Send mail to: mgnet@cs.yale.edu for the digests or bakeoff mgnet-requests@cs.yale.edu for comments or help Current editor: Craig Douglas douglas-craig@cs.yale.edu Anonymous ftp repository: casper.cs.yale.edu (128.36.12.1) World Wide Web: http://na.cs.yale.edu/mgnet/www/mgnet.html or http://www.cerfacs.fr/~douglas/mgnet.html or http://www.ccs.uky.edu/mgnet Today's editor: Craig Douglas (douglas-craig@cs.yale.edu) Volume 7, Number 4 (approximately April 30, 1997) Today's topics: New MGNet Site FEATFLOW1.0 on the Internet Query about Multi-grid Methods for Biharmonic Equation Postcard from Copper Mountain Multigrid Benchmarks Discussions Planning for conferences Publist Griebel ------------------------------------------------------- Date: Wed, 30 Apr 1997 16:04:01 -0400 From: douglas@ccs.uky.edu (Craig Douglas) Subject: New MGNet Site I have put a duplicate of MGNet at the University of Kentucky. It can be accessed through htpp://www.ccs.uky.edu/mgnet The web pages now include this site as well as Yale and CERFACS at the top. ------------------------------------------------------- Date: Fri, 18 Apr 1997 15:35:45 +0200 From: Stefan TurekSubject: FEATFLOW1.0 on the Internet Dear colleagues, Our FEM software for incompressible Navier-Stokes equations, FEATFLOW1.0, including all sources, manuals and many (!) demos for nonstationary flows (as MPEG movies), is "downloadable" via Internet, see http://gaia.iwr.uni-heidelberg.de/~featflow Stefan Turek Institut fuer Angewandte Mathematik, Universitaet Heidelberg, Germany ture@gaia.iwr.uni-heidelberg.de, http://gaia.iwr.uni-heidelberg.de/~ture ------------------------------------------------------- Date: Wed, 23 Apr 1997 15:07:50 -0700 (PDT) From: Matthew Cordery Subject: Query about Multi-grid Methods for Biharmonic Equation I am interested in multigrid methods for solving the biharmonic equation on unstructured 2D triangular meshes and am wondering if anyone has any experience in this problem that they might be willing to share. In particular, I am interested in solutions to the biharmonic equation that arises from the equations for creeping flow (Stoke's equations). The fluid itself has a strongly temperature-dependent viscosity that may vary sharply over short distances (relative to the size of the compuational domain). Thus, my biharmonic equation would have a viscosity term embedded within it. Thanks in advance for any help! Dr. Matthew J. Cordery cordery1@llnl.gov Environmental Computer Applications Lawrence Livermore National Laboratory L206 P.O. Box 808 Livermore, CA 94550 Editor's Note: Here is what I found on multigrid methods and Biharmonic problems in the MGNet bibliography by searching on biharmonic. Surely there is more that is not in the bibliography or does not have the word in the title. If you know of something, please e-mail both the inquirer and MGNet. Thanks. [1] R. N. Banerjee and M. W. Benson, An approximate inverse based multigrid approach to the biharmonic problem, Int. J. Comput. Math., 40 (1991), pp. 201-210. [2] A. Brandt and J. Dym, Effective boundary treatment for the biharmonic Dirichlet problem, in Seventh Copper Mountain Conference on Multigrid Methods, N. D. Melson, T. A. Man- teuffel, S. F. McCormick, and C. C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA, pp. 97-107. [3] S. C. Brenner, An optimal order nonconforming multigrid method for the biharmonic equation, SIAM J. Numer. Anal., 26 (1989), pp. 1124-1138. [4] M. R. Hanisch, Multigrid Preconditioning for Mixed Finite Element Methods, PhD thesis, Cornell, Ithaca, NY, 1991. [5] ______, Multigrid preconditioning for the biharmonic Dirichlet problem, SIAM J. Numer. Anal., 30 (1993), pp. 184-214. [6] W. Heinrichs, A stabilized treatment of the