Institut für Numerische und Angewandte Mathematik

[["dc.bibliographiccitation.artnumber","1"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","ACM Transactions on Graphics"],["dc.bibliographiccitation.volume","27"],["dc.contributor.author","Bergou, Miklós"],["dc.contributor.author","Wardetzky, Max"],["dc.contributor.author","Robinson, Stephen"],["dc.contributor.author","Audoly, Basile"],["dc.contributor.author","Grinspun, Eitan"],["dc.date.accessioned","2017-09-07T11:54:09Z"],["dc.date.available","2017-09-07T11:54:09Z"],["dc.date.issued","2008"],["dc.description.abstract","We present a discrete treatment of adapted framed curves, parallel transport, and holonomy, thus establishing the language for a discrete geometric model of thin flexible rods with arbitrary cross section and undeformed configuration. Our approach differs from existing simulation techniques in the graphics and mechanics literature both in the kinematic description---we represent the material frame by its angular deviation from the natural Bishop frame---as well as in the dynamical treatment---we treat the centerline as dynamic and the material frame as quasistatic. Additionally, we describe a manifold projection method for coupling rods to rigid-bodies and simultaneously enforcing rod inextensibility. The use of quasistatics and constraints provides an efficient treatment for stiff twisting and stretching modes; at the same time, we retain the dynamic bending of the centerline and accurately reproduce the coupling between bending and twisting modes. We validate the discrete rod model via quantitative buckling, stability, and coupled-mode experiments, and via qualitative knot-tying comparisons."],["dc.identifier.doi","10.1145/1360612.1360662"],["dc.identifier.gro","3146528"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4312"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Association for Computing Machinery (ACM)"],["dc.relation.issn","0730-0301"],["dc.title","Discrete elastic rods"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","665"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","PAMM"],["dc.bibliographiccitation.lastpage","666"],["dc.bibliographiccitation.volume","15"],["dc.contributor.author","Peter, Thomas"],["dc.contributor.author","Plonka-Hoch, Gerlind"],["dc.contributor.author","Schaback, Robert"],["dc.date.accessioned","2017-09-07T11:53:59Z"],["dc.date.available","2017-09-07T11:53:59Z"],["dc.date.issued","2015"],["dc.description.abstract","he problem of recovering translates and corresponding amplitudes of sparse sums of Gaussians out of sampling values as well as reconstructing sparse sums of exponentials are nonlinear inverse problems that can be solved for example by Prony's method. Here, we want to demonstrate a new extension to multivariate input data."],["dc.identifier.doi","10.1002/pamm.201510322"],["dc.identifier.gro","3146462"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4239"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.relation.issn","1617-7061"],["dc.title","Prony's Method for Multivariate Signals"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","11552"],["dc.bibliographiccitation.issue","10"],["dc.bibliographiccitation.journal","Optics Express"],["dc.bibliographiccitation.lastpage","11569"],["dc.bibliographiccitation.volume","22"],["dc.contributor.author","Hagemann, Johannes"],["dc.contributor.author","Robisch, Anna-Lena"],["dc.contributor.author","Luke, D. R."],["dc.contributor.author","Homann, C."],["dc.contributor.author","Hohage, Thorsten"],["dc.contributor.author","Cloetens, Peter"],["dc.contributor.author","Suhonen, H."],["dc.contributor.author","Salditt, Tim"],["dc.date.accessioned","2017-09-07T11:46:15Z"],["dc.date.available","2017-09-07T11:46:15Z"],["dc.date.issued","2014"],["dc.description.abstract","We illustrate the errors inherent in the conventional empty beam correction of full field X-ray propagation imaging, i.e. the division of intensities in the detection plane measured with an object in the beam by the intensity pattern measured without the object, i.e. the empty beam intensity pattern. The error of this conventional approximation is controlled by the ratio of the source size to the smallest feature in the object, as is shown by numerical simulation. In a second step, we investigate how to overcome the flawed empty beam division by simultaneous reconstruction of the probing wavefront (probe) and of the object, based on measurements in several detection planes (multi-projection approach). The algorithmic scheme is demonstrated numerically and experimentally, using the defocus wavefront of