Kreß, Rainer

[["dc.bibliographiccitation.firstpage","1221"],["dc.bibliographiccitation.issue","10"],["dc.bibliographiccitation.journal","Mathematical Methods in the Applied Sciences"],["dc.bibliographiccitation.lastpage","1232"],["dc.bibliographiccitation.volume","31"],["dc.contributor.author","Ivanyshyn, Olha"],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T11:13:02Z"],["dc.date.available","2018-11-07T11:13:02Z"],["dc.date.issued","2008"],["dc.description.abstract","We present a Newton-type method for reconstructing planar sound-soft or perfectly conducting cracks from far-field measurements for one time-harmonic scattering with plane wave incidence. Our approach arises from a method suggested by Kress and Rundell (Inv. Probl. 2005; 21(4):1207-1223) for an inverse boundary value problem for the Laplace equation. It was extended to inverse scattering problems for sound-soft obstacles (Mathematical Methods in Scattering Theory and Biomedical Engineering. World Scientific: Singapore, 2006; 39-50) and for sound-hard cracks (Inv. Probl. 2006; 22(6)). In both cases it was shown that the method gives accurate reconstructions with reasonable stability against noisy data. The approach is based on a pair of nonlinear and ill-posed integral equations for the unknown boundary. The integral equations are solved by linearization, i.e. by regularized Newton iterations. Numerical reconstructions illustrate the feasibility of the method. Copyright (C) 2007 John Wiley & Sons, Ltd."],["dc.identifier.doi","10.1002/mma.970"],["dc.identifier.isi","000257098100006"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/53800"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","John Wiley & Sons Ltd"],["dc.relation.issn","0170-4214"],["dc.title","Inverse scattering for planar cracks via nonlinear integral equations"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","3443"],["dc.bibliographiccitation.issue","9"],["dc.bibliographiccitation.journal","Journal of Computational Physics"],["dc.bibliographiccitation.lastpage","3452"],["dc.bibliographiccitation.volume","230"],["dc.contributor.author","Ivanyshyn, Olha"],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T08:56:46Z"],["dc.date.available","2018-11-07T08:56:46Z"],["dc.date.issued","2011"],["dc.description.abstract","We present a numerical comparison of a regularized Newton-type method and a direct method for reconstructing the surface impedance function of a three dimensional acoustic scatterer with known shape from the full far field pattern for scattering of one incident time-harmonic plane wave. Furthermore, we propose a modification of the Newton-type algorithm to recover a real-valued surface impedance from phase-less far field data. Numerical reconstructions illustrate the feasibility of the methods. (c) 2011 Elsevier Inc. All rights reserved."],["dc.description.sponsorship","SFB [755]"],["dc.identifier.doi","10.1016/j.jcp.2011.01.038"],["dc.identifier.isi","000289446800011"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/23229"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Academic Press Inc Elsevier Science"],["dc.relation.issn","0021-9991"],["dc.title","Inverse scattering for surface impedance from phase-less far field data"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","413"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Advances in Computational Mathematics"],["dc.bibliographiccitation.lastpage","429"],["dc.bibliographiccitation.volume","33"],["dc.contributor.author","Ivanyshyn, Olha"],["dc.contributor.author","Kress, Rainer"],["dc.contributor.author","Serranho, Pedro"],["dc.date.accessioned","2018-11-07T08:37:11Z"],["dc.date.available","2018-11-07T08:37:11Z"],["dc.date.issued","2010"],["dc.description.abstract","The inverse problem we consider in this paper is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the case of scattering from a sound-soft obstacle, we will interpret Huygens' principle as a system of two integral equations, named data and field equation, for the unknown boundary of the scatterer and the induced surface flux, i.e., the unknown normal derivative of the total field on the boundary. Reflecting the ill-posedness of the inverse obstacle scattering problem these integral equations are ill-posed. They are linear with respect to the unknown flux and nonlinear with respect to the unknown boundary and offer, in principle, three immediate possibilities for their iterative solution via linearization and regularization. In addition to presenting new results on injectivity and dense range for the linearized operators, the main purpose of this paper is to establish and illuminate relations between these three solution methods based on Huygens' principle in inverse obstacle scattering. Furthermore, we will exhibit connections and differences to the traditional regularized Newton type iterations as applied to the boundary to far field map, including alternatives for the implementation of these Newton iterations."],["dc.identifier.doi","10.1007/s10444-009-9135-6"],["dc.identifier.isi","000282585900003"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/18473"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Springer"],["dc.relation.issn","1019-7168"],["dc.title","Huygens' principle and iterative methods in inverse obstacle scattering"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]