biharmonic oper- ator with spectral methods, SIAM J. Sci. Stat. Comput., 12 (1991), pp. 1162-1172. [7] J. Linden, A multigrid method for solving the biharmonic equa- tion on rectangular domains, in Advances in Multi-Grid Methods, D. Braess, W. Hackbusch, and U. Trottenberg, eds., vol. 11 of Notes on Numerical Fluid Mechanics, Braun- schweig, 1984, Vieweg, pp. 64-76. [8] P. Oswald, Hierarchical conforming finite element methods for the biharmonic equation, SIAM J. Numer. Anal., 29 (1992), pp. 1610-1625. [9] P. Peisker, A multilevel algorithm for the biharmonic problem, Numer. Math., 46 (1985), pp. 623-634. [10] P. Peisker and D. Braess, A conjugate gradient method and a multigrid method for Morley's finite element approxima- tion of the biharmonic equation, Numer. Math., 50 (1987), pp. 567-586. [11] X. Zhang, Studies in domain decomposition: multilevel meth- ods and the biharmonic Dirichlet problem, PhD thesis, Courant Institute, New York University, New York City, 1991. ------------------------------------------------------- Date: Thu, 1 May 1997 12:04:01 -0400 From: douglas@ccs.uky.edu (Craig Douglas) Subject: Postcard from Copper Mountain The Copper Mountain Multigrid Conference was held for the eighth time from April 6-11, 1997. For the first time in years, there were no parallel sessions for talks, giving the conference the type of intimacy found in the GAMM parallel multigrid workshops held in Germany for many years and most recently in Austria. Two years ago there were many newcomers to the Copper Mountain conference. Once again this was the case. In part this is due to the large number of graduate students and fresh Ph.D.'s who have attended both conferences. Ski conditions were the best in a generation at Copper Mountain, though the conference attendees were much too busy to notice. Even when 7 inches, or 17.5 cm, of powder came down Thursday afternoon/evening, attendance was still quite high. (Well, maybe a few went out on the slopes during the afternoon breaks or before or after the conference.) However, with "parabolic" shaped skis for rent, and this being a conference with a strong influence from the PDE community, it was only a natural condition to assume that some of us tried out this style of skis. There were reports that it was much easier to turn, but harder to go straight on these skis. The conclusion drawn seemed to be that the ease of use of and preference for the parabolic skis was clearly time dependent. One of the amusing moments occurred at the conference dinner. Steve McCormick asked everyone to please stand up (quite a task at 9600 feet, or 3100 meters, above sea level in the evening after many lectures). People were asked to sit down based on the number of conferences attended. Quite a number sat down after one or two conferences. By 12 conferences (including the iterative method conferences held on even numbered years) only Joel Dendy and Steve were still standing. The banquet ended with birthday cakes celebrating Seymour Parter's pending seventieth birthday. One cake remained the next morning. The doors to the conference building were locked until the conference participants finished the cake off (Seymour did his part admirably). Counting the conference circus and workshop nights, there were 60 talks. As usual, the talks were held in the mornings and late afternoon/evenings. Talks were 25 minutes long (at most) with the session chairs rigorously enforcing the maximum time limits. Monday evening was devoted to multilevel archaeology, a topic first developed by Achi Brandt at the Seventh Copper Mountain Multigrid Conference during the banquet speeches [1]. This branch was devoted to unearthing fossils. However, the Boulder group insisted on misspelling