the hard X-ray nanoprobe setup at the European Synchrotron Radiation Facility (ESRF). (C) 2014 Optical Society of America"],["dc.identifier.doi","10.1364/OE.22.011552"],["dc.identifier.fs","604845"],["dc.identifier.gro","3142122"],["dc.identifier.isi","000336957700017"],["dc.identifier.pmid","24921276"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/12635"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4789"],["dc.language.iso","en"],["dc.notes.intern","WoS Import 2017-03-10 / Funder: [SFB 755]"],["dc.notes.intern","Merged from goescholar"],["dc.notes.intern","Merged from goescholar"],["dc.notes.status","final"],["dc.notes.submitter","PUB_WoS_Import"],["dc.relation.issn","1094-4087"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.orgunit","Fakultät für Physik"],["dc.relation.orgunit","Fakultät für Mathematik und Informatik"],["dc.relation.orgunit","Institut für Röntgenphysik"],["dc.relation.workinggroup","RG Salditt (Structure of Biomolecular Assemblies and X-Ray Physics)"],["dc.rights","Goescholar"],["dc.rights.uri","https://goescholar.uni-goettingen.de/licenses"],["dc.subject.gro","x-ray imaging"],["dc.title","Reconstruction of wave front and object for inline holography from a set of detection planes"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.subtype","original_ja"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Journal of Numerical Mathematics"],["dc.bibliographiccitation.volume","25"],["dc.contributor.author","Schröder, Philipp W."],["dc.contributor.author","Lube, Gert"],["dc.date.accessioned","2020-11-18T15:43:08Z"],["dc.date.available","2020-11-18T15:43:08Z"],["dc.date.issued","2017"],["dc.identifier.doi","10.1515/jnma-2016-1101"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/68810"],["dc.relation.issn","1570-2820"],["dc.relation.issn","1569-3953"],["dc.title","Pressure-robust analysis of divergence-free and conforming FEM for evolutionary incompressible Navier–Stokes flows"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.subtype","original_ja"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.lastpage","25"],["dc.contributor.author","Plonka-Hoch, Gerlind"],["dc.contributor.author","Strela, Vasily"],["dc.contributor.editor","Daehlen, Morten"],["dc.contributor.editor","Lyche, Tom"],["dc.contributor.editor","Schumaker, Larry. L."],["dc.date.accessioned","2017-09-07T11:49:19Z"],["dc.date.available","2017-09-07T11:49:19Z"],["dc.date.issued","1998"],["dc.description.abstract","This paper gives an overview of recent achievements of the multiwavelet theory. The construction of multiwavelets is based on a multiresolution analysis with higher multiplicity generated by a scaling vector. The basic properties of scaling vectors such as L 2 -stability, approximation order and regularity are studied. Most of the proofs are sketched."],["dc.identifier.gro","3145700"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3421"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.publisher","Vanderbilt University Press"],["dc.publisher.place","Nashville"],["dc.relation.isbn","0-8265-1315-8"],["dc.relation.ispartof","Mathematical Methods of Curves and Surfaces II"],["dc.title","From wavelets to multiwavelets"],["dc.type","book_chapter"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","105"],["dc.bibliographiccitation.lastpage","121"],["dc.contributor.author","Koutschan, Christoph"],["dc.contributor.author","Lehrenfeld, Christoph"],["dc.contributor.author","Schoeberl, Joachim"],["dc.contributor.editor","Langer, Ulrich"],["dc.date.accessioned","2021-03-04T07:48:22Z"],["dc.date.available","2021-03-04T07:48:22Z"],["dc.date.issued","2011-04-21"],["dc.description.abstract","We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric and magnetic field. Special emphasis is placed on an efficient implementation which is achieved by taking advantage of recurrence properties and the tensor-product structure of the chosen shape functions. These recurrences have been derived symbolically with computer algebra methods reminiscent of the holonomic systems approach."],["dc.identifier.arxiv","1104.4208v2"],["dc.identifier.doi","10.1007/978-3-7091-0794-2_6"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/79889"],["dc.relation.isbn","978-3-7091-0793-5"],["dc.relation.isbn","978-3-7091-0794-2"],["dc.relation.ispartof","Numerical and symbolic scientific computing: progress and prospects"],["dc.title","Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwell's Equations"],["dc.type","book_chapter"],["dc.type.internalPublication","unknown"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","50"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","ACM