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 Today's editor: Craig Douglas (douglas-craig@cs.yale.edu) Volume 7, Number 2 (approximately February 28, 1997) Today's topics: Multigrid Paper (Arnold, Falk, and Winther) Multigrid Paper (Malhotra et al) Deadline Change: DNS/LES Conference 8th Copper Mountain Conference on MG Methods, April 6-11 Copper Mountain Schedule MGNet Database Entries (Dureisseix et al) MGNet Database Entries (J. Zhang) Some of the new entries in the bibliography ------------------------------------------------------- Date: Fri, 28 Feb 1997 15:03:25 -0500 From dna@math.psu.edu Fri Feb 28 15:03 EST 1997 Subject: Multigrid Paper Title: Multigrid preconditioning in H(div) on non-convex polygons Authors: Douglas N. Arnold, Richard S. Falk, and Ragnar Winther Source: Computational and Applied Mathematics Status: Submitted Abstract: In an earlier paper we constructed and analyzed a multigrid preconditioner for the system of linear algebraic equations arising from the finite element discretization of boundary value problems associated to the differential operator I - grad div. In this paper we analyze the procedure without assuming that the underlying domain is convex and show that, also in this case, the preconditioner is spectrally equivalent to the inverse of the discrete operator. Keywords: preconditioner, finite element, multigrid, nonconvex domain Subj. class.: 65N55, 65N30 FTP site: ftp.math.psu.edu File name: pub/dna/papers/hdivn.dvi File format: TeX DVI file File name: pub/dna/papers/hdivn.ps File format: PostScript file URL-Pointer: http://www.math.psu.edu/dna/publications.html ------------------------------------------------------- Date: Fri, 28 Feb 1997 23:59:59 -0500 From: Sachit MalhotraSubject: Multigrid Paper Parallel Multigrid with ADI-like Smoothers in Two Dimensions Craig C. Douglas (University of Kentucky) Sachit Malhotra (Scientific Computing Associates) Martin H. Schultz (Yale University) Abstract Alternating direction iterative (ADI) methods do not usually work well on parallel computers due to having to do parallel rather than serial tridiagonal solves in all but one dimension. An ADI-like iteration is developed and analyzed which does not require parallel tridiagonal solves in any direction, has at least as good of a convergence rate as ADI, and has almost no communication when imbedded as a smoother inside of a multigrid solver. Numerical experiments on a network of workstations and a parallel computer are included. Editor's Note: in mgnet/papers/Malhotra-Douglas-Schultz/adimg.ps.gz ------------- ------------------------------------------------------- Date: Sun, 2 Mar 1997 22:46:15 GMT From: Chaoqun Liu Subject: Deadline Change: DNS/LES Conference FIRST AFOSR INTERNATIONAL CONFERENCE ON DIRECT NUMERICAL SIMULATION AND LARGE EDDY SIMULATION (DNS/LES) August 4-8, 1997 I have received responses from more than 90 people from 16 countries who are interested in attending the FAICDL conference . Around 60 abstracts have been received so far. Due to a number of requests by phone and email, we decide to change the deadline for submission of abstract to March 15th to give potential authors more time to prepare their abstracts. All other time schedules will be kept unchanged. ------------------------------------------------------- Date: Sat, 1 Mar 1997 12:34:24 -0700 (MST) From: Steve McCormick Subject: 8th Copper Mountain Conference on MG Methods, April 6-11 The schedule for the Eighth Copper Mountain Conference on Multigrid Methods (April 6-11) is now accessible from the conference home page: http://amath-www.colorado.edu:80/appm/faculty/copper/ Anyone interested in attending should reserve their room as soon as possible. This has been one of Copper's best ski seasons, so rooms are becoming more difficult to find. Anyone interested in sharing rooms or condos might want to use the bulletin board accessible from the conference home page. Steve McCormick: Appl. Math, C.B. 526, U. of CO, Boulder, CO 80309-0526 (303)492-0662 stevem@newton.colorado.edu ftp://amath.colorado.edu/pub -4066 fax http://amath-www.colorado.edu/appm/faculty/stevem/ ------------------------------------------------------- Date: Tue, 18 Feb 1997 13:32:48 -0700 (MST) From: Steve McCormick Subject: Copper Mountain Schedule Preliminary Program This program is preliminary and subject to modifications. