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FORSCHUNGSBERICHT 1999-2001

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Institut für Angewandte Mathematik Abt.f.Wiss.Rechnen u. Num.Simulation

Allgemeine Angaben:
Wegelerstraße 6, 53115 Bonn
Telefon: 0228 / 73-3437
Fax: 0228 / 73-7527
eMail: griebel@iam.uni-bonn.de
WWW: http://wissrech.iam.uni-bonn.de/

Hauptamtliche Professoren:
Prof. Dr. Michael Griebel

Wissenschaftliches Personal:
Universitätsstellen
Dr. Klaus Giebermann
Dr. Stephan Knapek
Dr. Gerhard Zumbusch

Drittmittelstellen
Dipl.-Math. Marcel Arndt (SFB 256)
Dipl.-Math. Attila Caglar (SFB 256, DFN)
Dipl.-Math. Jochen Garcke (DFN, BMBF, SFB 256)
Dipl.-Inform. Thomas Gerstner (SFB 350)
Dipl.-Math. Christian Hansen (SFB 350)
Dipl.-Math. Frank Kiefer (DFG, Norsk Hydro)
Dipl.-Math. Frank Koster (DFG)
Dipl.-Math. Daniel Oeltz (SFB 408)
Dipl.-Math. Thomas Schiekofer (BMBF, Norsk Hydro)
Dipl.-Math. Marc Alexander Schweitzer (SFB 256)
Dipl.-Math. Christian von Törne (DFG)

Forschungsschwerpunkte:
Adaptive multilevel methods for PDEs in complex geometries
(Arndt)

Microstructure and Shape Memory Alloys
(Arndt)

Numerical methods for the nanotechnology
(Caglar)

Smoothed particle hydrodynamics with applications in astrophysics
(Caglar)

Molecular dynamics simulation methods
(Caglar, Knapek, Oeltz, Zumbusch)

Meshless numerical methods for the simulation of 3D flows with free boundaries
(Caglar, Schweitzer)

Data mining with sparse grids
(Garcke)

Numerical Solution of the Schrödinger equation
(Garcke)

Hierarchical and adaptive methods for the compression and visualization of large data sets
(Gerstner)

Nonlinear multigrid methods for the numerical simulation of coupled systems
(Gerstner)

Numerical quadrature based on sparse grids with applications to physics and financial engineering
(Gerstner)

Fast methods for the numerical solution of boundary integral equations
(Giebermann)

Numerical methods for direct scattering problems
(Giebermann)

Numerical methods for inverse scattering problems
(Giebermann)

Fast-vision methods for the reconstruction of sedimentary surfaces
(Giebermann, Hansen)

Compression methods for the efficient storage and representation of relief data
(Hannappel)

Robust multilevel methods for stationary convection-diffusion equations
(Kiefer)

Wavelet based iterative methods and preconditioning
(Kiefer)

Multigrid based homogenization techniques for porous media
(Knapek)

Optimized wavelet approximation spaces for operator equations
(Knapek, Koster)

Efficient preconditioners for elliptic equations and sparse grid discretizations
(Koster)

Finite volume methods for free-surface flows and fluid-structure-interaction
(Koster)

Multiscale-based finite difference schemes on adapitve sparse grids
(Koster)

Wavelet-based Navier-Stokes solver for the simulation of turbulence
(Koster)

Algebraic multigrid methods for systems of PDEs
(Oeltz)

Development of efficient parallel methods for the simulation and optimization of CVD processes
(Schiekofer)

Sparse grid and prewavelet based methods for the solution of integral equations
(Schiekofer)

Finite-differences on sparse grids for the solution of partial differential equations
(Schiekofer, Zumbusch)

Parallel multilevel partition of unity for elliptic partial differential equations
(Schweitzer)

Parallel algebraic multigrid
(Schweitzer, Knapek, Oeltz)

Parnass2: A cluster of PCs
(Schweitzer, Zumbusch)

Adaptive parallel multigrid methods with space-filling curves and hash storage
(Zumbusch)

High-dimensional parallel sparse grids
(Zumbusch)

Parallel tree-codes for long range forces in molecular dynamics
(Zumbusch, Caglar)

Finite-difference schemes on sparse grids for time dependent problems
(Zumbusch, Oeltz)

Besondere Forschungsförderung:
Compression methods for efficient storage of sedimentary surfaces using block-structured sparse grids
(Hansen, SFB 350 "Interactions of Continental Geosystems and Modelling")

Compression methods for the efficient storage and representation of relief data
(Hannappel, Graduiertenkolleg: Landform - a structured and variable boundary layer )

