FULL IDENTIFICATION OF ACOUSTIC SOURCES WITH MULTIPLE FREQUENCIES AND BOUNDARY MEASUREMENTS

被引：28

作者：

Alves, Carlos J. S. ^{[1
]}

Martins, Nuno F. M. ^{[2
,3
]}

Roberty, Nilson C. ^{[4
]}

机构：

[1] Univ Tecn Lisboa, CEMAT IST, Dept Matemat, P-1049001 Lisbon, Portugal

[2] Fac Ciencias & Tecnol NULisbon, CEMAT IST, Quinta Da Torre, Caparica, Portugal

[3] Fac Ciencias & Tecnol NULisbon, Dept Matemat, Quinta Da Torre, Caparica, Portugal

[4] Univ Fed Rio de Janeiro, Nucl Engn Program, Rio De Janeiro, Brazil

来源：

INVERSE PROBLEMS AND IMAGING | 2009年 / 3卷 / 02期

关键词：

Inverse acoustic source problem; method of fundamental solutions for Cauchy data fitting; reciprocity gap functional; RECIPROCITY-GAP; FUNDAMENTAL-SOLUTIONS; INVERSE SCATTERING;

D O I：

10.3934/ipi.2009.3.275

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the identification of acoustic sources in a domain Omega from boundary data. With a single frequency, we show that identification is possible if, besides the boundary data, considerable information regarding the type of the source is considered. For the general case, we present an identification result using multiple frequencies and boundary measurements. We show that for compactly supported sources in Omega, the completion of Cauchy data has at most one solution and thus for this type of sources, identification is possible using variable frequencies and incomplete boundary measurements. A numerical method based on the reciprocity functional is proposed and tested for several numerical examples. For compact sources, a data completion method is proposed and tested in order to apply the previous method.

引用

页码：275 / 294

页数：20

共 14 条

[1]

ALVES C, J INTEGRAL IN PRESS

[2] Recovering the source term in a linear diffusion problem by the method of fundamental solutions [J].

Alves, Carlos J. S. ;

Colaco, Marcelo J. ;

Leitao, Vitor M. A. ;

Martins, Nuno F. M. ;

Orlande, Helcio R. B. ;

Roberty, Nilson C. .

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2008, 16 (08) :1005-1021

[3] A new method of fundamental solutions applied to nonhomogeneous elliptic problems [J].

Alves, CJS ;

Chen, CS .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2005, 23 (1-2) :125-142

[4] THE RECIPROCITY GAP - A GENERAL CONCEPT FOR FLAWS IDENTIFICATION PROBLEMS [J].

ANDRIEUX, S ;

BENABDA, A .

MECHANICS RESEARCH COMMUNICATIONS, 1993, 20 (05) :415-420

[5] On the use of the reciprocity-gap functional in inverse scattering from planar cracks [J].

Ben Abda, A ;

Delbary, F ;

Haddart, H .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2005, 15 (10) :1553-1574

[6]

CALDER\ON A. P., 1980, SEMINAR NUMERICAL AN, P65, DOI DOI 10.1590/S0101-82052006000200002

[7]

Chen G., 1992, COMPUTATIONAL MATH A

[8] Solution of the Cauchy problem using iterated Tikhonov regularization [J].

Cimetière, A ;

Delvare, F ;

Jaoua, M ;

Pons, F .

INVERSE PROBLEMS, 2001, 17 (03) :553-570

[9] An application of the reciprocity gap functional to inverse scattering theory [J].

Colton, D ;

Haddar, H .

INVERSE PROBLEMS, 2005, 21 (01) :383-398

[10]

Colton D., 1998, APPL MATH SCI

← 1 2 →