Kreß, Rainer

[["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","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","863"],["dc.bibliographiccitation.issue","6"],["dc.bibliographiccitation.journal","Complex Variables and Elliptic Equations"],["dc.bibliographiccitation.lastpage","882"],["dc.bibliographiccitation.volume","59"],["dc.contributor.author","Haddar, Houssem"],["dc.contributor.author","Kress, Rainer"],["dc.date.accessioned","2018-11-07T09:39:00Z"],["dc.date.available","2018-11-07T09:39:00Z"],["dc.date.issued","2014"],["dc.description.abstract","Akduman, Haddar and Kress [Akduman I, Kress R. Electrostatic imaging via conformal mapping. Inverse Prob. 2002;18:1659-1672; Haddar H, Kress R. Conformal mappings and inverse boundary value problems. Inverse Prob. 2005;21:935-953; Kress R. Inverse Dirichlet problem and conformal mapping. Math.Comput. Simul. 2004;66:255-265] have employed a conformal mapping technique for the inverse problem to reconstruct a perfectly conducting inclusion in a homogeneous background medium from Cauchy data for electrostatic imaging, that is, for solving an inverse boundary value problem for the Laplace equation. We propose an extension of this approach to inverse obstacle scattering for time-harmonic waves, that is, to the solution of an inverse boundary value problem for the Helmholtz equation. The main idea is to use the conformal mapping algorithm in an iterative procedure to obtain Cauchy data for a Laplace problem from the given Cauchy data for the Helmholtz problem. We present the foundations of the method together with a convergence result and exhibit the feasibility of the method via numerical examples."],["dc.identifier.doi","10.1080/17476933.2013.791687"],["dc.identifier.isi","000334080400008"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/33187"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Taylor & Francis Ltd"],["dc.relation.issn","1747-6941"],["dc.relation.issn","1747-6933"],["dc.title","A conformal mapping method in inverse obstacle scattering"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]