Kreß, Rainer

[["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"]]

[["dc.bibliographiccitation.firstpage","418"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Journal of Computational and Applied Mathematics"],["dc.bibliographiccitation.lastpage","427"],["dc.bibliographiccitation.volume","204"],["dc.contributor.author","Kress, Rainer"],["dc.contributor.author","Serranho, Pedro"],["dc.date.accessioned","2018-11-07T11:00:37Z"],["dc.date.available","2018-11-07T11:00:37Z"],["dc.date.issued","2007"],["dc.description.abstract","We are interested in solving the inverse problem of acoustic wave scattering to reconstruct the position and the shape of sound-hard obstacles from a given incident field and the corresponding far field pattern of the scattered field. The method we suggest is an extension of the hybrid method for the reconstruction of sound-soft cracks as presented in [R. Kress, P. Serranho, A hybrid method for two-dimensional crack reconstruction, Inverse Problems 21 (2005) 773-784] to the case of sound-hard obstacles. The designation of the method is justified by the fact that it can be interpreted as a hybrid between a regularized Newton method applied to a nonlinear operator equation with the operator that maps the unknown boundary onto the solution of the direct scattering problem and a decomposition method in the spirit of the potential method as described in [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Cannon, Hornung (Eds.), Inverse Problems, ISNM, vol. 77, 1986, pp. 93-102. Since the method does not require a forward solver for each Newton step its computational costs are reduced. By some numerical examples we illustrate the feasibility of the method. (c) 2006 Elsevier B.V. All rights reserved."],["dc.identifier.doi","10.1016/j.cam.2006.02.047"],["dc.identifier.isi","000246816900021"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/50964"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Elsevier Science Bv"],["dc.publisher.place","Amsterdam"],["dc.relation.conference","7th International Conference on Mathematical and Numerical Aspects of Waves"],["dc.relation.eventlocation","Brown Univ, Providence, RI"],["dc.relation.issn","0377-0427"],["dc.title","A hybrid method for sound-hard obstacle reconstruction"],["dc.type","conference_paper"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","055005"],["dc.bibliographiccitation.issue","5"],["dc.bibliographiccitation.journal","Inverse Problems"],["dc.bibliographiccitation.volume","25"],["dc.contributor.author","Alves, Carlos"],["dc.contributor.author","Kress, Rainer"],["dc.contributor.author","Serranho, Pedro"],["dc.date.accessioned","2018-11-07T08:30:19Z"],["dc.date.available","2018-11-07T08:30:19Z"],["dc.date.issued","2009"],["dc.description.abstract","We propose two methods for solving an inverse source problem for time-harmonic acoustic waves. Based on the reciprocity gap principle a nonlinear equation is presented for the locations and intensities of the point sources that can be solved via Newton iterations. To provide an initial guess for this iteration we suggest a range test algorithm for approximating the source locations. We give a mathematical foundation for the range test and exhibit its feasibility in connection with the iteration method by some numerical examples."],["dc.description.sponsorship","FCT [POCI/MAT/60863/2004]; Fundacao Calouste Gulbenkian"],["dc.identifier.doi","10.1088/0266-5611/25/5/055005"],["dc.identifier.isi","000264813000006"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/5997"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/16867"],["dc.notes.intern","Merged from goescholar"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Iop Publishing Ltd"],["dc.relation.issn","0266-5611"],["dc.rights","Goescholar"],["dc.rights.uri","https://goescholar.uni-goettingen.de/licenses"],["dc.title","Iterative and range test methods for an inverse source problem for acoustic waves"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]