Kreß, Rainer

[["dc.bibliographiccitation.artnumber","PII 908586241"],["dc.bibliographiccitation.firstpage","473"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Inverse Problems in Science and Engineering"],["dc.bibliographiccitation.lastpage","488"],["dc.bibliographiccitation.volume","17"],["dc.contributor.author","Kress, Rainer"],["dc.contributor.author","Yaman, Fatih"],["dc.contributor.author","Yapar, Ali"],["dc.contributor.author","Akduman, Ibrahim"],["dc.date.accessioned","2018-11-07T08:34:44Z"],["dc.date.available","2018-11-07T08:34:44Z"],["dc.date.issued","2009"],["dc.description.abstract","An inverse scattering problem is considered for arbitrarily shaped cylindrical objects that have inhomogeneous impedance boundaries and are buried in arbitrarily shaped cylindrical dielectrics. Given the shapes of the impedance object and the dielectric, the inverse problem consists of reconstructing the inhomogeneous boundary impedance from a measured far field pattern for an incident time-harmonic plane wave. Extending the approach suggested by Akduman and Kress [Direct and inverse scattering problems for inhomogeneous impedance cylinders of arbitrary shape. Radio Sci. 38 (2003), pp. 1055-1064] for an impedance cylinder in an homogeneous background medium, both the direct and the inverse scattering problem are solved via boundary integral equations. For the inverse problem, representing the scattered field as a potential leads to severely ill-posed linear integral equations of the first kind for the densities. For their stable numerical solution Tikhonov regularization is employed. Knowing the scattered field, the boundary impedance function can be obtained from the boundary condition either by direct evaluation or by a least squares approach. We provide a mathematical foundation of the inverse method and illustrate its feasibility by numerical examples."],["dc.description.sponsorship","University of Gottingen; DAAD"],["dc.identifier.doi","10.1080/17415970802131760"],["dc.identifier.isi","000265453300004"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/17889"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.relation.issn","1741-5977"],["dc.title","Inverse scattering for an impedance cylinder buried in a dielectric cylinder"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dspace.entity.type","Publication"]]

[["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.artnumber","074002"],["dc.bibliographiccitation.issue","7"],["dc.bibliographiccitation.journal","Inverse Problems"],["dc.bibliographiccitation.volume","26"],["dc.contributor.author","Haddar, Houssem"],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T08:41:45Z"],["dc.date.available","2018-11-07T08:41:45Z"],["dc.date.issued","2010"],["dc.description.abstract","Akduman and Kress (2002 Inverse Problems 18 1659-1672), Haddar and Kress (2005 Inverse Problems 21 935-953), and Kress (2004 Math. Comput. Simul. 66 255-265) have employed a conformal mapping technique for the inverse problem to recover a perfectly conducting or a non-conducting inclusion in a homogeneous background medium from the Cauchy data on the accessible exterior boundary. We propose an extension of this approach to two-dimensional inverse electrical impedance tomography with piecewise constant conductivities. A main ingredient of our method is the incorporation of the transmission condition on the unknown interior boundary via a nonlocal boundary condition in terms of an integral equation. We present the foundations of the method, a local convergence result and exhibit the feasibility of the method via numerical examples."],["dc.description.sponsorship","German Ministry of Education and Research"],["dc.identifier.doi","10.1088/0266-5611/26/7/074002"],["dc.identifier.isi","000279429000003"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/19539"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Iop Publishing Ltd"],["dc.relation.issn","0266-5611"],["dc.title","Conformal mapping and impedance tomography"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","193"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Journal of Integral Equations and Applications"],["dc.bibliographiccitation.lastpage","216"],["dc.bibliographiccitation.volume","22"],["dc.contributor.author","Delbary, Fabrice"],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T08:42:49Z"],["dc.date.available","2018-11-07T08:42:49Z"],["dc.date.issued","2010"],["dc.description.abstract","We consider the two-dimensional inverse electrical impedance problem in the case of piecewise constant conductivities with the currents injected at adjacent point electrodes and the resulting voltages measured between the remaining electrodes. Our approach is based on nonlinear integral equations for the unknown shape of an inclusion with conductivity different from the background conductivity. It extends a method that has been suggested by Kress and