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AG Prof. Kornhuber
 

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Publikationen

2012

Nonreviewed Publications

1. Nonsmooth Schur-Newton methods for vector-valued Cahn-Hilliard equations
   Carsten Gräser, Ralf Kornhuber, Uli Sack
   Preprint (2012) | Abstract | Article | BibTex
    
2. Energy Minimizers of the Coupling of a Cosserat Rod to an Elastic Continuum
   Oliver Sander, Anton Schiela
   submitted | Abstract | BibTex
    
3. Adaptive Modelling of Coupled Hydrological Processes with Application in Water Management
   P. Bastian, H. Berninger, A. Dedner, Ch. Engwer, P. Henning, R. Kornhuber, D. Kröner, M. Ohlberger, O. Sander, G. Schiffler, N. Shokina, K. Smetana
   In 'Progress in Industrial Mathematics at ECMI 2010 '
   Mathematics in Industry: The European Consortium for Mathematics in Industry 17, Springer, 2012, pp. 561-567 | Abstract | Article | BibTex
    

2011

Books

1. Domain Decomposition Methods in Science and Engineering IXX
   Y. Huang, R. Kornhuber, O. Widlund, J. Xu
   Lecture Notes in Computational Science and Engineering 78, Springer (2011) | BibTex
    

Reviewed Publications

1. The spatio-temporal arrangement of different tissues during bone healing as a result of simple mechanobiological rules
   Andreas Vetter, Florian Witt, Oliver Sander, Georg Duda, Richard Weinkamer
   To appear in Biomechanics and Modeling in Mechanobiology (2011) | Abstract | BibTex
    
2. The Mechanical Heterogeneity of the Hard Callus Influences Local Tissue Strains During Bone Healing
   Andreas Vetter, Yifei Liu, Florian Witt, Inderchand Manjubala, Oliver Sander, Devakara Rao Epari, Peter Fratzl, Georg Duda, Richard Weinkamer
   Journal of Biomechanics 44, 2011, pp. 517-523 | Abstract | BibTex
    
3. Fast and robust numerical solution of the Richards equation in homogeneous soil
   Heiko Berninger, Ralf Kornhuber and Oliver Sander
   SIAM Journal on Numerical Analysis 49 (6), 2011, pp. 2576-2597 | Abstract | Article | BibTex
    
4. Convergence behaviour of Dirichlet-Neumann and Robin methods for a nonlinear transmission problem
   Heiko Berninger, Ralf Kornhuber, Oliver Sander
   In 'Domain Decomposition Methods in Science and Engineering XIX'
   LNCSE 78, Springer , 2011, pp. 87-98 | Abstract | BibTex
    
5. Geodesic Finite Elements on Simplicial Grids
   Oliver Sander
   To appear in Int. J. Num. Meth. Eng. (2011) | Abstract | Article | BibTex
    
6. Coupling Geometrically Exact Cosserat Rods and Linear Elastic Continua
   Oliver Sander
   In 'Proc. of DD20'
   , 2011 | Abstract | Article | BibTex
    
7. Geodesic Finite Elements in Spaces of Zero Curvature
   Oliver Sander
   In 'Enumath 2011'
   , 2011 | Abstract | Article | BibTex
    
8. Hierarchical error estimates for the energy functional in obstacle problems
   Q. Zou, A. Veeser, R. Kornhuber and C. Gräser
   Numerische Mathematik 117 (4), 2011, pp. 653-677 | Article | BibTex
    
9. Efficient and Reliable Hierarchical Error Estimates for the Discretization Error of Elliptic Obstacle Problems
   Ralf Kornhuber, Qinsong Zou
   Mathematics of Computation 80, 2011, pp. 69-88. | Article | BibTex
    
10. Domain Decomposition Methods in Science and Engineering IXX
    Y. Huang, R. Kornhuber, O. Widlund, J. Xu
    Lecture Notes in Computational Science and Engineering 78, Springer (2011) | BibTex
     

Nonreviewed Publications

1. Polyhedral Gauss-Seidel Converges
   Carsten Gräser and Oliver Sander
   Preprint (2011) | Abstract | Article | BibTex
    
2. Time discretizations of anisotropic Allen-Cahn equations
   Carsten Gräser, Ralf Kornhuber, Uli Sack
   submitted to IMA Journal of Numerical Analysis | Abstract | Article | BibTex
    
