The linear sampling method for non-absorbing penetrable elastic bodies

Charalambopoulos, A; Gintides, D; Kiriaki, K

dc.contributor.author	Charalambopoulos, A	en
dc.contributor.author	Gintides, D	en
dc.contributor.author	Kiriaki, K	en
dc.date.accessioned	2014-03-01T01:19:37Z
dc.date.available	2014-03-01T01:19:37Z
dc.date.issued	2003	en
dc.identifier.issn	0266-5611	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15610
dc.subject	Linear Sampling Method	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Physics, Mathematical	en
dc.subject.other	Acoustic noise	en
dc.subject.other	Acoustic wave transmission	en
dc.subject.other	Algorithms	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Boundary element method	en
dc.subject.other	Elasticity	en
dc.subject.other	Green's function	en
dc.subject.other	Image reconstruction	en
dc.subject.other	Inverse problems	en
dc.subject.other	Sampling	en
dc.subject.other	Boundedness	en
dc.subject.other	Acoustic wave scattering	en
dc.title	The linear sampling method for non-absorbing penetrable elastic bodies	en
heal.type	journalArticle	en
heal.identifier.primary	10.1088/0266-5611/19/3/305	en
heal.identifier.secondary	http://dx.doi.org/10.1088/0266-5611/19/3/305	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	In this paper the linear sampling method for the shape reconstruction of a penetrable non-dissipative scatterer in two-dimensional linear elasticity is examined. We formulate the governing differential equations of the problem in dyadic form in order to acquire a symmetric and uniform representation for the underlying elastic fields. The corresponding far-field operator is defined in the appropriate space setting. Assuming that the inclusion has non-absorbing behaviour, we consider this problem as a degenerate case of a non-dissipative anisotropic inclusion. Results for the existence and uniqueness of the weak solution of the interior transmission problem are obtained. In this framework the main theorem for the shape reconstruction for the transmission case is established. As in the previous works referring to the linear sampling method in acoustics and linear elasticity, the inversion scheme which is proposed is based on the unboundedness of the solution of an equation of the first kind having as the known term the far-field of the free-space Green dyadic, generated by a source inside the inclusion approaching the boundary. Numerical results are presented for different inclusion geometries, assuring the simple and efficient implementation of the algorithm, using synthetic data derived from the boundary element method.	en
heal.publisher	IOP PUBLISHING LTD	en
heal.journalName	Inverse Problems	en
dc.identifier.doi	10.1088/0266-5611/19/3/305	en
dc.identifier.isi	ISI:000183838100005	en
dc.identifier.volume	19	en
dc.identifier.issue	3	en
dc.identifier.spage	549	en
dc.identifier.epage	561	en