Hohage, Thorsten

[["dc.bibliographiccitation.firstpage","341"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","SIAM Journal on Numerical Analysis"],["dc.bibliographiccitation.lastpage","360"],["dc.bibliographiccitation.volume","54"],["dc.contributor.author","König, Claudia"],["dc.contributor.author","Werner, Frank"],["dc.contributor.author","Hohage, Thorsten"],["dc.date.accessioned","2020-12-10T18:37:19Z"],["dc.date.available","2020-12-10T18:37:19Z"],["dc.date.issued","2016"],["dc.identifier.doi","10.1137/15M1022252"],["dc.identifier.eissn","1095-7170"],["dc.identifier.gro","3146387"],["dc.identifier.issn","0036-1429"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/76912"],["dc.language.iso","en"],["dc.notes.intern","DOI Import GROB-354"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.title","Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","A3552"],["dc.bibliographiccitation.issue","5"],["dc.bibliographiccitation.journal","SIAM Journal on Scientific Computing"],["dc.bibliographiccitation.lastpage","A3579"],["dc.bibliographiccitation.volume","43"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Lehrenfeld, Christoph"],["dc.contributor.author","Preuß, Janosch"],["dc.date.accessioned","2021-07-20T10:21:15Z"],["dc.date.available","2021-07-20T10:21:15Z"],["dc.date.issued","2020-10-29"],["dc.description.abstract","We study the numerical solution of scalar time-harmonic wave equations on unbounded domains which can be split into a bounded interior domain of primary interest and an exterior domain with separable geometry. To compute the solution in the interior domain, approximations to the Dirichlet-to-Neumann (DtN) map of the exterior domain have to be imposed as transparent boundary conditions on the artificial coupling boundary. Although the DtN map can be computed by separation of variables, it is a nonlocal operator with dense matrix representations, and hence computationally inefficient. Therefore, approximations of DtN maps by sparse matrices, usually involving additional degrees of freedom, have been studied intensively in the literature using a variety of approaches including different types of infinite elements, local non-reflecting boundary conditions, and perfectly matched layers. The entries of these sparse matrices are derived analytically, e.g. from transformations or asymptotic expansions of solutions to the differential equation in the exterior domain. In contrast, in this paper we propose to `learn' the matrix entries from the DtN map in its separated form by solving an optimization problem as a preprocessing step. Theoretical considerations suggest that the approximation quality of learned infinite elements improves exponentially with increasing number of infinite element degrees of freedom, which is confirmed in numerical experiments. These numerical studies also show that learned infinite elements outperform state-of-the-art methods for the Helmholtz equation. At the same time, learned infinite elements are much more flexible than traditional methods as they, e.g., work similarly well for exterior domains involving strong reflections, for example, for the atmosphere of the Sun, which is strongly inhomogeneous and exhibits reflections at the corona."],["dc.identifier.doi","10.1137/20M1381757"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/88272"],["dc.language.iso","en"],["dc.relation","SFB 1456 | Cluster C | C04: Correlations of solar oscillations: modeling and inversions"],["dc.relation","SFB 1456 | Cluster C: Data with Information in Their Dependency Structure"],["dc.relation","SFB 1456: Mathematik des Experiments: Die Herausforderung indirekter Messungen in den Naturwissenschaften"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.workinggroup","RG Lehrenfeld (Computational PDEs)"],["dc.rights","CC BY 4.0"],["dc.title","Learned infinite elements"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.subtype","original_ja"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","547"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","SIAM Journal on Mathematical Analysis"],["dc.bibliographiccitation.lastpage","560"],["dc.bibliographiccitation.volume","35"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Schmidt, Frank"],["dc.contributor.author","Zschiedrich, Lin"],["dc.date.accessioned","2017-09-07T11:52:57Z"],["dc.date.available","2017-09-07T11:52:57Z"],["dc.date.issued","2003"],["dc.description.abstract","In this paper we study the PML method for Helmholtz-type scattering problems with radially symmetric potential. The PML method consists of surrounding the computational domain with a perfectly matched sponge layer. We prove that the approximate solution obtained by the PML method converges exponentially fast to the true solution in the computational domain as the thickness of the sponge layer tends to infinity. This is a generalization of results by Lassas and Somersalo based on boundary integral equation techniques. Here we use techniques based on the pole condition instead. This makes it possible to treat problems without an explicitly known fundamental solution."],["dc.identifier.doi","10.1137/S0036141002406485"],["dc.identifier.gro","3146377"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4147"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.title","Solving time-harmonic scattering problems based on the pole condition. II: Convergence of the PML method"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1207"],["dc.bibliographiccitation.journal","Inverse Problems"],["dc.bibliographiccitation.lastpage","1227"],["dc.bibliographiccitation.volume","14"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Schormann, Christoph"],["dc.date.accessioned","2017-09-07T11:52:57Z"],["dc.date.available","2017-09-07T11:52:57Z"],["dc.date.issued","1998"],["dc.identifier.gro","3146378"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4148"],["dc.notes.status","public"],["dc.title","A Newton-type method for a transmission problem in inverse scattering"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