the word as FOSLS (or first order systems least-squares). This method adds a few variables to a problem. This (usually trivial extra expense) is offset by the fact that it allows you to measure the local and global error easily so that you know if you have solved your problem or not (quite a neat trick). The circus evening was quick due to the fact that almost everyone was already speaking at the conference. The highlight was Michael Griebel's daughter making it quite clear from outside of the conference room that she wanted her daddy right away. Rarely has a talk been concluded with such determination by the speaker. However, Michael made the point that using extremely simple computer science data methods (hashing in particular), accessing information about nonuniform grid data points could be done quite cheaply in comparison to the more common tree data structures. The workshop evening was devoted to discussing benchmarks. Bodo Parady was the virtual speaker (he was in California on a telephone hooked up to the conference microphone). As noted in the March MGNet digest (volume 7, number 3), the multigrid SPECmark is open to review. Bodo provided a number of clues as to what he wants to see from the multigrid community for a new set of benchmarks (see related digest article on benchmarks). There were many, many topics covered at this conference. This has been normal in the past conferences, which is why it still exists, and will be done a ninth time in two years. There were numerous talks devoted to algorithms, theory, applications, parallel computers, and problems not derived from PDE's. There were quite a few interesting applications included in the talks. Some of these included the following (in no particular order): o Radon transfer (J. Dym) o Material sciences (S. McKay) o Linear elasticity (S. D. Kim) o Sonic flow - sub/trans/super (B. Diskin) o Magneto hydrodynamics (A. J. Meir) o Image processing (K. Witsch, J. Dym) o Point forces (K. Witsch) o Reservoir simulation (H. Zhang) o Electrostatic/circuit simulation (R. Kulke) o Stress factors (S. Brenner) o Structural analysis (M. Bittencourt) o Multi-material heat transfer (W. Dai) Numerous other people talked about small applications as part of their presentations. The talks themselves dealt with many topics. These included the following, lengthy list: o Survey (A. Brandt) o Packaged codes (M. Bittencourt, R. Kulke, W. Mitchell) o Black box multigrid (J. Dendy) o Gray box multigrid (J. Dym) o Implementation efficiency (M. Griebel, U. Ruede, C. Douglas) o Sparse grids (H.-J. Bungartz, M. Griebel) o Anisotropic problems (D. Mavriplis, X. Zhang) o Convection diffusion problems (J. Kouatchou, W. Spotz) o Mixed finite element multigrid methods (Z. Cai) o Hierarchical bases (H.J. Bungartz) o Mortar method (M. Sarkis) o Exponential bases (M. Kuether, G. Starke) o Nonconforming finite elements (Z. Chen, S. Maliassov) o Coarsening strategies (D. Mavriplis, M. Bittencourt) o Algebraic multigrid (J. Ruge, V. Henson, L. Dutto, C.A. Thole) o Inter-grid operators (Z. Chen, W.-L. Wan) o Domain decomposition methods (J. Jones, W. Mitchell, C. Douglas) o Ficticious domains (S. Maliassov) o Locally refined grids (Y. Shapira, M. Bittencourt, S. Maliassov) o Multi-resolution, wavelets (A. Brandt, D. Gines, N. Coult, R. Lorentz) o FOSLS (R. Hiptmair, S. McCormick, T. Manteuffel, M. Berndt, P. Bochev, S. D. Kim, B. Lee) o Newton-Krylov multigrid methods (D. Knoll, T. Washio) o Helmholtz, wave problems (I. Livshits) o Stokes problems (Z. Cai) o Navier-Stokes problems (D. Mavriplis, E. Sterner, X. Vasseur, H. Oswald) o Algorithm comparisons (S. Fulton, B. Diskin, E. Sterner, X. Vasseur, G. Wade, B. Lee) o Explicitly parallel multigrid (W. Mitchell, C. Douglas, L. Dutto, V. Henson, H. Oswald, D. Xie) o Smoother properties (J. Jones, J. Pasciak, Y. Yavneh) o Well posedness, stability (A. Knyazev, J. Kouatchou, W. Spotz) My apologies to all of the people that I have mislabeled or left out. The next (number 9) Copper Mountain multigrid conference will be in April, 1999. Should there be a tenth, it will be in a famous year: 2001, which seems appropriate somehow. Many of us will re-appear at Copper Mountain next year for the iterative method conference. It will be March 29 - April 3, 1998. Ski ya then. Reference [1] A. Brandt, Multigrid history, in Seventh Copper Mountain Conference on Multigrid Methods, N. D. Melson, T. A. Manteuffel, S. F. McCormick, and C. C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA, p. ix. Editor's Note: If I left anyone out of a category or misfiled anyone, ------------- please send me an update immediately. Thanks. ------------------------------------------------------- Date: Thu, 1 May 1997 17:20:32 -0400 From: douglas@ccs.uky.edu (Craig Douglas) Subject: Multigrid Benchmarks Discussions Multigrid benchmarks were discussed at the Thursday evening (April 10) workshop at Copper Mountain. The first half was devoted to finding out what the new SPECmark for multigrid might be. Bodo Parady, who is on the SPEC floating point benchmarks committee, offered some hints as to what is wanted from the multigrid community. The new multigrid benchmarks for SPEC must ... o be hard, but not too difficult to optimize. C++ code has been eliminated due to the complexity of optimization. Fortran is considered ideal, but not 100% essential. o be optimizable on cache based machines, but not be cache resident o be optimizable on vector machines o come with the correct answer so that a comparison can be made to determine how close the optimized code is to the "correct" solution. The new multigrid benchmarks for SPEC must NOT ... o be a kernel benchmark. o be completely solvable by compiler writers. o be a BLAS or LINPACK style benchmark. What is wanted is a set of real world problems. Large (rather than small) kernels are wanted. The bigger the code the better up to a point. Multiple codes is wanted, not just a single one. After we ended our phone conversation with Bo (funded by a grant from the Douglas family), we turned to a general discussion of what might be useful to users of multigrid methods. Here are some points made: o We need a database of problems with solutions similar to the very successful Boeing-Harwell collection of matrices. o We need an index file of codes that work for each problem. o We need a lot of problems in a lot of different areas. The database should not be a mechanism to cancel lots of people's grants because they only solve a small collection of problems. o Two new mailing lists will be created for people interested in benchmark discussions: one for people who just want to discuss issues and one for contributors to either the SPECmark or the database. Not just the people at the conference will be included in this venture. Anyone can get involved. In fact, certain people who were not present were identified for contacting later. If you are interested in joining the mailing lists, please send a note to mgnet@ccs.uky.edu specifying whether you want to be on the discussion list or the contributor list (the latter automatically is on the former). If you signed up at the conference, you are already on the list(s). ------------------------------------------------------- Date: Tue, 29 Apr 97 19:36:40 +0300 From: Alexander Trofimov Subject: Planning for conferences Dr. A.V. Trofimov Dniepropetrovsk State University Faculty of Mechanics and Mathematics Theoretical and Applied Mechanics