@Preamble{"\input path.sty"}
@String{j-FUT-GEN-COMP-SYS = "Future Generation Computer Systems"}
@String{j-INT-J-HSC = "International Journal of High Speed
Computing"}
@String{j-KERNTECHNIK = "Kerntechnik"}
@String{j-LECT-NOTES-COMP-SCI = "Lecture Notes in Computer Science"}
@String{j-SIAM-J-NUMER-ANAL = "SIAM Journal on Numerical Analysis"}
@String{j-SIAM-J-SCI-COMP = "SIAM Journal on Scientific Computing"}
@String{j-SIAM-J-SCI-STAT-COMP = "SIAM J. Sci.~Stat.~Comput."}
@String{pub-AMS = "Amer. Math. Soc."}
@String{pub-AMS:adr = "Providence, RI, USA"}
@String{pub-BIRKHAUSER = "Birkh{\"{a}}user"}
@String{pub-BIRKHAUSER:adr = "Cambridge, MA, USA; Berlin, Germany; Basel,
Switzerland"}
@String{pub-DEKKER = "Marcel Dekker"}
@String{pub-DEKKER:adr = "New York, NY, USA"}
@String{pub-INST-ANG-ANA-STOCH = "Institut f{\"u}r Angewandte Analysis und
Stochastik"}
@String{pub-INST-ANG-ANA-STOCH:adr = "Berlin, Germany"}
@String{pub-NASA = "NASA"}
@String{pub-SIAM = "SIAM"}
@String{pub-SIAM:adr = "Philadelphia, PA, USA"}
@String{pub-SV = "Springer-Verlag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg, Germany~/
London, UK~/ etc."}
@TechReport{Ruede:1985:AMB,
author = "U. R{\"u}de",
title = "{Anwendung der Mehrgittermethode zur Berechnung von
digitalen H{\"o}henmodellen in der Photogrammetrie}",
type = "Bericht",
number = "I-8525",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = nov,
year = "1985",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
}
@InProceedings{Ruede:1986:DMM,
author = "U. R{\"u}de",
editor = "W. Hackbusch and U. Trottenberg",
booktitle = "Multigrid Methods: Special Topics and Applications,
Papers presented at the 2nd European Conference on
Multigrid Methods, October 1-4, 1985",
title = "Discretizations for Multigrid Methods",
volume = "110",
address = "Cologne",
pages = "??--?? (of 178)",
month = may,
year = "1986",
ISBN = "3-88457-110-9",
ISBN-13 = "978-3-88457-110-1",
LCCN = "QA377.E87 1985",
bibdate = "Mon Jul 11 13:00:25 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
note = "Also available as TU-Bericht I-8519",
series = "GMD Studien",
}
@InProceedings{Ruede:1986:TSM,
author = "U. R{\"u}de and C. Zenger",
editor = "W. Hackbusch and U. Trottenberg",
booktitle = "Lecture Notes in Mathematics 1228: Multigrid Methods
II, Proceedings of the Conference Held at Cologne,
October 1-4, 1985",
title = "On the Treatment of Singularities in the Multigrid
Method",
publisher = pub-SV,
address = pub-SV:adr,
pages = "??--?? (of vi + 335)",
year = "1986",
ISBN = "0-387-16491-X",
ISBN-13 = "978-0-387-16491-5",
LCCN = "QA3 .L35 v.1228",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
price = "DM50.00",
}
@TechReport{Ruede:1986:WMM,
author = "U. R{\"u}de and C. Zenger",
title = "A Workbench for Multigrid Methods",
type = "Bericht",
number = "I-8607",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = may,
year = "1986",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
}
@TechReport{Foessmeier:1987:OSS,
author = "R. F{\"o}{\ss}meier and U. R{\"u}de",
title = "Operating System Support for Parallel Numerical
Software Development",
type = "Bericht",
number = "I-8712",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = oct,
year = "1987",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
annote = "Foessmeier Ruede",
}
@TechReport{Ruede:1987:MTE,
author = "U. R{\"u}de",
title = "Multiple tau-Extrapolation for Multigrid Methods",
type = "Bericht",
number = "I-8701",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = jan,
year = "1987",
bibdate = "Mon May 23 09:36:47 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
}
@TechReport{Jaensch:1988:MET,
author = "Christian R. Jaensch and Ulrich Ruede and Klaus
Schnepper",
title = "Macro Expansion, a Tool for the Systematic Development
of Scientific Software",
type = "Report",
number = "I-8814",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
address = "M{\"u}nchen, West Germany",
month = nov,
year = "1988",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib;
https://www.math.utah.edu/pub/tex/bib/fortran2.bib;
Misc/TUBScsd.bib",
annote = "{der Bericht Beschreibt die Moeglichkeiten Bei der
Umsetzung von Konzepten H{\"o}herer Sprachen Mittels
eines Praeprozessorsnach Standard-fortran. es wird der
"macro-expander" M4 Vorgestellt.}",
descriptor = "Fortran, M4, Macro Expansion, Praeprozessor,
