The linear sampling method for the transmission problem in three-dimensional linear elasticity

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	2014-03-01T01:18:25Z
dc.date.available	2014-03-01T01:18:25Z
dc.date.issued	2002	en
dc.identifier.issn	0266-5611	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14997
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Physics, Mathematical	en
dc.subject.other	Adsorption	en
dc.subject.other	Approximation theory	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Elasticity	en
dc.subject.other	Green's function	en
dc.subject.other	Inclusions	en
dc.subject.other	Integrodifferential equations	en
dc.subject.other	Inverse problems	en
dc.subject.other	Problem solving	en
dc.subject.other	Penetrable scatterers	en
dc.subject.other	Shape reconstructions	en
dc.subject.other	Electromagnetic wave scattering	en
dc.title	The linear sampling method for the transmission problem in three-dimensional linear elasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1088/0266-5611/18/3/303	en
heal.identifier.secondary	http://dx.doi.org/10.1088/0266-5611/18/3/303	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	In this paper the sampling method for the shape reconstruction of a penetrable scatterer in three-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. We establish the interior transmission problem in the weak sense and consider the case where the nonhomogeneous boundary data are generated by a dyadic source point located in the interior domain. Assuming that the inclusion has absorbing behaviour, we prove the existence and uniqueness of the weak solution of the interior transmission problem. In this framework the main theorem for the shape reconstruction for the transmission case is established. As for the cases of the rigid body and the cavity an approximate far-field equation is derived with the known dyadic Green function term with the source point an interior point of the inclusion. The inversion scheme which is proposed is based on the unboundedness for the solution of an equation of the first kind. More precisely, the support of the body can be found by noting that the solution of the integral equation is not bounded as the point of the location of the fundamental solution approaches the boundary of the scatterer from interior points.	en
heal.publisher	IOP PUBLISHING LTD	en
heal.journalName	Inverse Problems	en
dc.identifier.doi	10.1088/0266-5611/18/3/303	en
dc.identifier.isi	ISI:000176750400004	en
dc.identifier.volume	18	en
dc.identifier.issue	3	en
dc.identifier.spage	547	en
dc.identifier.epage	558	en