Chair Dniepropetrovsk, Ukraine I ask you to send me information about multigrid and domain decomposition conferences that will take place this and next year. E:mail for contacts: Alexander.Trofimov@p8.f25.n464.z2.fidonet.org Editor's Note: Please send information about other conferences that I ------------- do not know about to both him and MGNet. Summer School on Multilevel preconditioning methods with parallel implementation aspects and applications in Scientific Computing, University of Nijmegen (NL), May 19-26, 1997, Conference on Preconditioned Iterative Solution Methods for Large Scale Problems in Scientific Computations, University of Nijmegen (NL), May 27-29, 1997 3rd IMACS Iterative Methods Conference, Jackson Hole, WY (USA), July 9-12, 1997 AFOSR International Conference on Direct Numerical Simulation and Large Eddy Simulation, Louisiana Tech University, Ruston, LA (USA), August 4-8, 1997 10th Domain Decomposition Symposium, Boulder, CO (USA), August 10-14, 1997 Guangzhou International Symposium on Computational Mathematics, Guangzhou (P.R. China), August 11-15, 1997 ? -> GAMM Workshops, Germany and Austria, sometime in 1998 5th Copper Mountain Iterative Methods Conference, Copper Mountain, CO (USA), March 29-April 3, 1998 ? -> 11th Domain Decomposition Symposium, somewhere, sometime in 1998 ------------------------------------------------------- Date: Fri, 25 Apr 1997 11:55:05 +0200 (MSZ) From: Michael Griebel Subject: Publist Griebel Attached you find the publication list of me for the MG-net archives and publication data base Best regards Michael Griebel REFERENCES [1] M. Griebel. Multilevelmethoden als Iterationsverfahren u"ber Erzeugendensystemen. Teubner Skripten zur Numerik, Teubner Verlag, Stuttgart, 1994. [2] M. Griebel und C. Zenger, Editoren. Numerical Simulation in Science and Engineering, Proceedings of the FORTWIHR Symposium on High Performance Scientific Computing in Munich, June 17-18 1993, Notes on Numerical Fluid Me- chanics 48, Vieweg-Verlag, Braunschweig, 1994. [3] M. Griebel, T. Dornseifer und T. Neunhoeffer. Numerische Simulation in der Str"omungsmechanik, eine praxisorientierte Einf"uhrung, Vieweg-Verlag, Braunschweig, 1995. [4] H.-J. Bungartz, M. Griebel und C. Zenger. Einf"uhrung in die Computergraphik: Grundlagen, Geometrische Modellierung, Algorithmen, Vieweg-Verlag, Braunschweig, 1996. Editor: REFERENCES [1] M. Griebel, D .Keyes, R. Niemienen, T .Schlick, D. Roose. Springer Lecture Notes in Computational Science and Engi- neering. Eine neue Lecture Notes Reihe im Springer Verlag. Zeitschriftenartikel: REFERENCES [1] I. Babuska, M. Griebel und J. Pitkaranta. The problem of selecting the shape functions for a p-type finite element. Int. J. Num. Meth. Engin., 28:1891-1908, 1989. also as Report MD88-36-IB-MG-JP, TR88-36, University of Mary- land, IPST, College Park, 1988. [2] M. Griebel. The combination technique for the sparse grid solu- tion of PDEs on multiprocessor machines. Parallel Process- ing Letters, 2(1):61-70, 1992. also as SFB Bericht 342/14/91 A, Institut f"ur Informatik, TU M"unchen, 1991. [3] M. Griebel und P. Oswald. On additive Schwarz preconditioners for sparse grid discretization. Numer. Math., 66(4):449-464, 1994. also as Bericht Math/92/7, Institut f"ur angewandte Mathematik, Friedrich-Schiller-Universit"at Jena, 1992. [4] M. Griebel, C. Zenger und S. Zimmer. Multilevel Gauss-Seidel- algorithms for full and sparse grid problems. Computing, 49:127-148, 1993. [5] M. Griebel und V. Thurner. Solving CFD-problems efficiently by the combination method. CFD-News, 3(4):19-31, 1993. [6] M. Griebel. Multilevel algorithms considered as iterative meth- ods on semidefinite systems. SIAM Int. J. Sci. Stat. Com- put., 15(3):547-565, 