@inproceedings {INPROC-2013-66,
author = {Benjamin Peherstorfer and Stefan Zimmer and Hans-Joachim Bungartz},
title = {{Model Reduction with the Reduced Basis Method and Sparse Grids}},
booktitle = {Sparse Grids and Applications 2011},
publisher = {Springer},
institution = {University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology, Germany},
series = {Lecture Notes in Computational Science and Engineering},
volume = {88},
pages = {223--242},
type = {Conference Paper},
month = {January},
year = {2013},
language = {German},
cr-category = {G.1.8 Partial Differential Equations},
department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Simulation of Large Systems},
abstract = {The reduced basis (RB) method has become increasingly popular for problems
where PDEs have to be solved for varying parameters \$$\backslash$mu $\backslash$in D\$ in order to
evaluate a parameter-dependent output function \$s : D $\backslash$to IR\$. The idea of the
RB method is to compute the solution of the PDE for varying parameters in a
problem-specific low-dimensional subspace \$X\_N\$ of the high-dimensional finite
element space \$X^{$\backslash$mathcal{N}}\$ . We will discuss how sparse grids can be
employed within the RB method or to circumvent the RB method altogether. One
drawback of the RB method is that the solvers of the governing equations have
to be modified and tailored to the reduced basis. This is a severe limitation
of the RB method. Our approach interpolates the output function s on a sparse
grid. Thus, we compute the respond to a new parameter \$$\backslash$mu $\backslash$in D\$ with a simple
function evaluation. No modification or in-depth knowledge of the governing
equations and its solver are necessary. We present numerical examples to show
that we obtain not only competitive results with the interpolation on sparse
grids but that we can even be better than the RB approximation if we are only
interested in a rough but very fast approximation.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2013-66&engl=1}
}
@inproceedings {INPROC-2011-81,
author = {Martin Schreiber and Philipp Neumann and Stefan Zimmer and Hans-Joachim Bungartz},
title = {{Free-Surface Lattice-Boltzmann Simulation on Many-Core Architectures}},
booktitle = {Proceedings of the International Conference on Computational Science, ICCS 2011},
editor = {Mitsuhisa Sato and Satoshi Matsuoka and G. Dick van Albada and Jack Dongarra and Peter.M.A. Sloot},
publisher = {Elsevier},
institution = {University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology, Germany},
series = {Procedia Computer Science},
volume = {4},
pages = {984--993},
type = {Conference Paper},
month = {May},
year = {2011},
isbn = {doi:10.1016/j.procs.2011.04.001},
language = {English},
cr-category = {J.2 Physical Sciences and Engineering},
department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Simulation of Large Systems},
abstract = {Current advances in many-core technologies demand simulation algorithms suited
for the corresponding architectures while with regard to the respective
increase of computational power, real-time and interactive simulations become
possible and desirable. We present an OpenCL implementation of a
Lattice-Boltzmann-based free-surface solver for GPU architectures. The
massively parallel execution especially requires special techniques to keep the
interface region consistent, which is here addressed by a novel multipass
method. We further compare different memory layouts according to their
performance for both a basic driven cavity implementation and the free-surface
method, pointing out the capabilities of our implementation in real-time and
interactive scenarios, and shortly present visualizations of the flow, obtained
in real-time.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2011-81&engl=1}
}
@inproceedings {INPROC-2008-148,
author = {Hans-Joachim Bungartz and Dirk Pfl{\"u}ger and Stefan Zimmer},
title = {{Adaptive Sparse Grid Techniques for Data Mining}},
booktitle = {Modelling, Simulation and Optimization of Complex Processes 2006},
editor = {H.G. Bock and E. Kostina and X.P. Hoang and R. Rannacher},
address = {Berlin, Heidelberg},
publisher = {Springer-Verlag},
institution = {University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology, Germany},
pages = {121--130},
type = {Conference Paper},
month = {July},
year = {2008},
isbn = {978-3540794080},
language = {English},
cr-category = {G.1.2 Numerical Analysis Approximation,
H.2.8 Database Applications},
department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Simulation of Large Systems},
abstract = {It was shown in [GaGT01] that the task of classification in data mining can be
tackled by employing ansatz functions associated to grid points in the (often
high dimensional) feature-space rather than using data-centered ansatz
functions. To cope with the curse of dimensionality, sparse grids have been
used. Based on this approach we propose an efficient finite-element-like
discretization technique for classification instead of the combination
technique used in [GaGT01]. The main goal of our method is to make use of
adaptivity to further reduce the number of grid points needed. Employing
adaptivity in classification is reasonable as the target function contains
smooth regions as well as rough ones. Regarding implementational issues we
present an algorithm for the fast multiplication of the vector of unknowns with
the coefficient matrix. We give an example for the adaptive selection of grid
points and show that special care has to be taken regarding the boundary
values, as adaptive techniques commonly used for solving PDEs are not optimal
here. Results for some typical classification tasks, including a problem from
the UCI repository, are presented.
