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Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems

  • Larisa Beilina
  • Michael Victor Klibanov

Table of contents

  1. Front Matter
    Pages i-xv
  2. Larisa Beilina, Michael Victor Klibanov
    Pages 95-167
  3. Larisa Beilina, Michael Victor Klibanov
    Pages 169-192
  4. Larisa Beilina, Michael Victor Klibanov
    Pages 295-334
  5. Larisa Beilina, Michael Victor Klibanov
    Pages 335-392
  6. Back Matter
    Pages 393-407

About this book

Introduction

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 approximation 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.

Keywords

Inverse problems for partial differential equations Tikhonov regularization theory adaptive finite element method for inverse problems coefficient inverse problems globally convergent numerical methods

Authors and affiliations

  • Larisa Beilina
    • 1
  • Michael Victor Klibanov
    • 2
  1. 1.Gothenburg University, Department of Mathematical SciencesChalmers University of TechnologyGothenburgSweden
  2. 2.University of North CarolinaCharlotteUSA

Bibliographic information