1994. [7] H. Bungartz, M. Griebel, D. R"oschke und C. Zenger. Pointwise convergence of the combination technique for Laplace's equa- tion. East-West Journal of Numerical Mathematics, 1(2):21- 45, 1994. also as SFB-Bericht 342/16/93A, Institut f"ur In- formatik, TU M"unchen, 1993. [8] H. Bungartz, M. Griebel und U. R"ude. Extrapolation, combina- tion and sparse grid techniques for elliptic boundary value problems. Computer Methods in Applied Mechanics and Engineering, Vol. 116:243-252, 1994. also in C. Bernardi und Y. Maday, Editoren, International conference on spec- tral and high order methods, ICOSAHOM 92. Elsevier, 1992, und als SFB Bericht, 342/10/92 A, Institut f"ur Informatik, TU M"unchen, 1992. [9] M. Griebel und V. Thurner. The efficient solution of fluid dy- namics problems by the combination technique. Int. J. Num. Meth. for Heat and Fluid Flow, 5(3):251-269, 1995. also as SFB Bericht 342/1/93 A, Institut f"ur Informatik. TU M"unchen, 1993. [10] M. Griebel. Parallel domain-oriented multilevel methods, SIAM Journal on Scientific Computing 16(5):1105-1125, 1995. [11] M. Griebel und P. Oswald. On the abstract theory of addi- tive and multiplicative Schwarz algorithms. Numer. Math., 70:163-180, 1995. [12] M. Griebel und P. Oswald. Tensor-product-type subspace split- tings and multilevel iterative methods for anisotropic prob- lems. Advances in Computational Mathematics, 4:171-206, 1995. also as SFB-Bericht 342/15/94A, Institut f"ur Infor- matik, TU M"unchen, 1994. [13] M. Griebel und T. Neunhoeffer. Parallel point- and domain- oriented multilevel methods for elliptic PDE's on workstation networks. J. Comp. Appl. Math., 66:267-268, 1996. [14] H. Bungartz, M. Griebel, D. R"oschke und C. Zenger. A proof of convergence for the combination technique for the Laplace equation using tools of symbolic computation. Mathemat- ics and Computers in Simulation, Vol. 42:595-605, 1996. also in G. Jacob, N. Oussous und S. Steinberg, Editoren, IMACS Symposium on Symbolic Computation, Lille, Juni 1993. IMACS/Universite des Sciences et Technologies de Lille, Villeneuve d'Ascq, 1993 und als SFB Bericht, 342/4/93 A, Institut f"ur Informatik, TU M"unchen, 1993. [15] T. Grauschopf, M. Griebel und H. Regler. Additive multilevel- preconditioners based on bilinear interpolation, matrix de- pendent geometric coarsening and algebraic multigrid coars- ening for second order elliptic PDEs. Applied Numeri- cal Mathematics, 23(1):63-96, 1997. also as SFB-Bericht 342/02/96A Institut f"ur Informatik, TU M"unchen, 1996. [16] M. Griebel, T. Neunhoeffer und H. Regler. Algebraic multi- grid methods for the solution of the Navier-Stokes equa- tions in complicated domains. Int. J. Numer. Methods for Heat and Fluid Flow, submitted, 1996. also as SFB Bericht 342/1/96A, Institut f"ur Informatik, TU M"unchen, 1996. [17] M. Griebel und G. Starke. Multilevel preconditioning based on discrete symmetrization for convection-diffusion equations. Journal of Computational and Applied Mathematics, sub- mitted, 1996. Serien- und Konferenzbeitr"age: REFERENCES [1] M. Griebel. Baumartige Strukturierung linearer Gleichungssys- teme mit d"unn besiedelter Matrix. In Berichte aus den Informatikinstituten, 9. Jahrestagung der o"sterreichischen Gesellschaft f"ur Informatik, S. 105-115. Fakult"at f"ur Math- ematik und Informatik, Universit"at Passau, Bericht MIP- 8604, 1986. [2] M. Griebel. Ein gemeinsamer Datentyp f"ur eine Baumstruk- turierung bei der Methode der finiten Elemente und beim geometrischen Modellieren. In VDI-Bericht 610.5 Daten- verarbeitung in der Konstruktion '86, CAD und Informatik, S. 543-557. VDI-Verlag, 1986. [3] M. Griebel. A parallelizable and vectorizable multi-level algo- rithm on sparse grids. In