Characterization of the Frechet derivative of the elasto-acoustic field with respect to Lipschitz domains

被引：5

作者：

Barucq, Helene ^{[1
,2
]}

Djellouli, Rabia ^{[3
,4
]}

Estecahandy, Elodie ^{[1
,2
]}

机构：

[1] INRIA Bordeaux Sud Ouest Res Ctr, Team Project Mag 3D, Bordeaux, France

[2] Univ Pau & Pays Adour, LMA, F-64010 Pau, France

[3] Calif State Univ Northridge, Dept Math, Northridge, CA 91330 USA

[4] Calif State Univ Northridge, Interdisciplinary Res Inst Sci, Northridge, CA 91330 USA

来源：

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS | 2014年 / 22卷 / 01期

关键词：

Acoustics; elastodynamics; shape derivative; inverse problems; Frechet derivatives; SCATTERING; CRACKS; BODY;

D O I：

10.1515/jip-2012-0098

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the continuous Frechet differentiability of the elasto-acoustic field with respect to Lipschitz continuous deformation of the shape of an elastic scatterer. We then characterize the derivative as a solution of a direct elasto-acoustic-type problem. Such a characterization has the potential to advance the state-of-the-art of the solution of inverse elasto-acoustic scattering problems.

引用

页码：1 / 8

页数：8

共 11 条

[1] On the characterization of the Frechet derivative with respect to a Lipschitz domain of the acoustic scattered field [J].

Djellouli, R ;

Farhat, C .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 238 (01) :259-276

[2] Continuous Frechet differentiability with respect to a Lipschitz domain and a stability estimate for direct acoustic scattering problems [J].

Djellouli, R ;

Farhat, C ;

Mandel, J ;

Vanek, P .

IMA JOURNAL OF APPLIED MATHEMATICS, 1999, 63 (01) :51-69

[3] On the analysis of boundary value problems in nonsmooth domains [J].

Fremiot, Gilles ;

Horn, Werner ;

Laurain, Antoine ;

Rao, Murali ;

Sokolowski, Jan .

DISSERTATIONES MATHEMATICAE, 2009, (462) :7-+

[4]

HARGE T, 1990, CR ACAD SCI I-MATH, V311, P857

[5] From shape variation to topological changes in constrained minimization: a velocity method-based concept [J].

Hintermueller, M. ;

Kovtunenko, V. A. .

OPTIMIZATION METHODS & SOFTWARE, 2011, 26 (4-5) :513-532

[6] LOW-FREQUENCY SCATTERING BY A BODY IN LUBRICATED CONTACT [J].

JONES, DS .

QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 1983, 36 (FEB) :111-138

[7]

Junger M.C., 1972, Sound, Structures, and Their Interaction, V1st

[8] Reconstruction of pressure and shear velocities and boundaries of thin layers in a thinly stratified stack [J].

Karchevsky, A.L. .

Numerical Analysis and Applications, 2012, 5 (01) :54-67

[9] On derivative of energy functional for elastic bodies with cracks and unilateral conditions [J].

Khludnev, AM ;

Ohtsuka, K ;

Sokolowski, J .

QUARTERLY OF APPLIED MATHEMATICS, 2002, 60 (01) :99-109

[10] Shape sensitivity of curvilinear cracks on interface to non-linear perturbations [J].

Kovtunenko, VA .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2003, 54 (03) :410-423

← 1 2 →