Preprozessor",
}
@TechReport{Muszynski:1988:AAM,
author = "P. Muszynski and U. R{\"u}de and C. Zenger",
title = "Application of Algebraic Multigrid {(AMG)} to
Constrained Quadratic Optimization",
type = "Bericht",
number = "I-8801",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = jan,
year = "1988",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
}
@InProceedings{Ruede:1988:ACS,
author = "U. R{\"u}de",
editor = "S. F. McCormick",
booktitle = "Multigrid Methods: Theory, Applications,
Supercomputing: Proceedings of the Third Copper
Mountain Conference on Multigrid Methods, April 5-10,
1987",
title = "On the Accurate Computation of Singular Solutions of
{Laplace's and Poisson's} Equation",
publisher = pub-DEKKER,
address = pub-DEKKER:adr,
pages = "??--?? (of xiv + 644)",
year = "1988",
ISBN = "0-8247-7979-7",
ISBN-13 = "978-0-8247-7979-5",
LCCN = "QA377 .M9431 1988",
bibdate = "Mon May 23 09:36:47 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
}
@TechReport{Ruede:1988:NBS,
author = "U. R{\"u}de",
title = "{Zur numerischen Behandlung von Singularit{\"a}ten in
elliptischen partiellen Differentialgleichungen}",
type = "Bericht",
number = "I-8810",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = aug,
year = "1988",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
}
@Article{Zenger:1988:BSE,
author = "C. Zenger and R. F{\"o}{\ss}meier and U. R{\"u}de",
title = "{Betriebssystem- und Software-Engineering-Aspekte bei
parallelen Algorithmen}",
journal = j-KERNTECHNIK,
volume = "52",
number = "2",
pages = "120--125",
year = "1988",
CODEN = "KERNEU",
ISSN = "0004-7198, 0932-3902, 0368-5276",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
annote = "Foessmeier Ruede",
fjournal = "Kerntechnik",
}
@TechReport{McCormick:1989:FVC,
author = "S. McCormick and U. R{\"u}de",
title = "A Finite Volume Convergence Theory for the Fast
Adaptive Composite Grid Method",
institution = "University of Colorado at Denver",
year = "1989",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
note = "To be published in Applied Numerical Mathematics (14)
1994, Elsevier",
annote = "Ruede",
}
@InProceedings{Ruede:1989:LCE,
author = "U. R{\"u}de",
editor = "J. Mandel",
booktitle = "Proceedings of the Fourth Copper Mountain Conference
on Multigrid Methods, April 9-14, 1989",
title = "Local Corrections for Eliminating the Pollution Effect
of Reentrant Corners",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "365--382",
year = "1989",
bibdate = "Mon May 23 09:36:47 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
}
@Article{Foessmeier:1990:KWP,
author = "R. F{\"o}{\ss}meier and U. R{\"u}de",
title = "{Konzepte und Werkzeuge zur parallelen Programmierung
auf der Unix-Kommando-Ebene}",
journal = "unix/mail",
volume = "8",
number = "2",
pages = "66--73",
year = "1990",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
}
@Article{McCormick:1990:LRH,
author = "S. McCormick and U. R{\"u}de",
title = "On Local Refinement Higher Order Methods for Elliptic
Partial Differential Equations",
journal = j-INT-J-HSC,
volume = "2",
number = "4",
pages = "311--334",
year = "1990",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
note = "Also available as TU-Bericht I-9034",
annote = "Ruede",
}
@TechReport{Slavkovsky:1990:SBK,
author = "P. Slavkovsky and U. R{\"u}de",
title = "{Schnellere Berechnung klassischer
Matrix-Multiplikationen}",
type = "SFB Bericht",
number = "342/17/90",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = sep,
year = "1990",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
annote = "Ruede",
}
@TechReport{Arbesmeier:1991:TMM,
author = "M. Arbesmeier and U. R{\"u}de",
title = "A Toolbox for Multigrid Methods",
type = "Bericht",
number = "I-9136",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = sep,
year = "1991",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
URL = "file://www.tu-chemnitz.de/pub/Local/mathematik/Ruede/mgwb.ps.Z",
abstract = "The multigrid workbench project is an ongoing effort
to design an interactive environment for multigrid
algorithms. Central components are a graphical user
interface and visualization modules. The workbench in
its present form is based on a specialized high level
toolset that provides the basic multigrid components
for two-dimensional stationary diffusion equations.
