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: ftp.ccs.uky.edu (128.163.209.106) World Wide Web: http://www.mgnet.org or http://www.cerfacs.fr/~douglas/mgnet.html or http://phase.etl.go.jp/mgnet or http://www.ccs.uky.edu/mgnet Today's editor: Craig Douglas (douglas-craig@cs.yale.edu) Volume 8, Number 1 (approximately January 31, 1998) Today's topics: Important Dates Parallel 2D/3D Multigrid Solver Learning Tool (SOR, Multigrid) GRUMMP Preprint available (Saad, Sosonkina, and Zhang) Two Fellowships at Sandia National Laboratories 14th GAMM-Seminar Kiel on Concepts of Numerical Software [DD11] - EmailAddress 4th International Conference on Numerical Methods and Applications Some of the new entries in the bibliography ------------------------------------------------------- Date: Sat, 31 Jan 1998 12:14:52 +0500 From: Craig C. DouglasSubject: Important Dates This is a busy month. All of these conferences are listed in the web page on conferences on MGNet. February 15 Abstracts due for the Workshop on Practical Aspects of Algebraic Multigrid Methods (March 25 - 27 in Stuttgart, Germany). February 15 Early registration due for the GAMM - Workshop on Multigrid Methods (October 5 - 8 in Bonn, Germany). February 25 Guaranteed availability of rooms for the 5th Copper Mountain Conference on Iterative Methods (March 30 - April 3) February 28 Submission of abstracts for the 11th Domain Decompostion Symposium (July 20 - 24 in Greenwich, England) Februrary 28 Submission of abstracts for C3AD (August 17 - 22 in Petropolis, Brazil) ------------------------------------------------------- Date: Tue, 06 Jan 1998 11:58:08 -0500 From: bernard bunner Subject: Parallel 2D/3D Multigrid Solver Hello Mr. Douglas, A brief introduction of myself. I am a Ph.D. student with Prof. Tryggvason at the U. of Michigan and I'm working on DNS of multiphase flows using a front-tracking method. Our code requires the solution of elliptic problems with variables coefficients on a rectangular, staggered, constant step grid (we use a finite-difference formulation similar to the MAC method). With our 2D and 3D serial codes, we typically use Mudpack.But we wanted to parallellize the codes and run large 3D simulations. Since I didn't find the equivalent of Mudpack in parallel, I developed my own programs and would like to know if you'd be interested in putting them on your site. The main features are: - MPI - staggered grid (unlike Mudpack), rectangular domain, constant dx, dy, (dz) - V or W cycling - full weighting for the restriction and bilinear interpolation for the correction - either vertex-centered or cell-centered operations - periodic, Neumann, or Dirichlet BCs I don't make any claim other than the codes work (I only checked on IBM-SP2 and HP-EXEMPLAR). They are fairly short and documentation is OK. Bernard Bunner Editor's Note: in mgnet/Codes/bunner. ------------- ------------------------------------------------------- Date: Wed, 07 Jan 1998 16:48:08 -0200 From: Armando de Oliveira Fortuna Subject: Learning Tool (SOR, Multigrid) I wrote a solver for the Laplace/Poisson equations which allows the user to select between multigrid, Line-SOR or Point-SOR. It is a nice tool to introduce multigrid to new students - they can see for themselves how multigrid compares to SOR. The program is fully configurable at run-time. The user can choose whether he or she wants to use multigrid or SOR, and then select: * if SOR: * the relaxation parameter * whether to use the Line or Point version if Multigrid: * the type of cycle (F,V,W) * whether to start on the fine grid or on the coarsest grid As for output, the program prints the iteration or mg cycle number and the residue. It also saves that information to a file, so it can be later plotted. I would like to make this program available through MGNet. Thank you very much, Armando de Oliveira Fortuna, Ph.D Av. Dr. Carlos Botelho, 1465 Inst. de Ciencias Matematicas de Sao Carlos CEP 13560-970, CP 668 Depto. de Ciencias de Comp. e Estatistica Sao Carlos, SP, Brasil Universidade de Sao Paulo (USP) FAX: +55 (0)16 274-9150 www.lcad.icmsc.sc.usp.br ======== ====== email:fortuna@lcad.icmsc.sc.usp.br Editor's Note: in mgnet/Codes/fortuna. ------------- ------------------------------------------------------- Date: Wed, 28 Jan 1998 12:48:15 -0800 (PST) From: Carl Ollivier-Gooch