Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems

by Beilina, Larisa; Klibanov, Michael Victor

• ISBN13: 9781441978042
• ISBN10: 1441978046
• Format: Hardcover
• Copyright: 2012-03-09
• Publisher: Springer Verlag

Summary

This is the first full-length book where globally convergent numerical methods for coefficient inverse problems for partial differential equations are presented. Conventional algorithms for these problems are known to converge locally. Globally convergent methods described in this book are synthesized with the Adaptive Finite Element technique (adaptivity for brevity). A broad range of applications is discussed, and a detailed convergence analysis is presented via a variety of numerical experiments. Computational studies include the work with both computationally simulated and experimental data. A special focus of the book is on specifics of numerical implementations of algorithms and instructions for these implementations. The authors also describe the many details of numerical implementation of the globally convergent method as well as of the adaptivity technique in the two-stage numerical procedure.