Because of its functional and stream-oriented
programming style the workbench can be used to solve
large systems with up to several million unknowns on
standard workstations. This report discusses the
related software engineering and efficiency issues. A
prototype of the interactive user environment and basic
visualization components is available.",
}
@InProceedings{Ruede:1991:AHO,
author = "U. R{\"u}de",
editor = "W. Hackbusch and U. Trottenberg",
booktitle = "Proceedings of the Third European Conference on
Multigrid Methods, October 1-4, 1990",
title = "Adaptive Higher Order Multigrid Methods",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "339--351",
year = "1991",
bibdate = "Mon May 23 09:36:47 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
note = "International Series of Numerical Mathematics,
Vol.~98",
}
@TechReport{Ruede:1991:ERT,
author = "U. R{\"u}de",
title = "Extrapolation and Related Techniques for Solving
Elliptic Equations",
type = "Bericht",
number = "I-9135",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = sep,
year = "1991",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
URL = "file://www.tu-chemnitz.de/pub/Local/mathematik/Ruede/extra_rel.ps.Z",
abstract = "Extrapolation is a well-known numerical technique for
raising the approximation order. Several variants of
extrapolation can be used for elliptic partial
differential equations. The basic algorithmic variants
are Richardson extrapolation, truncation error
extrapolation and extrapolation of the functional. In
multi-dimensional problems the error can be expanded
into multivariate polynomials with respect to mesh
parameters for the different coordinate directions.
This can be exploited by multivariate extrapolation and
the combination and sparse grid techniques. In this
paper these methods are introduced and discussed in
detail. The features and effectiveness are illustrated
in numerical experiments for model problems.",
}
@TechReport{Bonk:1992:PAO,
author = "T. Bonk and U. R{\"u}de",
title = "Performance Analysis and Optimization of Numerically
Intensive Programs",
type = "SFB Bericht",
number = "342/26/92 A",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = nov,
year = "1992",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
URL = "file://www.tu-chemnitz.de/pub/Local/mathematik/Ruede/performance.ps.Z",
abstract = "In this paper we explore the characteristics of
numerically intensive programs and explore their
efficient implementation on a variety of machine
architectures. It is demonstrated that different
architectures need different optimization techniques.
The emphasis of the paper is on modern RISC-CPUs on the
one side and advanced, recursive algorithms on the
other side.",
annote = "Ruede",
keywords = "Numerically intensive computing, supercomputing,
performance measurement, optimizing compilers, basic
linear algebra operations, recursion, matrix
multiplication, high dimensional numerical quadrature",
}
@TechReport{Bungartz:1992:ECS,
author = "H. Bungartz and M. Griebel and U. R{\"u}de",
title = "Extrapolation, Combination and Sparse Grid Techniques
for Elliptic Boundary Value Problems",
type = "SFB Bericht",
number = "342/10/92 A",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = may,
year = "1992",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
note = "to be published in {\em Computer Methods in Applied
Mechanics and Engineering} (1994)",
annote = "Ruede",
}
@TechReport{Griebel:1992:CTPa,
author = "M. Griebel and W. Huber and U. R{\"u}de and T.
St{\"o}rtkuhl",
title = "The Combination Technique for Parallel
Sparse-Grid-Preconditioning and -Solution of {PDEs} on
Multiprocessor Machines and Workstation Networks",
type = "SFB Bericht",
number = "342/11/92 A",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = may,
year = "1992",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
annote = "Ruede",
}
@InProceedings{Griebel:1992:CTPb,
author = "M. Griebel and W. Huber and U. R{\"u}de and T.
St{\"o}rtkuhl",
editor = "L. Boug{\'e} and M. Cosnard and Y. Robert and D.
