Synthesis of global convergence and adaptivity for a hyperbolic coefficient inverse problem in 3D

被引：20

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 | 2010年 / 18卷 / 01期

关键词：

Two-stage numerical procedure; globally convergent numerical method; adaptive finite element method; RECONSTRUCTION;

D O I：

10.1515/JIIP.2010.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A globally convergent numerical method for a 3-Dimensional Coefficient Inverse Problem for a hyperbolic equation is presented. A new globally convergent theorem is proven. It is shown that this technique provides a good first guess for the Finite Element Adaptive method (adaptivity) method. This leads to a synthesis of both approaches. Numerical results are presented.

引用

页码：85 / 132

页数：48

共 50 条

[1] New a posteriori error estimates for adaptivity technique and global convergence for the hyperbolic coefficient inverse problem
Beilina L.
Klibanov M.V.
Kuzhuget A.
[J]. Journal of Mathematical Sciences, 2011, 172 (4) : 449 - 476
[2] Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem
Beilina L.
Klibanov M.V.
Kokurin M.Y.
[J]. Journal of Mathematical Sciences, 2010, 167 (3) : 279 - 325
[3] A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem
Beilina, Larisa
Klibanov, Michael V.
[J]. INVERSE PROBLEMS, 2010, 26 (04)
[4] A Holder stability estimate for a 3D coefficient inverse problem for a hyperbolic equation with a plane wave
Klibanov, Michael V. V.
Romanov, Vladimir G. G.
[J]. JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2022, 31 (02): : 223 - 242
[5] Iterative Regularization and Adaptivity for an Electromagnetic Coefficient Inverse Problem
Malmberg, John Bondestam
Beilina, Larisa
[J]. PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2016 (ICNAAM-2016), 2017, 1863
[6] Approximate global convergence and quasireversibility for a coefficient inverse problem with backscattering data
Kuzhuget A.V.
Beilina L.
Klibanov M.V.
[J]. Journal of Mathematical Sciences, 2012, 181 (2) : 126 - 163
[7] Estimating the boundary condition in a 3D inverse hyperbolic heat conduction problem
Hsu, Pao-Tung
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 177 (02) : 453 - 464
[8] Convergence theorem for a numerical method of a 1D coefficient inverse problem
Ozbilge, Ebru
[J]. APPLICABLE ANALYSIS, 2014, 93 (08) : 1611 - 1625
[9] Adaptive FEM with Relaxation for a Hyperbolic Coefficient Inverse Problem
[J]. Beilina, L. (larisa@chalmers.se), 2013, Springer Science and Business Media, LLC (48):
[10] A new approximate mathematical model for global convergence for a coefficient inverse problem with backscattering data
Beilina, Larisa
Klibanov, Michael V.
[J]. JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2012, 20 (04): : 513 - 565

← 1 2 3 4 5 →