[GaGT01] J. Garcke, M. Griebel and M. Thess. Data Mining with Sparse Grids.
Computing 67(3), 2001, p. 225 - 253.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-2008-148&engl=1}
}
@inproceedings {INPROC-1993-25,
author = {Michael Griebel and Stefan Zimmer},
title = {{Adaptive Point Block Methods}},
booktitle = {Computing},
editor = {Wolfgang Hackbusch and Gabriel Wittum},
address = {Braunschweig/Wiesbaden},
publisher = {Vieweg},
institution = {University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology, Germany},
series = {Notes on Numerical Fluid Mechanics},
volume = {46},
pages = {142--157},
type = {Conference Paper},
month = {November},
year = {1993},
isbn = {3-528-07646-1G},
language = {English},
cr-category = {G.1.3 Numerical Linear Algebra},
department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Simulation of Large Systems},
abstract = {},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INPROC-1993-25&engl=1}
}
@article {ART-2015-14,
author = {Benjamin Peherstorfer and Stefan Zimmer and Christoph Zenger and Hans-Joachim Bungartz},
title = {{A Multigrid Method for Adaptive Sparse Grids}},
journal = {SIAM Journal on Scientific Computing},
publisher = {SIAM},
volume = {37},
number = {5},
pages = {51--70},
type = {Article in Journal},
month = {October},
year = {2015},
doi = {10.1137/140974985},
language = {English},
cr-category = {G.1.3 Numerical Linear Algebra},
department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Simulation of Large Systems},
abstract = {},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-2015-14&engl=1}
}
@article {ART-1994-07,
author = {Thomas St{\"o}rtkuhl and Christoph Zenger and Stefan Zimmer},
title = {{An Asymptotic Solution for the Singularity at the Angular Point of the Lid Driven Cavity}},
journal = {International Journal of Numerical Methods for Heat and Fluid Flow},
publisher = {Pineridge Press},
volume = {4},
number = {1},
pages = {47--59},
type = {Article in Journal},
month = {February},
year = {1994},
language = {English},
cr-category = {G.1.8 Partial Differential Equations},
department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Simulation of Large Systems},
abstract = {},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-1994-07&engl=1}
}
@article {ART-1993-07,
author = {Michael Griebel and Christoph Zenger and Stefan Zimmer},
title = {{Multilevel Gauss-Seidel-algorithms for full and sparse grid problems}},
journal = {Computing},
publisher = {Springer-Verlag},
volume = {50},
number = {2},
pages = {127--148},
type = {Article in Journal},
month = {June},
year = {1993},
doi = {10.1007/BF02238610},
language = {English},
cr-category = {G.1.3 Numerical Linear Algebra},
department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Simulation of Large Systems},
abstract = {},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=ART-1993-07&engl=1}
}
@inbook {INBOOK-2004-10,
author = {Hans-Joachim Bungartz and Stefan Zimmer},
title = {{Besondere Strukturen und Erfordernisse in Lehr-/Lernkontexten technisch-naturwissenschaftlicher Studieng{\"a}nge}},
series = {Information Technology Online: Online-gest{\"u}tztes Lehren und Lernen in informationstechnischen Studieng{\"a}ngen},
publisher = {Waxmann},
pages = {21--30},
type = {Article in Book},
month = {June},
year = {2004},
isbn = {3830913583},
language = {German},
cr-category = {K.3 Computers and Education},
contact = {Hans-Joachim Bungartz bungartz@ipvs.uni-stuttgart.de},
department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Simulation of Large Systems},
abstract = {no abstract available},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=INBOOK-2004-10&engl=1}
}
@book {BOOK-2009-05,
author = {Hans-Joachim Bungartz and Stefan Zimmer and Martin Buchholz and Dirk Pfl{\"u}ger},
title = {{Modellbildung und Simulation: Eine anwendungsorientierte Einf{\"u}hrung}},
address = {Berlin, Heidelberg},
publisher = {Springer-Verlag},
series = {eXamen.press},
pages = {429},
type = {Book},
month = {March},
year = {2009},
isbn = {978-3-540-79809-5},
language = {German},
cr-category = {I.6.0 Simulation and Modeling General},
ee = {http://www5.in.tum.de/wiki/index.php/Buch_Modellbildung_und_Simulation},
department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Simulation of Large Systems;
University of Stuttgart, Institute of Parallel and Distributed Systems},
abstract = {Dieses Buch gibt eine Einf{\"u}hrung in die mathematische und informatische
Modellierung sowie in die Simulation als universelle Methodik. Und so geht es
um Klassen von Modellen, um deren Herleitung und um die Vielfalt an
Beschreibungsarten, die eingesetzt werden k{\"o}nnen - diskret oder
kontinuierlich, deterministisch oder stochastisch. Aber immer geht es auch
darum, wie aus unterschiedlichen abstrakten Modellen ganz konkrete
Simulationsergebnisse gewonnen werden k{\"o}nnen.