Trystram",
booktitle = "Parallel Processing: {CONPAR 92 -- VAPP V}",
title = "The Combination Technique for Parallel
Sparse-Grid-Preconditioning or -Solution of {PDEs} on
Workstation Networks",
volume = "634",
publisher = pub-SV,
address = pub-SV:adr,
pages = "217--228",
year = "1992",
bibdate = "Mon May 23 09:36:47 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
note = "Proceedings of the Second Joint International
Conference on Vector and Parallel Processing, Lyon,
France, September 1--4, 1992",
series = "Lecture Notes in Computer Science",
annote = "Ruede",
}
@TechReport{Ruede:1992:DSM,
author = "U. R{\"u}de",
title = "Data Structures for Multilevel Adaptive Methods and
Iterative Solvers",
type = "Bericht",
number = "I-9217",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = may,
year = "1992",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
URL = "file://www.tu-chemnitz.de/pub/Local/mathematik/Ruede/data_structures.ps.Z",
abstract = "The adaptive solution of partial differential
equations by finite elements must be supported by
suitable data structures. Besides an overview of
existing adaptive mesh techniques, our analysis
provides an abstract treatment discussing the necessary
functionality independent of concrete representations.
The different aspects can be organized in topological,
geometric and the algebraic components. Further
considerations are necessary to support self-adaptivity
in a multilevel context. We distinguish between element
based and node based data structures and will discuss
their implementation in an object oriented language.",
}
@Article{Ruede:1992:HBE,
author = "U. R{\"u}de",
editor = "T. Manteuffel",
title = "The Hierarchical Basis Extrapolation Method",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "13",
number = "1",
pages = "307--318",
month = jan,
year = "1992",
CODEN = "SIJCD4",
DOI = "https://doi.org/10.1137/0913016",
ISSN = "0196-5204",
ISSN-L = "0196-5204",
MRclass = "65N50 (65F10 65N55)",
MRnumber = "92h:65181",
bibdate = "Mon Mar 31 10:00:51 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
note = "Proceedings of the First Copper Mountain Conference on
Iterative Methods, April 1-5, 1990, T. Manteuffel ed.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
onlinedate = "January 1992",
}
@InProceedings{Ruede:1992:REF,
author = "U. R{\"u}de",
editor = "A. Quarteroni",
booktitle = "Proceedings of the Sixth International Conference on
Domain Decomposition in Science and Engineering, Como,
Italy, June 15-19, 1992",
title = "On the robustness and efficiency of the fully adaptive
multigrid method",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "??--?? (of xxii + 484)",
year = "1992",
ISBN = "0-8218-5158-6",
ISBN-13 = "978-0-8218-5158-6",
LCCN = "QA402.2 .I55 1992",
bibdate = "Mon May 23 09:36:47 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
abstract = "The fully adaptive multigrid method (FAMe) is a finite
element based elliptic solver integrating
self-adaptivity, error estimation and efficient
iterative solution. Refined elements are not restricted
to predetermined regions and need not be grouped in
patches. Instead, whether an element is refined, is
decided individually for each element using an
integrated error indicator. The refinement process
induces a multilevel structure and therefore a natural
decomposition of the solution space into a nested
sequence. This can be exploited to define an efficient
solver and error estimator.",
annote = "Contemporary Mathematics",
}
@TechReport{Ruede:1992:TSF,
author = "U. R{\"u}de and C. Zenger",
title = "On the Treatment of Singularities in the Finite
Element Method",
type = "Bericht",
number = "I-9220",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = aug,
year = "1992",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
}
@TechReport{Ruede:1992:VCF,
author = "U. R{\"u}de",
title = "On the {V}-cycle of the fully adaptive multigrid
method",
type = "Bericht",
number = "I-9215",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = may,
year = "1992",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
note = "to be published in the proceedings of the 9th GAMM
Seminar, Kiel, January 22--24, 1993",
URL = "file://www.tu-chemnitz.de/pub/Local/mathematik/Ruede/kiel93.ps.Z",
abstract = "The Fully Adaptive Multigrid Method (FAMe) is a
concept for the effective solution of elliptic problems
including robust and efficient iterative solution,
error estimation, and self-adaptive refinement. In this
paper we introduce a variant of the FAMe similar in
structure to a multigrid V-cycle and a multiplicative
multilevel Schwarz method. This variant permits a
convergence analysis showing that the FAMe provides
optimal convergence rates when the classical methods
do. The FAMe, however, will be more efficient in a
local refinement context by exploiting the locality of
the computations and will be more robust, because it
