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Inverse Problems for Maxwell's Equations
V. Vladimir Gavrilovich RomanovSergei Igorevich Kabanikhin
出版VSP, 1994
主題Mathematics / Differential Equations / GeneralArchitecture / Interior Design / GeneralMathematics / Mathematical AnalysisScience / General
ISBN97890676417229067641723
URLhttp://books.google.com.hk/books?id=EIMLXfuT_jgC&hl=&source=gbs_api
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註釋The book offers a simultaneous presentation of the theory and numerical treatment of inverse problems for Maxwell's equations. The inverse problems are central to many areas of science and technology such as geophysical exploration, remote sensing, near-surface radar-location, dielectric logging, medical imaging, etc. The basic idea. of inverse methods is to extract from the evaluation of measured electromagnetic field the details of the medium considered. The inverse problems are investigated not only for Maxwell's equations but also for their guasistationary 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 multidimensional 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 numerical analysis ranges from the finite-difference scheme inversion to the linearization method and finally the dynamic variant of the Gel'fand-Levitan method. Computational results are presented. The book is intended to provide graduate students in applied mathematics and geophysics, as well as the researches in the field, with an understanding of inverse problem theory. Although the main part of the book is rather theoretical in nature, it is also of practical value to experimentalists and engineers.