W. Hackbusch, Editor, Parallel Algorithms for partial differential equations, Notes on Nu- merical Fluid Mechanics, Volume 31, S. 94-100. Vieweg Ver- lag, Braunschweig, 1991. also as SFB Bericht, 342/20/90 A, Institut f"ur Informatik, TU M"unchen, 1990. [4] M. Griebel. Parallel multigrid methods on sparse grids. In Multi- grid Methods III, International Series of Numerical Mathe- matics, Volume 98, S. 211-221. Birkh"auser Verlag, Basel, 1991. also as SFB Bericht, 342/30/90 A, Institut f"ur Infor- matik, TU M"unchen, 1990. [5] M. Griebel, M. Schneider und C. Zenger. A combination tech- nique for the solution of sparse grid problems. In P. de Groen und R. Beauwens, Editoren, Iterative Methods in Linear Al- gebra, S. 263-281. IMACS, Elsevier, North Holland, 1992. also as SFB Bericht, 342/19/90 A, Institut f"ur Informatik, TU M"unchen, 1990. [6] M. Griebel. Multilevel algorithms considered as iterative meth- ods on indefinite systems. In T. Manteuffel, Editor, Pro- ceedings of the 2nd Copper Mountain Conference on Itera- tive Methods. University of Colorado at Denver, 1992. also as SFB Bericht, 342/29/91 A, Institut f"ur Informatik, TU M"unchen, 1991. [7] M. Griebel. Eine Kombinationstechnik f"ur die L"osung von D"unn-Gitter-Problemen auf Multiprozessor-Maschinen. In H.G. Bock, W. Hackbusch und R. Rannacher, Editoren, Numerische Algorithmen auf Transputer-Systemen, Teubner Skripten zur Numerik. Teubner Verlag, Stuttgart, 1992. [8] M. Griebel. Grid- and point-oriented multilevel algorithms. In W. Hackbusch und G. Wittum, Editoren, Incomplete De- compositions (ILU) - Algorithms, Theory, and Applications, Notes on Numerical Fluid Mechanics, Volume 41, S. 32-46. Vieweg Verlag, Braunschweig, 1993. also as SFB Bericht, 342/14/92 A, Institut f"ur Informatik, TU M"unchen, 1992. [9] M. Griebel, W. Huber, U. R"ude und T. St"ortkuhl. The combi- nation technique for parallel sparse-grid-preconditioning and -solution of PDEs on multiprocessor machines and worksta- tion networks. In L. Bouge, M. Cosnard, Y. Robert und D. Trystram, Editoren, Lecture Notes in Computer Science 634, Parallel Processing: CONPAR92-VAPP V, S. 217-228. Springer Verlag, 1992. [10] M. Griebel, W. Huber und C. Zenger. A fast Poisson solver for turbulence simulation on parallel computers using sparse grids. In E.H. Hirschel, Editor, Flow Simulation with High- Performance Computers I, Notes on Numerical Fluid Me- chanics, Volume 38, S. 101-113. Vieweg Verlag, Braun- schweig, 1993. [11] M. Griebel. Sparse grid multilevel methods, their paralleliza- tion, and their applications to CFD. In J. H"auser, Editor, Parallel Computational Fluid Dynamics 92, S. 161-174. New Brunswick, USA, Elsevier, 1993. [12] M. Griebel. A domain decomposition method using sparse grids. In A. Quarteroni, Editor, Contemporary Mathematics, Vol. 157, DDM6, S. 255-261. American Mathematical Society, 1994. [13] M. Griebel, W. Huber, T. St"ortkuhl und C. Zenger. On the par- allel solution of 3D PDEs on a network of workstations and on vector computers. In A. Bode und M. Dal Cin, Editoren, Lecture Notes in Computer Science 732, Parallel Computer Architectures: Theory, Hardware, Software, Applications, S. 276-291. Springer Verlag, 1993. [14] M. Griebel und S. Zimmer. Adaptive point block methods. In W. Hackbusch und G. Wittum, Editoren, Adaptive Methods: Algorithms, Theory and Applications, Notes on Numerical Fluid Mechanics. Vieweg Verlag, Braunschweig, S. 142-157, 1993. [15] M. Griebel. Parallel point-oriented multilevel methods. In P. Hemker und P. Wesseling, Editoren, Multigrid Methods IV, International Series of Numerical Mathematics, EMG93. Birkh"auser Verlag, S. 215-232, 1994. [16] M. Griebel. Domain-oriented multilevel methods. In D. Keyes und