Transactions on Graphics"],["dc.bibliographiccitation.volume","26"],["dc.contributor.author","Bergou, Miklós"],["dc.contributor.author","Mathur, Saurabh"],["dc.contributor.author","Wardetzky, Max"],["dc.contributor.author","Grinspun, Eitan"],["dc.date.accessioned","2017-09-07T11:54:10Z"],["dc.date.available","2017-09-07T11:54:10Z"],["dc.date.issued","2007"],["dc.description.abstract","We combine the often opposing forces of artistic freedom and mathematical determinism to enrich a given animation or simulation of a surface with physically based detail. We present a process called tracking, which takes as input a rough animation or simulation and enhances it with physically simulated detail. Building on the foundation of constrained Lagrangian mechanics, we propose weak-form constraints for tracking the input motion. This method allows the artist to choose where to add details such as characteristic wrinkles and folds of various thin shell materials and dynamical effects of physical forces. We demonstrate multiple applications ranging from enhancing an artist's animated character to guiding a simulated inanimate object."],["dc.identifier.doi","10.1145/1276377.1276439"],["dc.identifier.gro","3146530"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4314"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Association for Computing Machinery (ACM)"],["dc.relation.issn","0730-0301"],["dc.title","TRACKS: toward directable thin shells"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.contributor.author","Bergou, Miklós"],["dc.contributor.author","Wardetzky, Max"],["dc.contributor.author","Harmon, David"],["dc.contributor.author","Zorin, Denis"],["dc.contributor.author","Grinspun, Eitan"],["dc.contributor.editor","Sheffer, Alla"],["dc.contributor.editor","Polthier, Konrad"],["dc.date.accessioned","2017-09-07T11:54:19Z"],["dc.date.available","2017-09-07T11:54:19Z"],["dc.date.issued","2006"],["dc.description.abstract","Relating the intrinsic Laplacian to the mean curvature normal, we arrive at a model for bending of inextensible surfaces. Due to its constant Hessian, our isometric bending model reduces cloth simulation times up to three-fold."],["dc.identifier.doi","10.2312/SGP/SGP06/227-230"],["dc.identifier.gro","3146535"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4319"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","The Eurographics Association"],["dc.relation.isbn","3-905673-24-X"],["dc.relation.ispartof","Symposium on Geometry Processing"],["dc.relation.issn","1727-8384"],["dc.title","A Quadratic Bending Model for Inextensible Surfaces"],["dc.type","conference_paper"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["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","576"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","SIAM Journal on Control and Optimization"],["dc.bibliographiccitation.lastpage","595"],["dc.bibliographiccitation.volume","42"],["dc.contributor.author","Burke, James V."],["dc.contributor.author","Luke, Russell"],["dc.date.accessioned","2017-09-07T11:50:30Z"],["dc.date.available","2017-09-07T11:50:30Z"],["dc.date.issued","2003"],["dc.description.abstract","We apply nonsmooth analysis to a well-known optical inverse problem, phase retrieval. The phase retrieval problem arises in many different modalities of electromagnetic imaging and has been studied in the optics literature for over forty years. The state of the art for this problem in two dimensions involves iterated projections for solving a nonconvex feasibility problem. Despite widespread use of these algorithms, current mathematical theory cannot explain their success. At the heart of projection algorithms is a nonconvex, nonsmooth optimization problem. We obtain some insight into these algorithms by applying techniques from nonsmooth analysis. In particular, we show that the weak closure of the set of directions toward the projection generate the subdifferential of the corresponding squared set distance function. Following a pattern of proof described in [F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer-Verlag, New York, 1998], this result is generalized to provide conditions under which the subdifferential of an integral function equals the integral of the subdifferential."],["dc.identifier.doi","10.1137/s0363012902406436"],["dc.identifier.gro","3147608"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/5084"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0363-0129"],["dc.title","Variational Analysis Applied to the Problem of Optical Phase Retrieval"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]