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[["dc.bibliographiccitation.artnumber","08012"],["dc.contributor.author","Feist, Armin"],["dc.contributor.author","Priebe, Katharina E."],["dc.contributor.author","Rathje, Christopher"],["dc.contributor.author","Bach, Nora"],["dc.contributor.author","Rubiano da Silva, Nara"],["dc.contributor.author","Danz, Thomas"],["dc.contributor.author","Möller, Marcel"],["dc.contributor.author","Domröse, Till"],["dc.contributor.author","Rittmann, Thomas"],["dc.contributor.author","Yalunin, Sergey Valerevich"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Sivis, Murat"],["dc.contributor.author","Schäfer, Sascha"],["dc.contributor.author","Ropers, Claus"],["dc.date.accessioned","2020-05-15T12:39:40Z"],["dc.date.available","2020-05-15T12:39:40Z"],["dc.date.issued","2019"],["dc.identifier.doi","10.1051/epjconf/201920508012"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/65455"],["dc.relation.conference","XXI International Conference on Ultrafast Phenomena 2018 (UP 2018)"],["dc.relation.eventend","2018-07-20"],["dc.relation.eventlocation","Hamburg"],["dc.relation.eventstart","2018-07-15"],["dc.relation.ispartof","XXI International Conference on Ultrafast Phenomena 2018 (UP 2018)"],["dc.title","Generation and attosecond shaping of high coherence free-electron beams for ultrafast TEM"],["dc.type","conference_paper"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.journal","Inverse Problems"],["dc.bibliographiccitation.volume","32"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Werner, Frank"],["dc.date.accessioned","2017-09-07T11:52:57Z"],["dc.date.available","2017-09-07T11:52:57Z"],["dc.date.issued","2016"],["dc.format.extent","093001:56pp"],["dc.identifier.doi","10.1088/0266-5611/32/9/093001"],["dc.identifier.gro","3146382"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4152"],["dc.notes.status","public"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.title","Inverse Problems with Poisson Data: statistical regularization theory, applications and algorithms"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","444"],["dc.bibliographiccitation.journal","Journal of Econometrics"],["dc.bibliographiccitation.lastpage","455"],["dc.bibliographiccitation.volume","178"],["dc.contributor.author","Dunker, Fabian"],["dc.contributor.author","Florens, Jean-Pierre"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Johannes, Jan"],["dc.contributor.author","Mammen, Enno"],["dc.date.accessioned","2017-09-07T11:52:31Z"],["dc.date.available","2017-09-07T11:52:31Z"],["dc.date.issued","2014"],["dc.description.abstract","This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence rate results. A particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption. We demonstrate for the case of a binary instrument that our approach allows the correct estimation of regression functions which are not identifiable with the standard model. This is illustrated in computed examples with simulated data."],["dc.identifier.doi","10.1016/j.jeconom.2013.06.001"],["dc.identifier.gro","3146345"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4113"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.title","Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

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