Fast-vision methods for the reconstruction of sedimentary surfaces
(Hansen, SFB 350 "Interactions of Continental Geosystems and their Modelling" )

Gitterlose numerische Verfahren zur Simulation dreidimensionaler Strömungen mit freien Rändern
(Arndt, SFB 256 "Nonlinear partial differential equations")

Meshless numerical methods for the simulation of 3D flows with free boundaries
(Caglar, Schweitzer, SFB 256 "Nonlinear partial differential equations")

Molecular dynamics simulations for long and short-range potentials
(Oeltz, SFB 408 "Anorganische Festkörper ohne Translationssymmetrie")

Multilevel methods for nonsymmetric problems as iterative methods on generating systems
(Kiefer, DFG)

Nonlinear multigrid methods for the numerical simulation of coupled systems
(Gerstner, SFB 350 "Interactions of Continental Geosystems and their Modelling" )

Numerical methods for molecular dynamics simulations
(Caglar, DFN)

Numerik und graphische Darstellung
(Garcke, SFB 256 "Nonlinear Partial Differential Equations")

Parallel multilevel particle methods combined with space-filling curves
(Caglar, SFB 256 "Nonlinear partial differential equations")

Parnass2: A cluster of PCs
(Schweitzer, SFB 256 "Nonlinear partial differential equations")

Partition of unity methods for instationary convection-diffusion equations
(Schweitzer, SFB 256 "Nonlinear Partial Differential Equations")

Pattern recognition with sparse grids
(Garcke, BMBF "Neue mathematische Verfahren in Industrie und Dienstleistung")

Smoothed particle hydrodynamics with applications in astrophysics
(Caglar, SFB 256 "Nonlinear partial differential equations" )

Wavelet-based Navier Stokes solver for the simulation of turbulence
(Koster, DFG)

Veröffentlichungen:

Boeker, P., Wallenfang, O., Koster, F., Croce, R., Diekmann, B., Griebel, M., Schulze-Lammers, P.
The modelling of odour dispersion with time-resolved models.
Agrartechnische Forschung, 4:E84-E89,

Boeker P., Wittkowski M., Wallenfang O., Koster F., Griebel M., Diekmann B., Schulze-Lammers P.
Tracermessungen zur Validierung von Geruchsmodellen.
Landtechnik-net, 2,

Bungartz H.-J., Griebel M.
A note on the complexity of solving Poisson's equation for spaces of bounded mixed derivatives.
J. Complexity, 15:167-199,

Caglar A., Griebel M.
On the numerical simulation of Fullerene nanotubes: $C_{100.000.000}$ and beyond!
In R. Esser, P. Grassberger, J. Grotendorst, and M. Lewerenz, editors, Molecular Dynamics on Parallel Computers, NIC, Jülich 8-10 February 1999. World Scientific

Caglar A., Griebel M. , Schweitzer M.A., Zumbusch G.
Dynamic load-balancing of hierarchical tree algorithms on a cluster of multiprocessor PCs and on the Cray T3E.
In H.W. Meuer, editor, Proceedings 14th Supercomputer Conference, Mannheim, ISBN 3-932178-08-4, Mannheim, Germany, Mateo SuParCup '99 Award Winning Paper,

Garcke J., Griebel M.
On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique.
Journal of Computational Physics, 165(2):694-716,

Garcke J., Griebel M.
On the parallelization of the sparse grid approach for data mining.
In S. Margenov, J. Wasniewski, and P. Yalamov, editors, Large-scale Scientific computations, Third International Conference, LSSC 2001, Sozopol, Bulgaria, volume 2179 of lecture Notes in Computer Science, pp. 22-32,

Garcke J., Griebel M.
Data mining with sparse grids using simplicial basis functions.
In F. Provost and R. Srikant, editors, Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, USA, pp. 87-96,

Garcke J., Griebel M., Thess M.
Data mining with sparse grids.
Computing, 67(3):225-253,

Gerstner T.
Adaptive Hierarchical Methods for Landscape Representation and Analysis,
Process Modelling and Landform Evolution, Lecture Notes in Earth Sciences 78, pp. 75-92, Springer

Gerstner T.
Multiresolution Visualization and Compression of Global Topographie Data.
In Proc. Spatial Data Handling 2000. P. Forer, A.G.O. Yeh, J. He(eds.), pp. 14-27, IGU/GISc,

Gerstner T.
Fast Multiresolution Extraction of Multiple Transparent Isosurfaces.
In Data Visualization '01, D.S. Ebert, J.M. Favre and R. Peikert (eds.), pp. 35-44, Springer,