Subject: New 2D/3D Unstructured Mesh Generator GRUMMP Generation and Refinement of Unstructured Mixed-Element Meshes in Parallel The goal of the GRUMMP project is to develop automatic mesh generation software for unstructured meshes with mixed element types. The software will be able to produce high-quality meshes which meet user-defined mesh density requirements, using elements appropriate for the geometry and physics of a particular problem. We envision a system in which common types of physical problems have pre-defined mesh sizing and element aspect ratio functions, allowing easy generation of meshes for these applications areas. For flexibility and generality, the user will also be able to prescribe these functions (for totally different applications) or modify the pre-defined behaviors (to provide a quality mesh in the wake of an airplane wing, for example). GRUMMP Features The initial version of the GRUMMP libraries has been released, including executables for two- and three-dimensional mesh generation and improvement and for three-dimensional scattered data interpolation. - Two-dimensional and three-dimensional simplicial mesh generation - Automatic creation and use of geometric length scale based on input data - Mesh quality assessment using numerous geometric quality measures - Improvement of existing two- and three-dimensional meshes - Complete set of mesh manipulation primitives: + Local reconnection --- face swapping and edge removal (latter in 3D only) + Optimization-based vertex smoothing --- guaranteed better than Laplacian + Point insertion and/or deletion to match local length scale - Mesh generation and improvement use the same primitives and length scale calculation, providing uniform results from both processes - Flexible I/O format (available in 2D; soon to be available in 3D) The software is available in source form via ftp at ftp://tetra.mech.ubc.ca/pub/GRUMMP/GRUMMP-0.1.0.tar.gz For more information, including an online copy of the User Guide, visit the GRUMMP home page at http://tetra.mech.ubc.ca/GRUMMP/index.html or send email to the developer at cfog@mech.ubc.ca. Carl Ollivier-Gooch cfog@mech.ubc.ca Department of Mechanical Engineering Voice: +1-604-822-1854 University of British Columbia Fax: +1-604-822-2403 2324 Main Mall URL: http://www.mech.ubc.ca/~cfog Vancouver, BC V6T 1Z4 Canada Editor's Note: A hyperlink to this has been added to the Codes' web page. ------------- ------------------------------------------------------- Date: Mon, 19 Jan 1998 17:02:51 -0600 (CST) From: JUN ZHANG Subject: Preprint available (Saad, Sosonkina, and Zhang) We are happy to announce the following preprint. Domain Decomposition and Multi-Level Type Techniques for General Sparse Linear Systems Yousef Saad Department of Computer Science and Engineering University of Minnesota 200 Union Street S.E., Minneapolis, MN 55455 E-mail:saad@cs.umn.edu, URL:http://www.cs.umn.edu/~saad Maria Sosonkina Department of Computer Science University of Minnesota, Duluth 320 Heller Hall, 10 University Drive, Duluth, Minnesota 55812-2496 masha@d.umn.edu Jun Zhang Department of Computer Science and Engineering University of Minnesota 200 Union Street S.E., Minneapolis, MN 55455 E-mail:jzhang@cs.umn.edu, URL:http://www.cs.umn.edu/~jzhang ABSTRACT Domain-decomposition and multi-level techniques are often formulated for those linear systems that arise from the solution of elliptic-type Partial Differential Equations. In this paper, generalizations of these techniques for irregularly structured sparse linear systems are considered. An interesting common approach used to derive successful preconditioners is to resort to Schur complements. In particular, we discuss a multi-level domain decomposition-type algorithm for iterative solution of large sparse linear systems based on independent subsets of nodes. We also discuss a Schur complement technique that utilizes incomplete LU factorizations of local matrices. Postscript file of the above preprint may be downloaded from the following web pages: http://www.cs.umn.edu/~saad or http://www.cs.umn.edu/~jzhang For those who do not have access to web facility, send an e-mail to jzhang@cs.umn.edu for a postscript file or a hard copy. ------------------------------------------------------- Date: Mon, 12 Jan 98 12:17:52 MST From: tuminaro@siesta.cs.sandia.gov (Ray S. Tuminaro) Subject: Two Fellowships at Sandia National Laboratories I would like the following job postings to appear on the next MGNet newsletter. Two Fellowships at Sandia National Laboratories The Computational Sciences and Mathematics Center at Sandia National Laboratories (Albuquerque/NM and Livermore/CA) is seeking qualified candidates for two post-doctoral fellowship positions. These positions offers an exceptional opportunity for innovative research in scientific computing. The successful candidates will hold a Ph.D. in a scientific computing discipline and have significant experience in iterative linear equation solvers, high performance computing, and numerical algorithms. The Center maintains strong research programs in a variety of areas, including numerical mathematics, discrete algorithms, computational physics/engineering, and advanced systems software and tools. A unique computing environment is supported which includes a 4500-node Intel TFlops computer, a 1800-processor Intel Paragon, a 192-processor SGI Origin system, an 84-processor DEC-8400 system, and experimental heterogeneous computer platforms. The position includes a competitive salary, moving expenses, and a professional travel allowance. Interested persons should submit a complete resume with names and addresses of three references to: Ray S. Tuminaro Sandia National Laboratories Department 9222 / MS 9214 P.O. Box 969 Livermore, CA 94551-0969 tuminaro@ca.sandia.gov (510) 294-2564 Applications will be accepted through March or until the position is awarded. Sandia National Labs is a U.S. Department of Energy multiprogram laboratory, operated by Sandia Corporation, a wholly owned subsidiary Lockheed Martin Corporation, with locations in Albuquerque, NM and Livermore, CA. Equal Opportunity Employer. Drug-free workplace. U.S. Citizenship is normally required. ------------------------------------------------------- Date: Sat, 31 Jan 1998 12:14:52 +0500 From: Craig C. Douglas Subject: 14th GAMM-Seminar Kiel on Concepts of Numerical Software The latest in the series of GAMM seminars at Kiel was held January 23rd to 25th with the topic being Concepts of Numerical Software. Below is the list of talks. P. Bastian (Stuttgart): Parallel unstructured grid computations K. Johannsen (Stuttgart): np - the Modular Numerical Subsystem of UG R. Roitzsch, B. Erdmann, J. Lang (Berlin): The benefits of modularization: From Kaskade to Kardos J. Schoeberl, G. Haase (Linz): Some Concepts of the Object Oriented Code FEPP Ch. Weiss, H. Hellwagner, L. Stals, U. Ruede (Augsburg): Data Locality Optimizations to Improve the Efficiency of Multigrid Methods Ch. Becker, S. Kilian, H. Oswald, St. Turek (Heidelberg): Some software and algorithmic concepts of FEAST J. Fuhrmann, H. Langmach, Th. Koprucki, M. Petzoldt, I. Schmelzer (Berlin): pdelib: An Open Modular Toolbox for the Numerical Solution of Partial Differential Equations K. Gerdes (Zurich): HP90: A general and flexible Fortran 90 hp-FE code K. Urban, T. Barsch (Aachen): Software tools for using wavelets on the interval for the numerical solution of operator equations D. di Serafino, A. Murli (Napoli, Italy): The PINEAPL Library: a Parallel Numerical Library for Industrial Applications M. Griebel, T. Schiekofer, G. Zumbusch (Bonn): Software concepts of a sparse grid finite difference code Ch. Lage (Zurich): Concept-Oriented Design of Numerical Software O. Steinbach (Stuttgart): Implementation and Parallelization of Boundary Element Methods M. Konik (Chemnitz): Object-oriented implementation of multiscale methods for boundary integral equations C. C.Douglas (Lexington, USA): Cache Based Multigrid on Structured/Unstructured Grids in 2D/3D W. Hackbusch (Kiel): Hierarchical structures and their representations K. G. Siebert, A. Schmidt (Freiburg): ALBERT: An adaptive hierarchical finite element toolbox M. Weidmann (Muenchen): On the Object-Oriented Redesign of a Real-World CFD Program H.