3. Heterogeneous Substructuring Methods for Coupled Surface and Subsurface Flows
   Heiko Berninger, Ralf Kornhuber, Oliver Sander
   In 'Proc. of DD20'
   , 2011 | BibTex
    
4. The PSurface Library
   Oliver Sander
   submitted to Computing and Visualization in Science | Abstract | Article | BibTex
    

2010

Reviewed Publications

1. On Hierarchical Error Estimators for Time-discretized Phase Field Models
   Carsten Gräser, Ralf Kornhuber, Uli Sack
   In 'Proceedings of ENUMATH 2009 '
   Springer, 2010, pp. 397-406 | Abstract | Article | BibTex
    
2. Substructuring of a Signorini-type problem and Robin's method for the Richards equation in heterogeneous soil
   Heiko Berninger, Oliver Sander
   Computing and Visualization in Science 13 (5), 2010, pp. 187--205 | Abstract | BibTex
    
3. Geodesic Finite Elements for Cosserat Rods
   Oliver Sander
   Int. J. Num. Meth. Eng. 82 (13), 2010, pp. 1645-1670 | Abstract | Article | BibTex
    
4. Infrastructure for the Coupling of Dune Grids
   Peter Bastian, Gerrit Buse, Oliver Sander
   In 'Proceedings of ENUMATH 2009'
   Springer, 2010, pp. 107-114 | Abstract | Article | BibTex
    
5. A Polynomial Chaos Approach to Stochastic Variational Inequalities
   Ralf Forster and Ralf Kornhuber
   Journal of Numerical Mathematics 18 (4), 2010, pp. 235-255 | Abstract | Article | BibTex
    

Nonreviewed Publications

1. Heterogeneous Domain Decomposition of Surface and Porous Media Flow
   Heiko Berninger, Ralf Kornhuber, and Oliver Sander
   Preprint (2010) | Abstract | Article | BibTex
    
2. Numerical determination of the medio-lateral force distribution in an ovine stifle joint
   O. Sander, L. Schmidt, R. Ehrig, M. Heller, B. Taylor, R. Kornhuber
   In 'Proceedings of BMT 2010'
   , 2010 | Abstract | BibTex
    
3. Mathematik hilft heilen
   Ralf Kornhuber
   In 'Wissenschaftsstadt Berlin'
   Berliner Wirtschaftsgespräche e.V, 2010, pp. 118 | Abstract | BibTex
    

2009

Books

1. Domain Decomposition Methods in Science and Engineering XVIII
   Eds.: M. Bercovier, M. Gander, R. Kornhuber, O. Widlund
   Lecture Notes in Computational Science and Engineering 70, Springer (2009) | Article | BibTex
    
2. Domain Decomposition Methods in Science and Engineering XVIII
   M. Bercovier, M. Gander, R. Kornhuber and O. Widlund
   LNCSE 70, Springer, Heidelberg (2009) | Article | BibTex
    

Reviewed Publications

1. Domain Decomposition Methods in Science and Engineering XVIII
   Eds.: M. Bercovier, M. Gander, R. Kornhuber, O. Widlund
   Lecture Notes in Computational Science and Engineering 70, Springer (2009) | Article | BibTex
    
2. The dune-subgrid Module and Some Applications
   Carsten Gräser, Oliver Sander
   Computing 8 (4), 2009, pp. 269-290 | Abstract | Article | BibTex
    
3. Multigrid Methods for Obstacle Problems
   Carsten Gräser, Ralf Kornhuber
   Journal of Computational Mathematics 27 (1), 2009, pp. 1-44 | Abstract | Article | BibTex
    
4. Nonsmooth Newton methods for set-valued saddle point problems
   Carsten Gräser, Ralf Kornhuber
   SIAM J. Numer. Anal. 47 (2), 2009, pp. 1251-1273 | Abstract | Article | BibTex
    
5. Truncated Nonsmooth Newton Multigrid Methods for Convex Minimization Problems
   Carsten Gräser, Uli Sack, Oliver Sander
   In 'Domain Decomposition Methods in Science and Engineering XVIII'
   LNCSE, Springer, 2009, pp. 129-136 | Abstract | Article | BibTex
    