Gerstner T., Hannappel M.
Error Measurement in Multiresolution Digital Elevation Models
Delft University Press, pp. 245-252,

Gerstner T., Pajarola R.
Topology Preserving and Controlled Topology Simplifying Multiresolution Isosurface Extraction,
Proceedings IEEE Visualization 2000, IEEE Computer Society Press, pp. 259-266,

Gerstner T., Rumpf M.
Multiresolutional Parallel Isosurface Extraction based on Tetrahedral Bisection,
Volume Graphics, pp. 267-278, Springer ,

Gerstner T., Rumpf M., Weikard U.
A Comparison of Error Indicators for Multilevel Visualization and Computing on Nested Grids.
In Data Visualization '99, E. Gröller, H. Löffelmann, W. Ribarsky (eds.), pp. 199-211, Springer,

Gerstner T., Rumpf M., Weikard U.
Error Indicators for Multilevel Visualization and Computing on Nested Grids,
Computer & Graphics, 24(3):363-373,

Griebel M., Knapek S.
Optimized tensor-product approximation spaces.
Constructive Approximation, 16(4):525-540,

Griebel M., Koster F.
Adaptive wavelet solvers for the unsteady incompressible Navier Stokes equations.
In J. Malek, J. Necas, and M. Rokyta, editors. Advances in Mathematical Fluid Mechanics. Lecture Notes of the Sixth International School "Mathematical Theory in Fluid Mechanics". Paseky, Czech Republic, September 1999. Springer Verlag

Griebel M., Merz W., Neunhoeffer T.
Mathematical modelling and numerical simulation of freezing processes of a supercooled melt under consideration of density changes.
Computing and Visualization in Science, 3:1-19,

Griebel M., Oswald P., Schiekofer T.
Sparse grids for boundary integral equations.
Numer. Mathematik, 83(2):279-312,

Griebel M., Schiekofer T.
PAR-CVD: Entwicklung leistungsfähiger paralleler Berechnungsverfahren zur Untersuchung und Optimierung von CVD-Prozessen.
Effiziente Algorithmen auf dünnen Gittern, chapter 7, pages 53-96. Berichte aus der Strömungsmechanik. Shaker, Aachen, L. Kadinski (ed.)

Griebel M., Schweitzer M.A.
A Particle-Partition of Unity Method for the solution of Elliptic, Parabolic and Hyperbolic PDE.
SIAM J. Sci. Comp., 22(3):853-890,

Griebel M., Zumbusch G.W.
Parallel multigrid in an adaptive PDE solver based on hashing and space-filling curves.
Parallel Computing, 25:827-843,

Griebel M., Zumbusch G.W.
Adaptive sparse grids for hyperbolic conservation laws.
In M. Fey and R. Jeltsch, editors, Hyperbolic Problems: Theory, Numerics, Applications. 7th International Conference in Zürich, February 1998, volume 1 of International Series of Numerical Mathematics 129, pages 411-422, Basel, Switzerland, Birkhäuser,

Griebel M., Zumbusch G.W.
Parallel adaptive subspace correction schemes with applications to elasticity.
Computer Methods in Applied Mechanics and Engineering, 184:303-332,

Koster F.
A proof of the consistency of the finite difference technique on sparse grids,
Computing, 65:247-261,

Koster F., Schneider K., Griebel M., Farge M.
Adaptive wavelet methods for the Navier-Stokes equations.
In E.H. Hirschel, editor, DFG/CNRS Workshop, Berlin 1999, Notes on Numerical Fluid Mechanics. Vieweg-Verlag, Braunschweig

Schiekofer T., Griebel M.
PAR-CVD: Entwicklung leistungsfähiger paralleler Berechnungsverfahren zur Untersuchung und Optimierung von CVD-Prozessen.
Berichte aus der Strömungsmechanik, Shaker Verlag, Aachen,

Zumbusch G.W.
Dynamic loadbalancing in a lightweight adaptive parallel multigrid PDE solver,
Proceedings of 9th SIAM Conference on Parallel Processing for Scientific Computing, San Antonio, Texas, ISBN 0-89871-435-4, p. 10,

Zumbusch G.W.
A sparse grid PDE solver,
Advances in Software Tools for Scientific Computing, volume 10 of Lecture Notes in Computational Science and Engineering, pp. 133-177, Springer, volume 10 of Lecture Notes in Computational Science and Engineering

Zumbusch G.W.
On the quality of space-filling curve induced partitions,
Z. Angew. Math. Mech., 81:25-28,


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