Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems

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Springer Science & Business Media, 9.3.2012 - 408 sivua
Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems is the first book in which two new concepts of numerical solutions of multidimensional Coefficient Inverse Problems (CIPs) for a hyperbolic Partial Differential Equation (PDE) are presented: Approximate Global Convergence and the Adaptive Finite Element Method (adaptivity for brevity).

Two central questions for CIPs are addressed: How to obtain a good approximations for the exact solution without any knowledge of a small neighborhood of this solution, and how to refine it given the approximation.

The book also combines analytical convergence results with recipes for various numerical implementations of developed algorithms. The developed technique is applied to two types of blind experimental data, which are collected both in a laboratory and in the field. The result for the blind backscattering experimental data collected in the field addresses a real world problem of imaging of shallow explosives.
 

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Sisältö

Chapter 1 Two Central Questions of This Book and an Introduction to the Theories of Illposed and Coefficient Inverse Problems
1
Chapter 2 Approximately Globally Convergent Numerical Method
95
Chapter 3 Numerical Implementation of the Approximately Globally Convergent Method
168
Chapter 4 The Adaptive Finite Element Technique and Its Synthesis with the Approximately Globally Convergent Numerical Method
193
Chapter 5 Blind Experimental Data
295
Chapter 6 Backscattering Data
335
References
393
Index
400
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