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Publications and Reports, Karsten Urban

If you are interested in one of the articles which -due to copyrights- are not available online, please email me.

    Recent Preprints

  1. Adaptive Wavelet Methods for Elliptic Variational Inequalitites I: Analysis
    - Mario Rometsch, Karsten Urban
    University of Ulm, 2010.

  2. Numerical Modelling and Simulation of Ship Hull Geometries
    - Michael Hopfensitz, Juan C. Matutat, Karsten Urban
    University of Ulm, 2010.

  3. Adaptive Wavelet Methods on unbounded domains
    - Sebastian Kestler, Karsten Urban
    University of Ulm, 2010.

  4. A coupled pressure based solution algorithm based on the volume-of-fluid approacg for two and more immiscible fluids
    - Kathrin Kissling, Julia Springer, Hrvoje Jasak, Steffen Schütz, Karsten Urban, Manfred Piesche
    University of Ulm, 2010.

  5. Wavelet Methods for the representation, analysis and simulation of optical surfaces
    - Philipp Jester, Christoph Menke, Karsten Urban
    University of Ulm, 2008.

    6. Published Lecture Notes and Monographs

  6. Partielle Differenzialgleichungen: Eine Einführung in analytische und numerische Methoden
    - Wolfgang Arendt, Karsten Urban
    Spektrum Akademischer Verlag (Springer) Heidelberg, 2010.

  7. Wavelet Methods for Elliptic Partial Differential Equations
    - Karsten Urban
    Oxford University Press, 2009 (482 pages).

  8. Wavelets in Numerical Simulation: Problem Adapted Construction and Applications
    9. - Karsten Urban
    Springer Lecture Notes in Computational Science and Engineering, Vol. 22, ISBN 3-540-43055-5, 2002.
     
  9. "Eine Einführung in C++" (in german)
    10. - Karsten Urban
    Skripte im Shaker Verlag at Shaker Verlag, 1998, ISBN 3-8265-3749-1.
    Die Beispielprogramme findet man hier.

    Refereed Papers in Books and Journals

  10. A B-Spline Representation of Optical Surfaces and its Accuracy in a Ray Trace Algorithm
    - Philipp Jesterm Christoph Menke, Karsten Urban
    University of Ulm, 2010. To appear in Applied Optics, 2011.

  11. Comparison of the Reduced-Basis and POD a-Posteriori Error Estimators for an Elliptic Linear-Quadratic Optimal Control Problem
    - Timo Tonn, Karsten Urban, Stefan Volkwein
    University of Ulm, 2010. To appear in Mathematical and Computer Modelling of Dynamical Systems (NMCM), 2011.

  12. Automatic Differentiation for the Optimization of a Ship Propulsion and Steering System
    - Ralf Leidenberger, Karsten Urban
    J. Golb. Optim. 10-1641 (online first), 2010.

  13. Optimal Control of Parameter-Dependent Convection-Diffusion Problems Around Rigid Bodies
    - Timo Tonn, Karsten Urban, Stefan Volkwein
    SIAM J. Scient. Comput. 32 no. 3, 1237-1260 (2010).

  14. A Mathematical Model for All Solid-State Lithium Ion Batteries
    - Katharina Becker-Steinberger, Stefan Funken, Manual Landstorfer, Karsten Urban
    ECS Trans. 25 (36), 285 (2010).

  15. Simulation of Nasal Air Flow from MRI Data – a feasibility study
    - A. P. Wunderlich, B. Doll, M. Scheithauer, W. Freund, K. Urban, and U. Simon
    Proc. of the 17th ISMRM Meeting (2009), p. 4668.

  16. A-posteriori Error Analysis of the Reduced Basis Method for Non-Affine Parameterized Nonlinear PDE's
    - Claudio Canuto, Timo Tonn, Karsten Urban
    SIAM J. Numer. Anal. 47 3, 2001-2022 (2009)

  17. "Adaptive Wavelet Methods using Semiorthogonal Spline Wavelets:  Sparse Evaluation of Nonlinear Functions"
    - Kai Bittner, Karsten Urban
    Appl. Comp. Harm. Anal. 24 (2008), 94-119.

  18. Simulation and Optimization in Fracture Healing
    - Daniel Nolte, Karsten Urban, Frank Niemeyer, Lutz Claes, Ulrich Simon
    The Finite Element Method in Biomedical Engineering. Biomechanics and Related Fields, ISBN: 978-3-9806183-9-7, p. 34-43.

  19. "On Interpolatory Divergence-Free Wavelets"
    - Kai Bittner, Karsten Urban
    Math. Comp. 76 (2007) 903-929.

  20. Numerical Optimization of the Voith-Schneider Propeller
    - Dirk Jürgens, Michael Palm, Sebastian Singer, Karsten Urban
    ZAMM 87, No. 10 (2007), 698-710.