-J. Bungartz, Ch. Zenger (Muenchen): What we can learn from computer science for the design of numerical programs A. Langer (Dortmund): LiMA - A generic class library for mesh representation in 2D/3D M. Metscher (Bonn): Efficient hierarchical Searching on arbitrary nested Grids, Application to Particle Tracing G. Bader, G. Berti (Cottbus): Reusable software components for sequential and distributed solution of PDE problems K. Birken (Stuttgart): Towards automatic parallelization of numerical software based on formal specification concepts L. Stals (Bath, UK): Flexible Data Structure For the Adaptive Refinement on Unstructured Grids in Parallel Ch. Wieners (Stuttgart): Parallel linear algebra and the application to multigrid methods ------------------------------------------------------- From: Date: Wed, 4 Feb 1998 08:40:45 GMT Subject: [DD11] - EmailAddress As some of you pointed out that there could be a problem with the email address D.Decomposition@gre.ac.uk I suggest you to use dd11@gre.ac.uk which certainly works with no problems while I am asking the system people to look at D.Decomposition@gre.ac.uk I hope this will help during the crucial time when abstracts are on their way. DD11 ------------------------------------------------------- Date: Thu, 22 Jan 1998 11:41:14 +0000 From: Olivier Goyon Subject: 4th International Conference on Numerical Methods and Applications Dear collegue I am writing to you in connection with the mini symposium entitled "Multilevel methods for incompressible viscous flows" which will be held in sofia from 19 to 23 August, 1998 during the 4th International Conference on Numerical Methods and Applications. As you can see the aim of this symposium is to bring together groups, which are actively involved in the development of multilevel methods for incompressible flows. We would be very pleased if you express interest in attending this symposium. Sincerely yours, Dr Dimitris DRIKAKIS and Dr Olivier GOYON 4th International Conference on Numerical Methods and Applications: NM\&A-O($h^4$)'98 Bulgarian Academy of Sciences in Cooperation with SIAM Call for Papers for the Mini Symposium "Multilevel methods for incompressible viscous flows" The above mini symposium is organized during the 4th International Conference on Numerical Methods and Applications: NM\&A-O($h^4$)'98, which will be held in Sofia from 19 to 23 August, 1998. The goal of this Symposium is to provide means for presenting both final results of research and especially early informal communication of research in progress, as well as to encourage discussion and interchange of ideas between diverse disciplines interested in the topic of "Multilevel Methods for Incompressible Viscous Flows". The Symposium intentionally covers a wide range of algorithms and methods including classical multigrid methods, nonlinear Galerkin methods, adaptive mesh refinement, local solution techniques and cyclic-like reduction methods. Authors should send three copies of an extended abstract to the Mini Symposium Organizers. Abstracts can also be sent as ASCII files via e-mail. Contributions will be reviewed for relevancy and technical content on the basis of the abstract. Instructions for the preparation of the final manuscript will be sent around May 1, 1998. Further information about the conference proceedings can be provided by Dr Oleg Iliev (Conference Organizer, see address below). Deadline Schedule: ================== Abstract Due: 15th of March, 1998. Abstract Acceptance: 30th of April, 1998. Mini Symposium Organizers: ========================== Dr. D. Drikakis and Dr O. Goyon UMIST Department of Mechanical Engineering PO Box 88, Manchetser M60 1QD United Kingdom Fax: (44) 161 200 3723 Email: mcjtsog@sgo.me.umist.ac.uk Further information about the conference is available on the Web Page: http://banmatpc.math.acad.bg/~nma98/ or http://orca.st.usm.edu/marcin/mp/cfp/sofia.html. For any further enquiry about the conference you can also contact the conference organizer: NMA'98, c/o Dr. Oleg Iliev Institute of Mathematics and Informatics Bulgarian Academy of Sciences Acad. G. Bonchev Str., Bl.8, 1113 Sofia, BULGARIA Fax-No. (++359 2) 971 36 49 ------------------------------------------------------- Date: Sat, 31 Jan 1998 14:42:12 -0400 From: Craig Douglas Subject: Some of the new entries in the bibliography Here are some recent new entries. As usual, please send additions and corrections. Many corrections and small changes occurred to the bibliography in late January. This was due to Professor Wolfgang Hackbusch allowing me to spend time going through his extensive library. Many more entries will go into the bibliography thanks to his helpfulness. [1] O. Axelsson