Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation
maximize

Dr. Stephan Knapek

URL: http://wissrech.ins.uni-bonn.de/people/knapek.html

Former member of the institute

Publications

Articles:

[1] M. Griebel and S. Knapek. Optimized general sparse grid approximation spaces for operator equations. Mathematics of Computations, 78(268):2223-2257, Oct. 2009. Also available as SFB611 preprint No 402.
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[2] S. Knapek and F. Koster. Integral operators on sparse grids. SIAM J. Num. Anal., 39(5):1794-1809, 2002.
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[3] M. Griebel and S. Knapek. Optimized tensor-product approximation spaces. Constructive Approximation, 16(4):525-540, 2000.
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[4] R. Hochmuth, S. Knapek, and G. Zumbusch. Tensor products of Sobolev spaces and applications. submitted, 2000. also as Technical Report 685, SFB 256, Univ. Bonn.
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[5] S. Knapek. Hyperbolic cross approximation of integral operators with smooth kernel. submitted, 2000. also as Technical Report 665, SFB 256, Univ. Bonn.
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[6] S. Knapek. Matrix-dependent multigrid homogenization for diffusion problems. SIAM J. Sci. Comp., 20(2):515-533, 1999.
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[7] S. Knapek. Upscaling techniques based on subspace correction and coarse-grid approximation. InSitu, 22(1):35-58, 1998. Special issue on reservoir simulation.
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Unrefereed proceedings, technical reports:

[1] S. Knapek. Compression of anisotropic tensor-product discretizations. INS Preprint 0200, Institut für Numerische Simulation, Universität Bonn, 2002.
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[2] J. Moulton, S. Knapek, and J. Dendy. Multilevel upscaling in heterogeneous porous media. Technical report, CNLS Research highlight, Los Alamos Nat. Lab., Jan. 1999.
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[3] M. Griebel and S. Knapek. Optimized approximation spaces for operator equations. Technical Report 568, SFB 256, Univ. Bonn, 1999.
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[4] M. Griebel and S. Knapek. A multigrid-homogenization method. In R. Helmig, W. Jäger, W. Kinzelbach, P. Knabner, and G. Wittum, editors, Modeling and Computation in Environmental Sciences, volume 59 of Notes on Numerical Fluid Mechanics, pages 187-202, Braunschweig, 1997. Vieweg-Verlag.
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Theses:

[1] S. Knapek. Approximation und Kompression mit Tensorprodukt-Multiskalenräumen. Dissertation, Universität Bonn, April 2000.
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[2] S. Knapek. Multiskalenverfahren bei der Modellierung, Diskretisierung und Lösung von Diffusionsproblemen. Diplomarbeit, Instit. für Informatik, TU München, 1995.
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Talks

Conference contributions

[1] Optimized cross approximation spaces,
Foundations of Computational Mathematics, Oxford, UK, July 18-28, 1999.
[2] Optimized tensor-product approximation spaces for operator equations,
2nd Workshop on Large-Scale Scientific Computations, Sozopol, Bulgaria, May 6-9, 1999.
[3] Coarse scale models for diffusion in heterogeneous media and for multi-level iterative solvers,
NMA'98 - 4th International Conference on Numerical Methods and Applications, Sofia, Bulgaria, August 19-23, 1998.