6. Non-overlapping Domain Decomposition for the Richards Equation via Superposition Operators
   Heiko Berninger
   In 'Domain Decomposition Methods in Science and Engineering XVIII'
   Lecture Notes in Computational Science and Engineering 70, Springer, 2009, pp. 169-176 | Abstract | Article | BibTex
    
7. Domain Decomposition Methods in Science and Engineering XVIII
   M. Bercovier, M. Gander, R. Kornhuber and O. Widlund
   LNCSE 70, Springer, Heidelberg (2009) | Article | BibTex
    

2008

Reviewed Publications

1. Globalization of Nonsmooth Newton Methods for Optimal Control Problems
   Carsten Gräser
   In 'Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2007'
   Springer, 2008, pp. 605-612 | Article | BibTex
    
2. A Generic Interface for Adaptive and Parallel Scientific Computing. Part I: Abstract Framework
   P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, M. Ohlberger, O. Sander
   Computing 82 (2-3), 2008, pp. 103-119 | Abstract | BibTex
    
3. A Generic Interface for Adaptive and Parallel Scientific Computing. Part II: Implementation and Tests in DUNE
   P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, O. Sander
   Computing 82 (2-3), 2008, pp. 121-138 | Abstract | BibTex
    
4. Fast and reliable pricing of American options with local volatility
   R. Forster, R. Kornhuber, K. Mautner, O. Sander
   In 'Domain Decomposition Methods in Science and Engineering XVII'
   LNCSE 60, Springer, 2008, pp. 383 - 390 | Article | BibTex
    
5. Multigrid Methods for Discrete Elliptic Problems on Triangular Surfaces
   R. Kornhuber and H. Yserentant
   Comp. Visual. Sci. 11, 2008, pp. 251-257 | Article | BibTex
    
6. A Monotone Multigrid Solver for Two Body Contact Problems in Biomechanics
   R. Kornhuber, R. Krause, O. Sander, P. Deuflhard, S. Ertel
   Comp. Vis. Sci. 11, 2008, pp. 3--15 | Article | BibTex
    

2007

Reviewed Publications

Forster, R., Kornhuber, R., Mautner, K., Sander, O.: Fast and reliable pricing of American options with local volatility. In: U. Langer et al. (eds.), 'Domain Decomposition Methods in Science and Engineering XVII', LNCSE 60, Springer, 383 - 390.

Nonreviewed Publications / Preprints

Kornhuber, R., Yserentant, H.: Multigrid Methods for Discrete Elliptic Problems on Triangular Surfaces. Preprint 411, Matheon.

Bastian,P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Ohlberger, M., Sander, O.: A Generic Interface for Adaptive and Parallel Scientific Computing. Part I: Abstract Framework. Matheon Preprint 403.

Bastian,P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Kornhuber, R., Ohlberger, M., Sander, O.: A Generic Interface for Adaptive and Parallel Scientific Computing. Part II:Implementation and Tests in DUNE. Matheon Preprint 404.

2006

Reviewed Publications

Berninger, H., Kornhuber, R., Sander, O.: On nonlinear Dirichlet-Neumann Algorithms for jumping nonlinearities In: O.B. Widlund and D.E. Keyes (eds.), 'Domain Decomposition Methods in Science and Engineering XVI', LNCSE 55, Springer, 483 - 490.

Gräser, C., Kornhuber, R.: On preconditioned Uzawa-type iterations for a saddle point problem with inequality constraints. In: O.B. Widlund and D.E. Keyes (eds.), 'Domain Decomposition Methods in Science and Engineering XVI', LNCSE 55, Springer, 91 - 102.

Kornhuber, R., Krause, R.: Robust multigrid methods for vector-valued Allen-Cahn equations with logarithmic free energy. Comp. Visual. Sci. 9, 103-116.

Gebauer, S., Kornhuber, R., Yserentant, H.: Hierarchical Decomposition of Domains with Fractures. Math. Comp. 75, 73-90.

V. Caselles, L. Igual, O. Sander: An Axiomatic Approach to Scalar Data Interpolation on Surfaces. Numer. Math. 102, 383-411.

R. Krause, O. Sander: Automatic Construction of Boundary Parametrizations for Geometric Multigrid Solvers. Computing and Visualization in Science 9, 11 - 22.

P. Bastian, M. Blatt, C. Engwer, A. Dedner, R. Köfkorn, S. P. Kuttanikkad, M. Ohlberger, O. Sander: The Distributed and Unified Numerics Environment (DUNE). In Proc. of the 19th Symposium on Simulation Technique in Hannover.

