Kreß, Rainer

[["dc.bibliographiccitation.firstpage","23"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Applicable Analysis"],["dc.bibliographiccitation.lastpage","38"],["dc.bibliographiccitation.volume","96"],["dc.contributor.author","Cakoni, Fioralba"],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T10:29:32Z"],["dc.date.available","2018-11-07T10:29:32Z"],["dc.date.issued","2017"],["dc.description.abstract","We propose a new integral equation formulation to characterize and compute transmission eigenvalues for constant refractive index that play an important role in inverse scattering problems for penetrable media. As opposed to the recently developed approach by Cossonniere and Haddar [1,2] which relies on a two by two system of boundary integral equations our analysis is based on only one integral equation in terms of Dirichlet-to-Neumann or Robin-to-Dirichlet operators which results in a noticeable reduction of computational costs. We establish Fredholm properties of the integral operators and their analytic dependence on the wave number. Further we employ the numerical algorithm for analytic non-linear eigenvalue problems that was recently proposed by Beyn [3] for the numerical computation of transmission eigenvalues via this new integral equation."],["dc.description.sponsorship","AFOSR [FA9550-13-1-0199]; NSF [DMS1602802]"],["dc.identifier.doi","10.1080/00036811.2016.1189537"],["dc.identifier.isi","000390670600003"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/43660"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","PUB_WoS_Import"],["dc.publisher","Taylor & Francis Ltd"],["dc.relation.issn","1563-504X"],["dc.relation.issn","0003-6811"],["dc.title","A boundary integral equation method for the transmission eigenvalue problem"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","095012"],["dc.bibliographiccitation.issue","9"],["dc.bibliographiccitation.journal","Inverse Problems"],["dc.bibliographiccitation.volume","26"],["dc.contributor.author","Cakoni, Fioralba"],["dc.contributor.author","Kress, Rainer"],["dc.contributor.author","Schuft, Christian"],["dc.date.accessioned","2018-11-07T08:39:45Z"],["dc.date.available","2018-11-07T08:39:45Z"],["dc.date.issued","2010"],["dc.description.abstract","In a simply connected planar domain D a pair of Cauchy data of a harmonic function u is given on an accessible part of the boundary curve, and on the non-accessible part u is supposed to satisfy a homogeneous impedance boundary condition. We consider the inverse problems to recover the non-accessible part of the boundary or the impedance function. Our approach extends the method proposed by Kress and Rundell (2005 Inverse Problems 21 1207-23) for the corresponding problem to recover the interior boundary curve of a doubly connected planar domain and can be considered complementary to the potential approach developed by Cakoni and Kress (2007 Inverse Problems Imaging 1 229-45). It is based on a system of nonlinear and ill-posed integral equations which is solved iteratively by linearization. We present the mathematical foundation of the method and, in particular, establish injectivity for the linearized system at the exact solution when the impedance function is known. Numerical reconstructions will show the feasibility of the method."],["dc.identifier.doi","10.1088/0266-5611/26/9/095012"],["dc.identifier.isi","000280962800012"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/19073"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Iop Publishing Ltd"],["dc.relation.issn","0266-5611"],["dc.title","Integral equations for shape and impedance reconstruction in corrosion detection"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","229"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Inverse Problems and Imaging"],["dc.bibliographiccitation.lastpage","245"],["dc.bibliographiccitation.volume","1"],["dc.contributor.author","Cakoni, Fioralba"],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T11:02:43Z"],["dc.date.available","2018-11-07T11:02:43Z"],["dc.date.issued","2007"],["dc.description.abstract","We consider the inverse problem to recover a part c of the boundary of a simply connected planar domain D from a pair of Cauchy data of a harmonic function u in D on the remaining part partial derivative D\\Gamma(c) when u satisfies a homogeneous impedance boundary condition on Gamma(c). Our approach extends a method that has been suggested by Kress and Rundell [17] for recovering the interior boundary curve of a doubly connected planar domain from a pair of Cauchy data on the exterior boundary curve and is based on a system of non-linear integral equations. As a byproduct, these integral equations can also be used for the problem to extend incomplete Cauchy data and to solve the inverse problem to recover an impedance profile on a known boundary curve. We present the mathematical foundation of the method and illustrate its feasibility by numerical examples."],["dc.identifier.isi","000255216700001"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/51450"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Inst Mathematical Sciences"],["dc.relation.issn","1930-8337"],["dc.title","Integral equations for inverse problems in corrosion detection from partial Cauchy data"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","105009"],["dc.bibliographiccitation.issue","10"],["dc.bibliographiccitation.journal","Inverse Problems"],["dc.bibliographiccitation.volume","30"],["dc.contributor.author","Cakoni, Fioralba"],["dc.contributor.author","Hu, Yuqing"],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T09:34:28Z"],["dc.date.available","2018-11-07T09:34:28Z"],["dc.date.issued","2014"],["dc.description.abstract","Determining the geometry and the physical nature of an inclusion within a conducting medium from voltage and current measurements on the accessible boundary of the medium can be modeled as an inverse boundary value problem for the Laplace equation subject to appropriate boundary conditions on the inclusion. We continue the investigations on the particular inverse problem with a generalized impedance condition started in Cakoni and Kress (2013 Inverse Problems 29 015005) by presenting an inverse algorithm for the simultaneous reconstruction of both the shape of the inclusion and the two impedance functions via a boundary integral equation approach. In addition to describing the reconstruction algorithm and illustrating its feasibility by numerical examples we also provide some extensions to the uniqueness results in Cakoni and Kress (2013 Inverse Problems 29 015005)."],["dc.description.sponsorship","AFOSR [FA9550-13-1-0199]; NSFC [91330109]"],["dc.identifier.doi","10.1088/0266-5611/30/10/105009"],["dc.identifier.isi","000343131300009"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/32176"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Iop Publishing Ltd"],["dc.relation.issn","1361-6420"],["dc.relation.issn","0266-5611"],["dc.title","Simultaneous reconstruction of shape and generalized impedance functions in electrostatic imaging"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","015005"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Inverse Problems"],["dc.bibliographiccitation.volume","29"],["dc.contributor.author","Cakoni, Fioralba"],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T09:30:47Z"],["dc.date.available","2018-11-07T09:30:47Z"],["dc.date.issued","2013"],["dc.description.abstract","Determining the shape of an inclusion within a conducting medium from voltage and current measurements on the accessible boundary of the medium can be modeled as an inverse boundary value problem for the Laplace equation. We present a solution method for such an inverse boundary value problem with a generalized impedance boundary condition on the inclusion via boundary integral equations. Both the determination of the unknown boundary and the determination of the unknown impedance functions are considered. In addition to describing the reconstruction algorithms and illustrating their feasibility by numerical examples, we also obtain a uniqueness result on determining the impedance coefficients."],["dc.identifier.doi","10.1088/0266-5611/29/1/015005"],["dc.identifier.isi","000312910600005"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/31390"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Iop Publishing Ltd"],["dc.relation.issn","0266-5611"],["dc.title","Integral equation methods for the inverse obstacle problem with generalized impedance boundary condition"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]