A new approximate mathematical model for global convergence for a coefficient inverse problem with backscattering data

作者：Beilina Larisa^*; Klibanov Michael V

来源：Journal of Inverse and Ill-Posed Problems, 2012, 20(4): 513-565.

DOI：10.1515/jip-2012-0063

• Coefficient inverse problems
• approximate global convergence
• new approximate mathematical model
• convergence analysis
• numerical studies

An approximately globally convergent numerical method for a 3d coefficient inverse problem for a hyperbolic equation with backscattering data is presented. A new approximate mathematical model is presented as well. An approximation is used only on the first iteration and amounts to the truncation of a certain asymptotic series. A significantly new element of the convergence analysis is that the so-called %26quot;tail functions%26quot; are estimated. Numerical results in 2d and 3d cases are discussed, including the one for a quite heterogeneous medium.

• 出版日期2012-10