Nonreviewed Publications / Preprints

Forster, R., Kornhuber, R., Mautner, K., Sander, 0.: Fast and reliable pricing of American options with local volatility. Preprint-A-5-06, FU Berlin.

Gräser C., Kornhuber, R.: Nonsmooth Newton methods for set-valued saddle point problems. Preprint-A-4-06, FU Berlin.

Kornhuber, R., Krause, R., Sander, O., Deuflhard, P., Ertel, S.: A Monotone Multigrid Solver for Two Body Contact Problems in Biomechanics. Preprint-A-3-06, FU Berlin.

Sander, O.: A Fast Solver for Finite Deformation Contact Problems Preprint-A-2-06.

2005

Books

Kornhuber, R.; Hoppe, R.; Périaux, J.; Pironneau, O.; Widlund, O.; Xu, J. (Eds.) Domain Decomposition Methods in Science and Engineering Series : Lecture Notes in Computational Science and Engineering Vol. 40, Springer.

Nonreviewed Publications / Preprints

Gräser C., Kornhuber, R. `On preconditioned Uzawa-type iterations for a saddle point problem with inequality constraints'. Preprint-A-5-05, FU Berlin.

Berninger H., Kornhuber, R., Sander, O. `On nonlinear Dirichlet-Neumann Algorithms for jumping nonlinearities'. Preprint-A-4-05, FU Berlin.

Kornhuber, R., Krause, R. `Robust multigrid methods for vector-valued Allen-Cahn equations with logarithmic free energy'. Preprint-A-2-05, FU Berlin.

2003

Reviewed Publications

Berninger, H. and Werner, D.: Lipschitz spaces and M-Ideals In: Extracta Math.

Kornhuber, R. and Krause, R.: On multigrid methods for vector-valued Allen-Cahn equations. In: I. Herrera et al. (eds.), 'Domain Decomposition Methods in Science and Engineering', UNAM, Mexico City, Mexico, 307 - 314.

Krause, R. and Sander, O.: Fast Solving of Contact Problems on Complicated Geometries. In: Proceedings of the 15th Conference on Domain Decomposition Methods, Berlin, Germany.

Sander, O. and Caselles, V. and Bertalmío, M.: Axiomatic Scalar Data Interpolation on Manifolds. Proceedings of the International Congress on Image Processing, ICIP 2003, Barcelona, Spain, pp. 681-684.

Wohlmuth, B. and Krause, R.: Monotone methods on non-matching grids for non-linear contact problems. SIAM Journal of Scientific Computing, Vol. 25, Number 1, pp. 324-347.

Nonreviewed Publications / Preprints

Sander, O., Krause, R.: Automatic Construction of Boundary Parametrizations for Geometric Multigrid Solvers. ZIB Report 03-02, 2003. to appear in: Computing and Visualization in Science.

2002

Reviewed Publications

Krause, R., Wohlmuth, B.: A Dirichlet-Neumann type algorithm for cont act problems with friction. Comp. Vis. Sci., Volume 5, Issue 3, pp 139-148.

Kornhuber, R.: On constrained Newton linearization and multigrid for variational. Volume 91, pp. 699-721.

Nonreviewed Publications / Preprints

Kornhuber, R. and Krause, R.: On multigrid methods for vector-valued Allen-Cahn equations. Preprint Nr. A-04-2002, FU Berlin. submitted to: Proceedings of DD14

Krause, R., Wohlmuth, B.: Monotone methods on non-matching grids for non-linear contact problems. Preprint SFB404 #2002-06.

Gebauer, S., Neunhäuserer, L., Kornhuber, R., Ochs, S., Hinkelmann, R., Helmig, R.: Equidimensional modelling of flow and transport processes in fractured porous systems I. In: XIV International Conference on Computational Methods in Water Resources, Delft, The Netherlands.

Neunhäuserer, L., Gebauer, S., Kornhuber, R., Ochs, S., Hinkelmann, R., Helmig, R.: Equidimensional modelling of flow and transport processes in fractured porous systems II. In: XIV International Conference on Computational Methods in Water Resources, Delft, The Netherlands.

Ochs, S., Hinkelmann, R., Neunhäuserer, L., Süß, M., Helmig, R., Gebauer, S., Kornhuber, R.: Adaptive methods for the equidimensional modelling of flow and transport processes in fractured aquifers. In: 5th International Conference on Hydroscience and Engineering, Warschau, Polen.