and B. Polman, A robust preconditioner based on algebraic substructurig and two-level grids, in Robust Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braunschweig, 1989, Vieweg, pp. 1-26. [2] A. Barker and B. Gervang, Relaxed ILU preconditioning for the CG solution of a singular boundary value problem, in In- complete Decompositions (ILU) - Algorithms, Theory, and Applications, W. Hackbusch and G. Wittum, eds., vol. 41 of Notes on Numerical Fluid Mechanics, Braunschweig, 1993, Vieweg, pp. 1-11. [3] P. Bastian, J. H. Ferziger, G. Horton, and J. Volk- ert, Adaptive multigrid solution of the convection-diffusion equation on the DIRMU processor, in Robust Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braunschweig, 1989, Vieweg, pp. 27-36. [4] R. Beauwens, Incomplete factorizations with S/P and modi- fied S/P consistently ordered M-factors, in Incomplete De- compositions (ILU) - Algorithms, Theory, and Applications, W. Hackbusch and G. Wittum, eds., vol. 41 of Notes on Numerical Fluid Mechanics, Braunschweig, 1993, Vieweg, pp. 22-31. [5] C. Becker, J. H. Ferziger, M. Peric, and G. Scheuerer, Finite volume multigrid solution of the two-dimensional in- compressible Navier-Stokes equations, in Robust Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braunschweig, 1989, Vieweg, pp. 37-47. [6] J. W. Boerstoel, A. E. P. Veldman, J. Van Der Vooren, and A. J. Van Der Wees, Trends in CFD for aeronautical 3-D steady applications: the Dutch situation, in Research in Numerical Fluid Mechanics, P. Wesseling, ed., vol. 17 of Notes on Numerical Fluid Mechanics, Braun- schweig, 1987, Vieweg, pp. 1-18. [7] F. Brezzi and JPit"aranta, On the stabilization of finite el- ement approximations of the Stokes equations, in Efficient Solution of Elliptic Systems, W. Hackbusch, ed., vol. 10 of Notes on Numerical Fluid Mechanics, Braunschweig, 1984, Vieweg, pp. 11-19. [8] P. Conradi and D. Schr"oder, Concepts for a dimension independent application of multigrid algorithms to semicon- ductor device simulation, in Robust Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braunschweig, 1989, Vieweg, pp. 48-57. [9] C. Cuvelier, On the computation of free boundaries, in Re- search in Numerical Fluid Mechanics, P. Wesseling, ed., vol. 17 of Notes on Numerical Fluid Mechanics, Braun- schweig, 1987, Vieweg, pp. 18-29. [10] W. Dahmen and L. Elsner, Algebraic multigrid methods and the Schur complement, in Robust Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Me- chanics, Braunschweig, 1989, Vieweg, pp. 58-68. [11] E. Dick, A multigrid method for the steady Euler equations, based on flux-difference splitting with respect to primitive variables, in Robust Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braun- schweig, 1989, Vieweg, pp. 69-85. [12] J. H. D"orfer, Treatment of singular perturbation problems with multigrid methods, in Robust Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braunschweig, 1989, Vieweg, pp. 86-95. [13] C. C. Douglas, Multigrid methods in science and engineering, IEEE Comput. Sci. Eng., 3 (1997), pp. 55-68. [14] C. C. Douglas, A. Ern, and M. D. Smooke, Multigrid solution of flame sheet problems on serial and parallel com- puters, Paral. Alg. Appl., 10 (1997), pp. 225-236. [15] D.Van Essen, G. Kupers, and H. Mes, Thermal hydraulic modelling studies on heat exchanging components, in Re- search in Numerical Fluid Mechanics, P. Wesseling, ed., vol. 17 of Notes on Numerical Fluid Mechanics, Braun- schweig, 1987, Vieweg, pp. 30-44. [16] B. Gustafsson and G. Lindskog, Parallelizing incomplete factoarization preconditioning methods, in Incomplete De- compositions (ILU) - Algorithms, Theory, and Applications, W. Hackbusch and G. Wittum, eds., vol. 41 of Notes on Numerical Fluid Mechanics, Braunschweig, 1993, Vieweg, pp. 47-56. [17] W. Hackbusch, The frequency decomposition multi-grid al- gorithm, in Robust Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braun- schweig, 1989, Vieweg, pp. 96-104. [18] W. Hackbusch and A. Reusken, On global multigrid conver- gence for nonlinear problems, in Robust Multi-Grid Meth- ods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braunschweig, 1989, Vieweg, pp. 105-113. [19] D. H"anel, W. Schr"oder, and G. Seider, Multigrid meth- ods for the solution of the compressible Navier-Stokes equa- tions, in