Rundell [7] for the case of a perfectly conducting inclusion. We describe the method in detail and illustrate its feasibility by numerical examples."],["dc.description.sponsorship","German Ministry of Education and Research"],["dc.identifier.doi","10.1216/JIE-2010-22-2-193"],["dc.identifier.isi","000279048300003"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/19794"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Rocky Mt Math Consortium"],["dc.relation.issn","0897-3962"],["dc.title","ELECTRICAL IMPEDANCE TOMOGRAPHY WITH POINT ELECTRODES"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","65"],["dc.bibliographiccitation.journal","The ANZIAM Journal"],["dc.bibliographiccitation.lastpage","78"],["dc.bibliographiccitation.volume","42"],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T10:40:20Z"],["dc.date.available","2018-11-07T10:40:20Z"],["dc.date.issued","2000"],["dc.description.abstract","In this survey we consider a regularized Newton method for the approximate solution of the inverse problem to determine the shape of an obstacle from a knowledge of the far field pattern for the scattering of time-harmonic acoustic or electromagnetic plane waves. Our analysis is in two dimensions and the numerical scheme is based on the solution of boundary integral equations by a Nystrom method. We include an example of the reconstruction of a planar domain with a corner both to illustrate the feasibility of the use of radial basis functions for the reconstruction of boundary curves with local features and to connect the presentation to some of the research work of Professor David Elliott."],["dc.identifier.isi","000089492600008"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/46281"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Australian Mathematics Publ Assoc Inc"],["dc.relation.issn","1442-4436"],["dc.title","Integral equation 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","2192"],["dc.bibliographiccitation.issue","10"],["dc.bibliographiccitation.journal","IEEE Transactions on Geoscience and Remote Sensing"],["dc.bibliographiccitation.lastpage","2199"],["dc.bibliographiccitation.volume","43"],["dc.contributor.author","Yapar, A."],["dc.contributor.author","Sahinturk, H."],["dc.contributor.author","Akduman, I."],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T10:55:21Z"],["dc.date.available","2018-11-07T10:55:21Z"],["dc.date.issued","2005"],["dc.description.abstract","A method to reconstruct the one-dimensional profile of a cylindrical layer with an inhomogeneous impedance boundary is proposed. Through the finite Fourier transformation of the field expressions the problem is first reduced to the solutions of a two-coupled system of operator equations which is solved iteratively starting from an initial estimate of the profile. The reconstruction of the profile is achieved by linearizing one of the equations in the Newton sense. The method is tested by considering several numerical examples and yields satisfactory reconstructions. As is typical for Newton-type methods, the convergence of the iteration depends on the initial guess."],["dc.identifier.doi","10.1109/TGRS.2005.855068"],["dc.identifier.isi","000232192800004"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/49765"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.relation.issn","0196-2892"],["dc.title","One-dimensional profile inversion of a cylindrical layer with inhomogeneous impedance boundary: A Newton-type iterative solution"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","179"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Journal of Integral Equations and Applications"],["dc.bibliographiccitation.lastpage","198"],["dc.bibliographiccitation.volume","27"],["dc.contributor.author","Kress, Rainer"],["dc.contributor.author","Rundell, William"],["dc.date.accessioned","2018-11-07T09:56:03Z"],["dc.date.available","2018-11-07T09:56:03Z"],["dc.date.issued","2015"],["dc.description.abstract","We consider the inverse problem of recovering the shape of an extended source of known homogeneous strength within a conducting medium from one voltage and current measurement on the accessible boundary of the medium and present an iterative solution method via boundary integral equations. The main idea of our approach is to equivalently reformulate the inverse source problem as an inverse boundary value problem with a non-local Robin condition on the boundary of the source domain. Following our approach in [12] for an inverse Dirichlet problem, from Green's representation formula we obtain a nonlinear integral equation for the unknown boundary curve which can be solved by regularized Newton iterations. We present the foundations of the inverse algorithm and illustrate its feasibility by some numerical examples."],["dc.description.sponsorship","NSF [DMS-1319052]"],["dc.identifier.doi","10.1216/JIE-2015-27-2-179"],["dc.identifier.isi","000365155700002"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/36884"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Rocky Mt Math Consortium"],["dc.relation.issn","1938-2626"],["dc.relation.issn","0897-3962"],["dc.title","A NONLINEAR INTEGRAL EQUATION AND AN ITERATIVE ALGORITHM FOR AN INVERSE SOURCE PROBLEM"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","757"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Applicable Analysis"],["dc.bibliographiccitation.lastpage","771"],["dc.bibliographiccitation.volume","91"],["dc.contributor.author","Altundag, Ahmet"],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T09:15:20Z"],["dc.date.available","2018-11-07T09:15:20Z"],["dc.date.issued","2012"],["dc.description.abstract","The inverse problem under consideration is to reconstruct the shape of a homogeneous dielectric infinite cylinder from the far-field pattern for scattering of a time-harmonic E-polarized electromagnetic plane wave. We propose an inverse algorithm that extends the approach suggested by Johansson and Sleeman [T. Johansson and B. Sleeman, Reconstruction of an acoustically sound-soft obstacle from one incident field and the far-field pattern, IMA J. Appl. Math. 72 (2007), pp. 96-112] for the case of the inverse problem for a perfectly conducting scatterer. It is based on a system of nonlinear boundary integral equations associated with a single-layer potential approach to solve the forward scattering problem. We present the mathematical foundations of the method and exhibit its feasibility by numerical examples."],["dc.identifier.doi","10.1080/00036811.2011.619981"],["dc.identifier.isi","000304274500008"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/27657"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Taylor & Francis Ltd"],["dc.relation.issn","0003-6811"],["dc.title","On a two-dimensional inverse scattering problem for a dielectric"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","2477"],["dc.bibliographiccitation.issue","10"],["dc.bibliographiccitation.journal","Mathematical Methods in the Applied Sciences"],["dc.bibliographiccitation.lastpage","2487"],["dc.bibliographiccitation.volume","39"],["dc.contributor.author","Haddar, Houssem"],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T10:12:24Z"],["dc.date.available","2018-11-07T10:12:24Z"],["dc.date.issued","2016"],["dc.description.abstract","We propose a new numerical method for the solution of the Bernoulli free boundary value problem for harmonic functions in a doubly connected domain D in R2 where an unknown free boundary (0) is determined by prescribed Cauchy data on (0) in addition to a Dirichlet condition on the known boundary (1). Our main idea is to involve the conformal mapping method as proposed and analyzed by Akduman, Haddar, and Kress for the solution of a related inverse boundary value problem. For this, we interpret the free boundary (0) as the unknown boundary in the inverse problem to construct (0) from the Dirichlet condition on (0) and Cauchy data on the known boundary (1). Our method for the Bernoulli problem iterates on the missing normal derivative on (1) by alternating between the application of the conformal mapping method for the inverse problem and solving a mixed Dirichlet-Neumann boundary value problem in D. We present the mathematical foundations of our algorithm and prove a convergence result. Some numerical examples will serve as proof of concept of our approach. Copyright (c) 2015 John Wiley & Sons, Ltd."],["dc.identifier.doi","10.1002/mma.3708"],["dc.identifier.isi","000378726800005"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/40227"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Wiley-blackwell"],["dc.relation.issn","1099-1476"],["dc.relation.issn","0170-4214"],["dc.title","A conformal mapping algorithm for the Bernoulli free boundary value problem"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","S229"],["dc.bibliographiccitation.journal","ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK"],["dc.bibliographiccitation.lastpage","S232"],["dc.bibliographiccitation.volume","80"],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T11:16:35Z"],["dc.date.available","2018-11-07T11:16:35Z"],["dc.date.issued","2000"],["dc.description.abstract","After outlining some of the foundations for the application of regularized Newton iterations for the solution of the inverse obstacle scattering problem with full far field data we report on the inverse problem with modified data such as limited-aperture observations, amplitude of the far field, or backscattering data."],["dc.identifier.isi","000086621000058"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/54627"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Wiley-v C H Verlag Gmbh"],["dc.relation.issn","0044-2267"],["dc.title","Inverse obstacle scattering with modified ar reduced data"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]