J. Xu, Editoren, Contemporary Mathematics, Vol. 180, DDM7, S. 223-229. American Mathematical Society, 1994. [17] H. Bungartz, M. Griebel, D. R"oschke und C. Zenger. Two proofs of convergence for the combination technique for the efficient solution of sparse grid problems. In D. Keyes und J. Xu, Editoren, Contemporary Mathematics, Vol. 180, DDM7, S. 15-20. American Mathematical Society, 1994. [18] M. Griebel und W. Huber. Turbulence simulation on sparse grids using the combination method. In N. Satofuka, J. Periaux, A. Ecer Editoren, Parallel Computational Fluid Dynamics, New Algorithms and Applications, S. 75-84. North-Holland, Elsevier, 1995. [19] N. R"osch, S. Kr"uger, M. Griebel und C. Zenger. Quanten- chemie auf Parallelrechnern, Zur Perspektive der Dichte- funktionaltheorie. Proceedings der BMWF-Tagung HPSC95, Aachen, 1996. [20] M. Griebel und S. Knapek. Matrix-dependent multigrid- homogenization for diffusion problems. Proceedings of the GAMM-Seminar "Modelling and Computation in Environ- mental Sciences". Notes on Numerical Fluid Mechanics, to appear. Vieweg-Verlag, Braunschweig, 1996. [21] M. Griebel, W. Huber und C. Zenger. Numerical Turbulence Simulation on a parallel computer using the combination method. DFG-SPP "Flow Simulations with High Perfor- mace Computers". Notes on Numerical Fluid Mechanics, to appear. Vieweg-Verlag, Braunschweig, 1996. Technische Berichte: (Soweit nicht als Zeitschrifte- nartikel oder Konferenzbeitrag erschienen) REFERENCES [1] M. Griebel. On the combination of the ideas of multilevel solvers using hierarchical bases and the substructuring technique for the finite element method. Bericht I8709, Institut f"ur Infor- matik, TU M"unchen, 1987. [2] M. Griebel. Zur L"osung von Finite-Differenzen- und Finite- Element-Gleichungen mittels der Hierarchischen Transformations-Mehrgitter-Methode. SFB Bericht 342/4/90 A, Institut f"ur Informatik, TU M"unchen, 1990. [3] M. Griebel, C. Zenger und S. Zimmer. Improved multilevel al- gorithms for full and sparse grid problems. SFB Bericht 342/15/92 A, Institut f"ur Informatik, TU M"unchen, 1992. [4] U. G"artel, M. Griebel, W. Huber, H. Schwichtenberg, T. St"ortkuhl, U. Trottenberg, G. Winter, C. Zenger. The parallel ASMG algorithm for 3D Poisson-like equations on multi-workstations. Arbeitspapiere der GMD 767, Gesellschaft f"ur Mathematik und Datenverarbeitung, Sankt Augustin, 1993. [5] M. Griebel und P. Oswald. Remarks on the theory of addi- tive and multiplicative Schwarz algorithms. SFB Bericht 342/6/93A, Institut f"ur Informatik, TU M"unchen, 1993. [6] M. Griebel und T. Neunhoeffer. A domain-oriented multilevel algorithm - implementation and parallelization. SFB Bericht 342/18/94A, Institut f"ur Informatik, TU M"unchen, 1994. [7] M. Griebel und W. Huber. Turbulence simulation on sparse grids using the combination method. SFB Bericht 342/19/94A, Institut f"ur Informatik, TU M"unchen, 1994. [8] T. Grauschopf und M. Griebel. Parallelization of a multigrid algorithm on the KSR1. in LRZ Bericht 9401, Overview of Research on the Parallel Computer SNI-KSR at the Leibnitz- Rechenzentrum M"unchen, M. Brehm, C. Schaller, (eds). Leibniz-Rechenzentrum der Bayerischen Akademie der Wis- senschaften, M"unchen, S. 63-69, 1994. [9] M. Griebel und W. Huber. Parallel turbulence simualtion on the IBM SP2 using a sparse grid method. Contribution Sup'Prize 1995, Sup'Eur User Group Organization, 1995. [10] M. Griebel, R. Kreissl, M. Rykaschewski und C. Zenger. Re- sults of Benchmark Computations for the DFG-SPP "Flow Simulations with High Performace Computers", 1995. Editor's Note: The bibliography will be revised with these included in ------------- early May. ------------------------------ End of MGNet Digest **************************