naturally provides diagnostic information that can
serve as rigorous error bounds.",
}
@TechReport{Pflaum:1993:GAR,
author = "C. Pflaum and U. R{\"u}de",
title = "{Gau{\ss}}' adaptive relaxation for the multilevel
solution of partial differential equations on sparse
grids",
type = "SFB-Bericht",
number = "342/13/93 A",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = sep,
year = "1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
note = "to appear in the proceedings of the 2nd Gau{\ss}
Symposium, Munich, Aug.~2--7, 1993",
URL = "file://www.tu-chemnitz.de/pub/Local/mathematik/Ruede/gauss.ps.Z",
abstract = "In combination with the multilevel principle,
relaxation methods are among the most efficient
numerical solution techniques for elliptic partial
differential equations. Typical methods used today are
derivations of the Gauss -Seidel or Gauss -Jacobi
method. Recently it has been recognized that in the
context of multilevel algorithms, the original method
suggested by Gauss has specific advantages. For this
method the iteration is concentrated on unknowns where
fast convergence can be obtained by intelligently
monitoring the residuals. We will present this
algorithm in the context of a sparse grid multigrid
algorithm. Using sparse grids the dimension of the
discrete approximation space can be reduced
additionally.",
annote = "Ruede",
}
@InProceedings{Regler:1993:LOA,
author = "H. Regler and U. R{\"u}de",
booktitle = "Proceedings of the Sixth Copper Mountain Conference on
Multigrid Methods, Copper Mountain, April 4-9, 1993",
title = "Layout optimization with Algebraic Multigrid Methods
{(AMG)}",
publisher = pub-NASA,
year = "1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
series = "Conference Publication",
URL = "file://www.tu-chemnitz.de/pub/Local/mathematik/Ruede/amg.ps.Z",
annote = "Ruede",
}
@Article{Rude:1993:FAM,
author = "Ulrich R{\"u}de",
title = "Fully Adaptive Multigrid Methods",
journal = j-SIAM-J-NUMER-ANAL,
volume = "30",
number = "1",
pages = "230--248",
month = feb,
year = "1993",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65N55",
MRnumber = "93i:65117",
bibdate = "Mon Jan 20 15:27:00 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
abstract = "Adaptivity is a key concept for the effective
numerical solution of differential equations. The
multilevel solution of elliptic partial differential
equations can be combined with adaptive mesh refinement
and an adaptive choice of the discretization order.
Additionally, adaptivity may be built into the
relaxation and the multilevel cycling strategy. The
goal of these {\em fully adaptive} methods is to spend
work only where it is most effective in the solution
process. This approach includes concepts like {\em
local relaxation} and not only leads to particularly
fast convergence but also to additional robustness and
generality. The efficient implementation of fully
adaptive multilevel methods in a finite element
framework will be discussed.",
acknowledgement = ack-nhfb,
amsmos = "65N22, 65N30, 65N50, 65N55",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "adaptivity, multilevel techniques, elliptic PDE,
finite elements",
}
@InProceedings{Ruede:1993:DAT,
author = "U. R{\"u}de",
booktitle = "Proceedings of the GAMM-Seminar on Multigrid Methods,
Sept. 21 -- 25, 1992 in Gosen, Germany",
title = "Data abstraction techniques for multilevel
algorithms",
publisher = pub-INST-ANG-ANA-STOCH,
address = pub-INST-ANG-ANA-STOCH:adr,
year = "1993",
bibdate = "Mon May 23 09:36:47 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
note = "Report 5, ISSN 0942--9077",
URL = "file://www.tu-chemnitz.de/pub/Local/mathematik/Ruede/gosen92.ps.Z",
abstract = "Multilevel methods are fast and efficient solvers for
a wide range of technical and scientific applications.
Their structural complexity makes the construction of
powerful multilevel based software difficult.
Conventional software engineering concepts do not
provide a sufficient basis for the implementation of
general, fast, and robust multilevel applications. In
particular, there is a severe tradeoff between the
generality of such software and its efficiency. These
problems can be alleviated on the basis of a consequent
data abstraction. To equally satisfy the demands for
generality and efficiency it is necessary to introduce
a two level software model based on a generation and an
execution phase. Suitable implementation techniques are
discussed.",
editors = "S. Hengst",
}
@Unpublished{Ruede:1993:EEB,
author = "U. R{\"u}de",
title = "Error estimators based on stable splittings",
year = "1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
note = "Submitted to the proceedings of the 7th International
Conference On domain Decomposition, Penn State
University",
URL = "file://www.tu-chemnitz.de/pub/Local/mathematik/Ruede/ddm7.ps.Z",
abstract = "Multilevel- and domain decomposition methods are
generally based on a splitting of the solution space.