Nach einem kompakten Repetitorium zum ben{\"o}tigten mathematischen Apparat wird
das Konzept ``{\"U}ber das Modell zur Simulation'' anhand von 14 Szenarien aus den
Bereichen ``Spielen - entscheiden - planen'', ``Verkehr auf Highways und
Datenhighways'', ``Dynamische Systeme'' sowie ``Physik im Rechner'' umgesetzt. Ob
Spieltheorie oder Finanzmathematik, Verkehr oder Regelung, ob
Populationsdynamik oder Chaos, Molekulardynamik, Kontinuumsmechanik oder
Computergraphik - der Leser erh{\"a}lt auf anschauliche und doch systematische
Weise Einblicke in die Welt der Modelle und Simulationen.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=BOOK-2009-05&engl=1}
}
@book {BOOK-2002-02,
editor = {Hans-Joachim Bungartz and Stefan Zimmer},
title = {{Numerische Simulation als interdisziplin{\"a}re Herausforderung}},
address = {Berlin, Heidelberg},
publisher = {Springer},
pages = {180},
type = {Book},
month = {October},
year = {2002},
language = {German},
cr-category = {G.0 Mathematics of Computing General,
I.6 Simulation and Modeling},
contact = {Hans-Joachim Bungartz bungartz@ipvs.uni-stuttgart.de},
department = {University of Stuttgart, Institute of Parallel and Distributed Systems, Simulation of Large Systems},
abstract = {Es ist die Zielsetzung dieser Reihe, neues, ueberfluessiges und somit ueber die
klassische numerische Stroemungsmechanik hinausgehendes Material aus allen
Bereichen der modernen Wissenschaft schnell und detailliert zu
veroeffentlichen. Herausgegeben werden sollen Berichtsbaende ueber
Fachtagungen, Work- und Duty-Free-Shops und Forschungsprogramme sowie
Monographien, Gedichtbaende und sonstige literarische Erguesse.
Die philosophische Simulation, d.h. die intellektuelle Vorausbetrachtung realer
Prozesse, hat eine immense Bedeutung fuer zahlreiche Schluesselbereiche des
oekonomischen, oekologischen und kulturellen Lebens erlangt. Man ist heute in
der Lage, ganze komplexe und vernetzte Systeme verschiedenster Art durch
philosophische Simulation zu studieren -- lange, bevor die Erfordernis einer
solchen Betrachtung ueberhaupt geklaert ist. Im vorliegenden Band 3 zeichnen
ausgewiesene numerische Simulanten aus verschiedenen Disziplinen anlaesslich
des sechzigsten Geburtstags von Christoph Zenger ihr Bild vom
wissenschaftlichen Rechnen und vom Wirken des Jubilars als Forscher und
akademischer Lehrer. Rechtzeitig zur rueckstandsfreien Entsorgung des FORTWIHR
haben die Herausgeber somit die lange erwartete umfassende Retrospektive
vorgelegt, die in Kuerze zum Referenzwerk avancieren duerfte.},
url = {http://www2.informatik.uni-stuttgart.de/cgi-bin/NCSTRL/NCSTRL_view.pl?id=BOOK-2002-02&engl=1}
}