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

被引：24

作者：

Beilina, Larisa ^{[1
,2
]}

Klibanov, Michael V. ^{[3
]}

机构：

[1] Chalmers Univ Technol, Dept Math Sci, SE-42196 Gothenburg, Sweden

[2] Gothenburg Univ, SE-42196 Gothenburg, Sweden

[3] Univ N Carolina, Dept Math & Stat, Charlotte, NC 28223 USA

来源：

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS | 2012年 / 20卷 / 04期

基金：

瑞典研究理事会;

关键词：

Coefficient inverse problems; approximate global convergence; new approximate mathematical model; convergence analysis; numerical studies; NUMERICAL-METHOD;

D O I：

10.1515/jip-2012-0063

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 "tail functions" are estimated. Numerical results in 2d and 3d cases are discussed, including the one for a quite heterogeneous medium.

引用

页码：513 / 565

页数：53

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