The subspaces in such a splitting and their Hilbert
space structure define elementary operations, called
subspace corrections which can in turn be used to
construct iterative methods and preconditioners. In
this general setup many solution methods can be
described, including classical relaxation schemes and
domain decomposition algorithms. We are particularly
interested in the special case of (variational)
multigrid methods, based on a nested system of
subspaces and the multiplicative combination of the
subspace corrections, or the corresponding additive
methods that lead to efficient preconditioners. The
discussion of methods in this setup turns out to be
useful, because the performance of solvers and
preconditioners can be described by abstract features
of the subspace system. The stability of the splitting
has been introduced as the basic property that
determines the efficiency of the corresponding methods.
Furthermore, however, the splitting of the space can be
used to derive error estimators. If the splitting is
stable, the lower and upper bounds obtained for the
error are uniformly bounded. Depending on the
interpretation of the spaces, the bounds apply to the
(algebraic) iteration error or the (continuous)
discretization error. In any case, the estimate is
based on subspace corrections, as they are computed in
each iteration step. Therefore the error estimate does
not create any additional cost. In the paper we review
the theory of stable splittings and the derivation of
the abstract error estimates. Furthermore we discuss
their performance in realistic algorithms and their
efficient integration with the multilevel adaptive
iteration and the virtual global mesh refinement
technique to a fully adaptive multilevel technique for
the solution of partial differential equations.",
}
@TechReport{Ruede:1993:ETC,
author = "U. R{\"u}de",
title = "Extrapolation techniques for constructing higher order
finite element methods",
type = "Bericht",
number = "I-9304",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
year = "1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
URL = "file://www.tu-chemnitz.de/pub/Local/mathematik/Ruede/extrapolation.ps.Z",
abstract = "The p-version of the finite element methods requires
the exact calculation of the stiffness matrix by a
special form of numerical integration. As an
alternative to classical techniques that are based on
Gauss quadrature, we propose to use low order methods
combined with extrapolation. To this purpose we derive
asymptotic expansions for basic integration methods on
triangles. In contrast to conventional extrapolation
methods for elliptic equations these results use only a
local analysis and can thus be used on unstructured
meshes. We present a complete analysis and examples
with practical suggestions for extrapolation-based high
order finite element methods.",
}
@Book{Ruede:1993:MCT,
author = "U. R{\"u}de",
title = "Mathematical and computational techniques for
multilevel adaptive methods",
volume = "13",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xii + 140",
year = "1993",
ISBN = "0-89871-320-X",
ISBN-13 = "978-0-89871-320-6",
LCCN = "QA377 .R87 1993",
bibdate = "Mon May 23 09:36:47 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
series = "Frontiers in Applied Mathematics",
}
@TechReport{Ruede:1993:MES,
author = "U. R{\"u}de",
title = "Multilevel, Extrapolation, and Sparse Grid Methods",
type = "SFB Bericht",
number = "342/10/93 A/ I-9319",
institution = "Institut f{\"u}r Informatik, TU M{\"u}nchen",
month = jul,
year = "1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
note = "to appear in the Proceedings of the \ European
Conference on Multigrid Methods, Amsterdam, July 6--9,
P. Hemker and P. Wesseling eds.",
URL = "file://www.tu-chemnitz.de/pub/Local/mathematik/Ruede/emg93.ps.Z",
abstract = "Multigrid Methods are asymptotically optimal solvers
for discretized partial differential equations (PDE).
For the optimal solution of PDEs, however, the quality
of the discretization is of the same importance as the
speed of the algebraic solution process. Especially for
high accuracy requirements, high order discretizations
become increasingly attractive. We describe higher
order techniques, like extrapolation and sparse grid
combination that are particularly interesting in the
context of multilevel algorithms, because they are
based on discretizing the problems on grids with
different mesh sizes. Classical Richardson
extrapolation can be extended and generalized in many
ways. One generalization is to consider the mesh widths
in the different coordinate directions as distinct
parameters. This leads to the so-called multivariate
extrapolation and the combination technique.",
}
@InProceedings{Balder:1994:SGE,
author = "R. Balder and U. R{\"u}de and S. Schneider and C.