Robust Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braun- schweig, 1989, Vieweg, pp. 114-127. [20] W. Heinrichs, Effective preconditioning for spectral multigrid methods, in Robust Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braun- schweig, 1989, Vieweg, pp. 139-144. [21] R. Hiptmair, Multilevel Preconditioning for Mixed Problems in Three Dimensions, PhD thesis, Technischen Universit"at Augsburg, Augsburg, Germany, 1996. [22] M. Hoekstra, Computation of steady viscous flow near a ship's stern, in Research in Numerical Fluid Mechanics, P. Wessel- ing, ed., vol. 17 of Notes on Numerical Fluid Mechanics, Braunschweig, 1987, Vieweg, pp. 45-57. [23] C. J. Hoogendoorn and Th. H.Van Der Meer, Convection-diffusion phenomena and a Navier-Stokes pro- cessor, in Research in Numerical Fluid Mechanics, P. Wes- seling, ed., vol. 17 of Notes on Numerical Fluid Mechanics, Braunschweig, 1987, Vieweg, pp. 58-72. [24] G. Horton, R. Knirsch, and G. Wittum, Modification of the ILU-methd for enhanced parallel efficiency, in Incom- plete Decompositions (ILU) - Algorithms, Theory, and Ap- plications, W. Hackbusch and G. Wittum, eds., vol. 41 of Notes on Numerical Fluid Mechanics, Braunschweig, 1993, Vieweg, pp. 57-66. [25] M. A. Hulsen and J.Van Der Zanden, Problems, analy- ses and solutions of the equations for viscoelastic flow, in Research in Numerical Fluid Mechanics, P. Wesseling, ed., vol. 17 of Notes on Numerical Fluid Mechanics, Braun- schweig, 1987, Vieweg, pp. 73-86. [26] M. Hunek, K. Kozel, and M. Vavrincova, Numerical so- lution of transonic potential flow in 2d compressor cascades using multi-grid techniques, in Robust Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Me- chanics, Braunschweig, 1989, Vieweg, pp. 145-154. [27] B. Koren, Multigrid and defect correction for the steady Navier-Stokes equations, in Robust Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braunschweig, 1989, Vieweg, pp. 165-177. [28] Y. P. Marx and J. Piquet, Towards multigrid accelera- tion of 2d compressible Navier-Stokes finite volume implicit schemes, in Robust Multi-Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braun- schweig, 1989, Vieweg, pp. 178-187. [29] P. Neittaanm"aki and M. Kr'izek, Conforming FE-method for obtaining the gradient of a solution to the Ppoisson equa- tion, in Efficient Solution of Elliptic Systems, W. Hackbusch, ed., vol. 10 of Notes on Numerical Fluid Mechanics, Braun- schweig, 1984, Vieweg, pp. 74-86. [30] A. J. Renkema, R. Verstappen, R. W.De Vries, and P. J. Zandbergen, Some experiences with spectral multi- grid, in Research in Numerical Fluid Mechanics, P. Wessel- ing, ed., vol. 17 of Notes on Numerical Fluid Mechanics, Braunschweig, 1987, Vieweg, pp. 101-114. [31] H. Schippers, Multiple Grid Methods for Equations of the Sec- ond Kind with Applications in Fluid Mechanics, PhD thesis, Mathematisch Centrum, Amsterdam, 1983. [32] V. V. Shaidurov, Multigrid Methods for Finite Elements, vol. 318 of Mathematics and Its Applications, Kluwer Aca- demic Publishers, Dordrecht, Boston, London, 1995. [33] G. K. Verboom and A. Segal, Weakly-reflective boundary conditions for shallow water equations, in Research in Nu- merical Fluid Mechanics, P. Wesseling, ed., vol. 17 of Notes on Numerical Fluid Mechanics, Braunschweig, 1987, Vieweg, pp. 115-129. [34] R. Verf"urth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley Teubner, New York, Stuttgart, 1996. ISBN 0-471-96795-5. [35] P. Wesseling, Research in Numerical Fluid Mechanics, vol. 17 of Notes on Numerical Fluid Mechanics, Vieweg, Braun- schweig, 1987. [36] G. Wittum, Distributive Iterationen f"ur Indefinite Systeme, PhD thesis, Christian-Albrechts-Universt"at, Kiel, Ger- many, 1986. [37] ______, On the robustness of ILU-smoothing, in Robust Multi- Grid Methods, W. Hackbusch, ed., vol. 23 of Notes on Numerical Fluid Mechanics, Braunschweig, 1989, Vieweg, pp. 217-239. [38] B. Wohlmuth, Adaptive Multilevel-Finite-Elemente Meth- ode zur L"osung elliptischer Randwertprobleme, PhD thesis, Technischen Universit"at M"unchen, Mathematisches Institut, 1995. [39] H. Yserentant, Ober die Aufspaltung von Finite-Element- R"aumen in Teilr"aume Verschiedener Verfeinerungsstufen, PhD thesis, Rheinisch-Westf"alischen Technischen Hochschule Aachen, Aachen, Germany, 1984. ------------------------------ End of MGNet Digest **************************