  21. "Adaptive Optimization in Convex Banach Spaces"
    22. - Claudio Canuto, Karsten Urban
    SIAM J. Numer. Anal. 42 no. 5, (2004), 2043 - 2075.
     
  22. "A convergent Wavelet-Rothe Method for Elastoplastic Hardening"
    - Giovanni Naldi, Karsten Urban, Paolo Venini
    Arabian Journal for Science and Engineering, Theme Issue Wavelet and Fractal Methods in Science and Engineering, Part II, 29:2C (2004), 17-32.

  23. "On Fictitious Domain Formulations for Maxwell's Equations"
    24. - Wolfgang Dahmen, Torben Klint, Karsten Urban
    Found. Comput. Math. 3 No. 2, 135-160 (2003) .
     
  24. "Adaptive Wavelet Methods -- Basic Concepts and Applications to the Stokes Problem"
    25. - Wolfgang Dahmen, Karsten Urban, Jürgen Vorloeper
    In: Wavelet Analysis, D.-X. Zhou (ed.), World Scientific, New Jersey, 2002, 39-80.
    PDF-version of the preprint.
     
  25. "Adaptive Wavelet Methods for Saddle Point Problems - Optimal Convergence Rates"
    26. - Stephan Dahlke, Wolfgang Dahmen, Karsten Urban
    SIAM Journal on Numerical Analysis 40, No. 4 (2002)1230-1262.
     
  26. "Divergence-free wavelet analysis of turbulent flows"
    27. - Cem Albukrek, Karsten Urban, Dietmar Rempfer, John Lumley
    Journal of Scientific Computing 17(1) (2002), 49-66.
     
  27. "Adaptive Wavelet Schemes for Elliptic Problems - Implementation and Numerical Experiments"
    28. - Arne Barinka, Titus Barsch, Philippe Charton, Albert Cohen, Stephan Dahlke, Wolfgang Dahmen, Karsten Urban
    SIAM Journal of Scientific Computing 23, No. 3 (2001), 910-939.
     
  28. "A Wavelet-Galerkin Method for Elastoplasticity Problems"
    29. - Giovanni Naldi, Karsten Urban, Paolo Venini
    Mathematical Modelling and Scientific Computing 10 (2000).
     
  29. "Adaptive Wavelet Methods for Saddle Point Problems"
    30. - Stephan Dahlke, Reinhard Hochmuth, Karsten Urban
    M2AN 34, No. 5, 1003-1022 (2000).
     
  30. "Convergent Adaptive Wavelet Methods for the Stokes Problem"
    31. - Stephan Dahlke, Reinhard Hochmuth, Karsten Urban
    In Multigrid Methods VI, E. Dick, K. Riemslagh, J. Vierendeels (eds.), Springer-Verlag, 2000, 66-72
     
  31. "Adaptive Wavelet Galerkin Methods on Distorted Domains: Setup of the Algebraic System"
    32. - Stefano Berrone, Karsten Urban
    In Curve and Surface Fitting: Saint-Malo 1999, Albert Cohen, Christophe Rabut, and Larry L. Schumaker (eds.), Vanderbilt University Press, Nashville, TN, ISBN 0-8265-1357-3, 2000, 65-74.
     
  32. "Wavelet bases in H(div) and H(curl)"
    33. - Karsten Urban
    Math. Comp. 70 (2001), 739-766.
     
  33. "On the adaptive computation of integrals of wavelets"
    34. - Silvia Bertoluzza, Claudio Canuto, Karsten Urban
    Appl. Numer. Math. 34, 13-38 (2000).
     
  34. "Software Tools for using wavelets on the interval for the numerical solution of operator equations"
    35. - Titus Barsch, Karsten Urban
    RWTH Aachen, IGPM report 158, 1998.
    In Concepts of Numerical Software, W. Hackbusch and G. Wittum (eds.), Univ. Kiel, 2000, 13-25.
     
  35. "Numerical Solution of Elliptic Problems by the Wavelet Element Method"
    36. - Claudio Canuto, Anita Tabacco, Karsten Urban
    In: ENUMATH 97, H.G. Bock et al. (eds.), World Scientific, Singapore, 1998, 17-37.
     
  36. "The Wavelet Element Method, Part II: Realization and additional features in 2D and 3D"
    37. - Claudio Canuto, Anita Tabacco, Karsten Urban
    Appl. Comp. Harm. Anal. 8, 123-165 (2000).
     
  37. "The Wavelet Element Method, Part I: Construction and Analysis"
    38. - Claudio Canuto, Anita Tabacco, Karsten Urban
    Appl. Comp. Harm. Anal. 6, 1-52 (1999).
     
