V. G. Romanov

Inverse Problems for Maxwell's Equations - Inverse and Ill-Posed Problems Series V. G. Romanov Reprint 2014 edition

This text offers a simultaneous presentation of the theory and numerical treatment of inverse problems for Maxwell's equations. Inverse problems are central to many areas of science and technology such as geophysical exploration, remote sensing, near-surface radar location, di-electric logging and medical imaging. The basic idea of inverse methods is to extract from the evaluation of measured electromagnetic fields the details of the medium considered. The inverse problems are investigated not only for Maxwell's equations, but also for their quasistationary approximation and, in the case of harmonic dependence, in time. Starting with the simplest one-dimensional inverse problems, the book leads its readers to more complicated multi-dimensional ones studied for media of various kinds. The unique solvability of a number of the considered problems is shown, as well as the stability of their solutions. The numberical analysis ranges from the finited-difference scheme inversion to the linearization methods, and to a dynamic variant of the Gel'fand-Levitan methods. The book should be of interest to researchers in the fields of applied mathematics and geophysics. The applications in the book should be of use to experimentalists and engineers.