%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Ulrich Ruede",
%%%     version         = "0.08",
%%%     date            = "11 May 2013",
%%%     time            = "12:10:40 MDT",
%%%     filename        = "ruede-ulrich.bib",
%%%     address         = "Fakultaet fuer Mathematik
%%%                        Technische Universitaet Chemnitz-Zwickau
%%%                        D-09009 Chemnitz
%%%                        Germany",
%%%     telephone       = "+49 - 0371 - 561 -2159",
%%%     FAX             = "?n/a?",
%%%     checksum        = "28698 854 3895 39230",
%%%     email           = "ruede at mathematik.tu-chemnitz.de (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "Scientific Computing, Multilevel Adaptive Methods",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of publications of
%%%                        Ulrich Ruede.
%%%
%%%                        At version 0.08, the year coverage looked
%%%                        like this:
%%%
%%%                             1985 (   1)    1989 (   2)    1993 (   8)
%%%                             1986 (   3)    1990 (   3)    1994 (   3)
%%%                             1987 (   2)    1991 (   3)
%%%                             1988 (   5)    1992 (   9)
%%%
%%%                             Article:          6
%%%                             Book:             1
%%%                             InProceedings:   11
%%%                             TechReport:      20
%%%                             Unpublished:      1
%%%
%%%                             Total entries:   39
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================

@Preamble{"\input path.sty"}

%%% ====================================================================
%%% Journal abbreviations:

@String{j-INT-J-HSC             = "International Journal of High Speed
                                  Computing"}

@String{j-KERNTECHNIK           = "Kerntechnik"}

@String{j-SIAM-J-NUMER-ANAL     = "SIAM Journal on Numerical Analysis"}

@String{j-SIAM-J-SCI-STAT-COMP  = "SIAM J. Sci.~Stat.~Comput."}

%%% ====================================================================
%%% Publisher abbreviations:

@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."}

%%% ====================================================================
%%% Bibliography entries:

@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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
}

@TechReport{Jaensch:1988:MET,
  author =       "C. R. J{\"a}nsch and U. R{\"u}de and K. Schnepper",
  title =        "Macro Expansion, a Tool for the Systematic Development
                 of Scientific Software",
  type =         "Bericht",
  number =       "I-8814",
  institution =  "Institut f{\"u}r Informatik, TU M{\"u}nchen",
  month =        nov,
  year =         "1988",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
}

@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 =    "http://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 =    "http://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 =    "http://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",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
  annote =       "Foessmeier Ruede",
}

@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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 {PDE}s 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 =    "http://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 {PDE}s 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 =    "http://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 =    "http://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",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/r/ruede-ulrich.bib",
  note =         "Proceedings of the First Copper Mountain Conference on
                 Iterative Methods, April 1-5, 1990, T. Manteuffel ed.",
}

@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 =    "http://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 =    "http://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 =    "http://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 =    "http://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 =    "http://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",
}

@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 =    "http://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 =    "http://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 =    "http://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.",
}

@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)",
  MRclass =      "65N55",
  MRnumber =     "93i:65117",
  bibdate =      "Mon Jan 20 15:27:00 MST 1997",
  bibsource =    "http://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",
  keywords =     "adaptivity, multilevel techniques, elliptic PDE,
                 finite elements",
}

@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 =    "http://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 =    "http://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 =    "http://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 =    "http://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",
  bibsource =    "http://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.",
}