Berninger, H., Werner, D.: Lipschitz Spaces and M-Ideals. Preprint FUB Nr. A-02-02, to appear in Extr. Math., 2003.

2001

Reviewed Publications

Kober, C. and M. Müller-Hannemann: A Case Study in Hexahedral Mesh Generation: Simulation of the Human Mandible, Engineering with Computers, vol. 17, pp. 249-260.

Müller-Hannemann, M., Kober, C., Sader,R. and Zeilhofer, H.-F.: Anisotropic Validation of Hexahedral Meshes for Composite Materials in Biomechanics, Proceedings of the 10th International Meshing Roundtable, Newport Beach, CA, pp. 249-260.

Kornhuber, R.: Nonlinear multigrid techniques. In: 'Theory and Numerics of Differential Equations', J.F.Blowey, J.P.Coleman & A.W.Craig (eds.), pp. 179-229, Springer.

Kornhuber, R. and Krause, R.: Adaptive multigrid methods for Signorini's problem in linear elasticity. Computing and Visualization in Science (Comp. Vis. Sci.) Volume 4, Issue 1, pp 9-20.

Wohlmuth, B., Krause, R.: A multigrid method based on the unconstrained product space for mortar finite element discretizations. SIAM J. Numer. Anal., 39, pp. 192-213.

Krause, R., Wohlmuth, B.: Domain Decomposition methods on nonmatching grids and some applications to linear elasticity problems. ZAMM, Z. Angew. Math. Mech. 81, Suppl. 1, pp. 21-24.

Nonreviewed Publications / Preprints

Kober,C., Sader,R., Zeilhofer, H.-F., Prohaska, S., Zachow, S. and Deuflhard, P.: Anisotrope Materialmodellierung für den menschlichen Unterkiefer, erscheint in Workshop '01, "Die Methode der Finiten Elemente in der Biomechanik, Biomedizin und angrenzenden Gebieten", Univ. Ulm, 23./24.7. 2001, Report ZIB 01-31, 2001, Konrad-Zuse-Zentrum.

Erdmann, B., Kober, C., Lang, J., Deuflhard, P., Zeilhofer, H.-F. and Sader,R.: Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible, to appear in Proceedings of Medicine Meets Mathematics, Hartgewebe-Modellierung, Kloster Banz/Staffelstein, April 2001, Report ZIB 01-14, 2001, Konrad-Zuse-Zentrum.

Kober, C.: Composite Material with Shape Memory Alloy Fibers. to appear in 'Proceedings of Bexbach Colloquium on Science', Bexbach, 29./30. Okt. 2000.

Kornhuber, R.: On constrained Newton linearization and multigrid for variational inequalities. Preprint Nr. A-2-2001, FU Berlin, submitted to: Numer. Math.

2000

Reviewed Publications

R. Krause, B. Wohlmuth:   Nonconforming Decomposition methods techniques for linear elasticity. East-West Journal of Numerical Mathematics, 8, No. 3, 177-206.

Krause, R., Wohlmuth, B.: Multigrid methods for mortar finite elements. In Multigrid Methods VI, Springer, Berlin, Heidelberg, New York, (E. Dick, K. Riemslagh, J. Vierendeels; eds.), pp. 136-142.

Nonreviewed Publications

C. Kober, R. Sader, H. Thiele, H.-J. Bauer, H.-F. Zeilhofer, K.-H. Hoffmann:   FEM-Simulations versus biomechanical experiments concerning the human mandible: a comparison of the results of a frontal and a molar biting study. Preprint A-21-2000, FU Berlin.

R. Kornhuber, R. Krause:   Adaptive Multigrid Methods for Signorini's Problem in Linear Elasticity. Preprint A-15-2000, FU Berlin.

L. Neunhäuserer, S. Gebauer, R. Hinkelmann, R. Kornhuber, R. Helmig:   Mehrgittermethoden und adaptive Diskretisierungsverfahren zur Simulation von Strömungs- und Transportprozessen in Kluftaquiferen. Preprint A-19-2000, FU Berlin.
In: Proceedings zum 3. Workshop -Kluftaquifere-, Hannover, 2.-3.11.2000, O. Kolditz und W. Ziehlke (eds.)