Zenger",
booktitle = "Proceedings of the 10th International Conference on
Computational Methods in Water Resources, Heidelberg,
19.-22. Juli 1994",
title = "Sparse Grid and Extrapolation Methods for Parabolic
Problems",
year = "1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
URL = "file://www.tu-chemnitz.de/pub/Local/mathematik/Ruede/heidel94.ps.Z",
}
@InProceedings{Jung:1994:IEM,
author = "M. Jung and U. R{\"u}de",
editor = "T. Manteuffel",
booktitle = "Preliminary Proceedings of the Colorado Conference on
Iterative Methods, Breckenridge, Colorado, April 4-10,
1994",
title = "Implicit extrapolation methods for multilevel finite
element computations",
year = "1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
URL = "file://www.tu-chemnitz.de/pub/Local/mathematik/Ruede/impl_extrapolation.ps.Z",
}
@Article{Ruede:1994:MAI,
author = "U. R{\"u}de",
title = "On the Multilevel Adaptive Iterative Method",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "15",
year = "1994",
CODEN = "SIJCD4",
ISSN = "0196-5204",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
note = "also available as TU-Bericht I-9216, and published in
the Preliminary Proceedings of the 2nd Copper Mountain
Conference on Iterative Methods, April 9--14, 1992, ed.
T. Manteuffel, University of Colorado at Denver.",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
}
@Article{Ruede:2002:CEP,
author = "U. Ruede",
title = "Computational Engineering Programs at the {University
of Erlangen-Nuremberg}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2331",
pages = "852--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:36 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2331.htm;
https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2002b.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2331/23310852.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2331/23310852.pdf",
acknowledgement = ack-nhfb,
}
@Article{Renaut:2003:E,
author = "Rosemary A. Renaut and Ulrich Ruede",
title = "Editorial",
journal = j-FUT-GEN-COMP-SYS,
volume = "19",
number = "8",
pages = "1265--1265",
month = nov,
year = "2003",
CODEN = "FGSEVI",
ISSN = "0167-739X (print), 1872-7115 (electronic)",
ISSN-L = "0167-739X",
bibdate = "Sat Jan 10 10:03:38 MST 2004",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib;
https://www.math.utah.edu/pub/tex/bib/futgencompsys.bib",
acknowledgement = ack-nhfb,
fjournal = "Future Generation Computer Systems",
journal-URL = "http://www.sciencedirect.com/science/journal/0167739X",
remark = "Selected papers from the Workshop on Education in
Computational Sciences held at the International
Conference on Computational Science.",
}
@InCollection{Koestler:2004:ETC,
author = "H. Koestler and U. Ruede",
booktitle = "Computational science---{ICCS} 2004. {Part} {IV}",
title = "Extrapolation techniques for computing accurate
solutions of elliptic problems with singular
solutions",
volume = "3039",
publisher = "Springer, Berlin",
pages = "410--417",
year = "2004",
DOI = "https://doi.org/10.1007/978-3-540-25944-2_54",
MRclass = "65N06",
MRnumber = "2233222",
bibdate = "Thu Sep 21 12:20:50 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
series = "Lecture Notes in Comput. Sci.",
acknowledgement = ack-nhfb,
}
@Article{Johnson:2008:SIC,
author = "Chris Johnson and David Keyes and Ulrich Ruede",
title = "Special Issue on Computational Science and
Engineering",
journal = j-SIAM-J-SCI-COMP,
volume = "30",
number = "6",
pages = "vii--vii",
month = "????",
year = "2008",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/SJOCE3000030000006000vii000001",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65-06",
MRnumber = "2452362",
bibdate = "Wed May 19 10:44:10 MDT 2010",
bibsource = "http://epubs.siam.org/toc/sjoce3/30/6;
https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Dumitrasc:2021:EAB,
author = "Andrei Dumitrasc and Philippe Leleux and Constantin
Popa and Ulrich Ruede and Daniel Ruiz",
title = "Extensions of the Augmented Block {Cimmino} Method to
the Solution of Full Rank Rectangular Systems",
journal = j-SIAM-J-SCI-COMP,
volume = "43",
number = "5",
pages = "S516--S539",
month = "????",
year = "2021",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/20M1348261",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed Jan 19 08:22:14 MST 2022",
bibsource = "http://epubs.siam.org/toc/sjoce3/43/5;
https://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2021",
}
