This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative–based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.
Habib Ammari is director of research at the French National Center for Scientific Research and professor of mathematics at the École Normale Superiéure. Elie Bretin is a postdoctoral researcher in mathematics at the École Polytechnique. Josselin Garnier is professor of mathematics at Université Paris VII. Hyeonbae Kang is the Jungseok Chair Professor of Mathematics at Inha University in South Korea. Hyundae Lee is assistant professor of mathematics at Inha University. Abdul Wahab is a postdoctoral researcher in mathematics at Université Paris VII.
"This timely book that is devoted to a topic of paramount importance is very well written and it contains useful and interesting material. I strongly believe that it will be a valuable resource for researchers in elasticity imaging and related areas of nondestructive testing and inverse problems."—Akhtar A. Khan, MathSciNet
"This book covers recent mathematical, numerical, and statistical approaches for elasticity imaging of inclusions and cracks. A precise and timely book, it is easy to follow and will interest readers."—Yanyan Li, Rutgers University
"This book is the first to provide readers with a comprehensive overview of mathematical and computational studies of elasticity imaging. It is a useful resource for scientists and engineers in the relevant fields and a solid reference for any newcomers to elasticity imaging."—Gang Bao, Zhejiang University
"This well-organized book explains recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. It makes an important contribution to the understanding of trade-offs between data size, computational complexity, signal-to-noise ratio, and resolution in multistatic imaging."—Jin Keun Seo, Yonsei University