  38. "Wavelets in Numerical Analysis and their Quantitative Properties"
    39. - Wolfgang Dahmen, Angela Kunoth, Karsten Urban
    In: Surface Fitting and Multiresolution Methods, A. Le Mehaute, C. Rabut, L.L. Schumaker (eds.),
    Vanderbilt University Press, Nashville, TN, 1997, 93-130.
     
  39. "Biorthogonal Spline-Wavelets on the Interval - Stability and Moment Conditions"
    40. - Wolfgang Dahmen, Angela Kunoth, Karsten Urban
    Appl. Comp. Harm. Anal. 6, 132-196 (1999).
     
  40. "Towards Object Oriented Software Tools for Numerical Multiscale Methods for P.D.E.s using Wavelets"
    41. - Titus Barsch, Angela Kunoth, Karsten Urban
    In: Multiscale Methods for Partial Differential Equations, W. Dahmen, A. Kurdilla, P. Oswald (eds.), Academic Press, 1997, 383-412.
     
  41. "A Wavelet-Galerkin Method applied to Separation Processes"
    42. - Rüdiger v. Watzdorf, Karsten Urban, Wolfgang Dahmen, Wolfgang Marquardt
    In Scientific Computing in Cemical Engineering, S. Keil, W. Mackens, H. Voß, J. Werther (eds.), Springer-Verlag, Berlin, 1996, 246-252.
     
  42. "A Wavelet-Galerkin Method for the Stokes-Equations"
    43. - Wolfgang Dahmen, Angela Kunoth, Karsten Urban
    Computing, 56, No. 3 (1996), 259-302. Abstract.
     
  43. "Using divergence free wavelets for the numerical solution of the Stokes problem"
    44. - Karsten Urban
    In Algebraic Multilevel Iterations, O. Axelsson, B. Polman (ed.), Nijmegen, 1996, 259-278.
     
  44. "On Divergence-free Wavelets"
    45. - Karsten Urban
    Advances in Computational Mathematics 4, No. 1,2, 51-82, 1995, Abstract.

    Theses and Published Lecture Notes

  45. "Multiskalenverfahren für das Stokes-Problem und angepaßte Wavelet-Basen" (PhD thesis, in german)
    46. - Karsten Urban
    Verlag der Augustinus-Buchhandlung, Aachen, 1995. ISBN 3-86073-424-5.
    Zusammenfassung
     
  46. "Beschränktheitsprinzipien in der Theorie der Rationalen Approximation" (in german)
    47. - Karsten Urban
    Diplomarbeit (masters thesis), RWTH Aachen, 1992.

    Software Documentations

  47. "The Multilevel Library: Software Tools for Multiscale Methods and Wavelets, Version 1.0, Documentation"
    48. - Arne Barinka, Titus Barsch, Karsten Urban, Jürgen Vorloeper
    RWTH Aachen, IGPM report 156, 1998.
     
  48. "The Multilevel Library: Software Tools for Multiscale Methods and Wavelets, Version 2.1, Documentation"
    49. - Arne Barinka, Titus Barsch, Karsten Urban, Jürgen Vorloeper
    RWTH Aachen, IGPM report 205, 2001.

    Other Articles and Manuscripts

  49. A Reduced-Basis Method for Solving Parameter-Dependent Convection-Diffusion Problems Around Rigid Bodies
    - Timo Tonn, Karsten Urban
    Proceedings of the ECCOMAS CFD 2006, no. 542, online (2006).

  50. "Adaptive Wavelet Methods for the Numerical Solution of Operator Equations"
    - Karsten Urban
    Oberwolfach report 10/2004, 522-525.

  51. "Quantitative Behaviour of Wavelet Bases"
    - Karsten Urban
    Oberwolfach report 10/2004, 537-540.

  52. "Wavelet Based Methods in Elastoplasticity and Damage Analysis"
    53. - Giovanni Naldi, Paolo Venini, Karsten Urban
    To appear in Proceedings of ``Fifth World Congress on Computational Mechanics'', July 7-12, 2002, Vienna (Austria), H.A. Mang, F.G. Rammerstorfer, J. Eberhardsteiner (eds.), 2002.
     
  53. "On the Negative Invariance of Inertial Manifolds"
    54. - Gero Nießen, Karsten Urban
    RWTH Aachen, IGPM report 141, 1997. Revised version Feb. 1998.
     
  54. "A Wavelet-Galerkin Algorithm for the Driven-Cavity-Stokes-Problem in two space dimensions",
    55. - Karsten Urban
    In: Numerical Modelling in Continuum Mechanics, M. Feistauer, R. Rannacher, K. Kozel (eds.), Charles-University Prague, 278-289, 1995, Abstract.
10.1.2011