Springer, 1998) with Rainer Kress.
Peter Monk is a professor in the Department of Mathematical Sciences at the University of Delaware, where he was appointed Unidel Professor in 2000. He is author of Finite Element Methods for Maxwell’s Equations (Oxford University Press, 2003).
2011 / x + 142 pages / Softcover / ISBN 978-0-898719-39-0
List Price $57.50 / SIAM/CBMS Member Price $40.25 / Order Code CB80