Lehrenfeld, Christoph

[["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.issue","4"],["dc.bibliographiccitation.journal","SN partial differential equations and applications"],["dc.bibliographiccitation.volume","1"],["dc.contributor.author","Preuß, Janosch"],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Lehrenfeld, Christoph"],["dc.date.accessioned","2020-11-10T10:24:00Z"],["dc.date.available","2020-11-10T10:24:00Z"],["dc.date.issued","2020"],["dc.identifier.doi","10.1007/s42985-020-00019-x"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/68631"],["dc.relation.issn","2662-2963"],["dc.relation.issn","2662-2971"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.workinggroup","RG Lehrenfeld (Computational PDEs)"],["dc.title","Sweeping preconditioners for stratified media in the presence of reflections"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.subtype","original_ja"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.issue","64"],["dc.bibliographiccitation.journal","The Journal of Open Source Software"],["dc.bibliographiccitation.volume","6"],["dc.contributor.author","Lehrenfeld, Christoph"],["dc.contributor.author","Heimann, Fabian"],["dc.contributor.author","Preuß, Janosch"],["dc.contributor.author","von Wahl, Henry"],["dc.creator.author","Christoph Lehrenfeld"],["dc.creator.author","Fabian Heimann"],["dc.creator.author","Janosch Preuß"],["dc.creator.author","Henry von Wahl"],["dc.date.accessioned","2022-11-04T21:37:29Z"],["dc.date.available","2022-11-04T21:37:29Z"],["dc.date.issued","2021"],["dc.identifier.doi","10.21105/joss.03237"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/116948"],["dc.identifier.url","https://doi.org/10.21105/joss.03237"],["dc.language.iso","en"],["dc.relation.workinggroup","RG Lehrenfeld (Computational PDEs)"],["dc.title","ngsxfem: Add-on to NGSolve for geometrically unfitted finite element discretizations"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.contributor.author","Lehrenfeld, Christoph"],["dc.contributor.author","Heimann, Fabian"],["dc.contributor.author","Preuß, Janosch"],["dc.contributor.author","von Wahl, Henry"],["dc.date.accessioned","2022-11-04T22:16:45Z"],["dc.date.available","2022-11-04T22:16:45Z"],["dc.date.issued","2021"],["dc.description.edition","2.0"],["dc.identifier.doi","10.5281/zenodo.5081123"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/116951"],["dc.language.iso","en"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.workinggroup","RG Lehrenfeld (Computational PDEs)"],["dc.rights.license","LGPL-3"],["dc.subject.gro","unfitted finite elements"],["dc.title","ngsxfem"],["dc.title.subtitle","Add-on to ngsolve for geometrically unfitted finite element discretizations"],["dc.type","software"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]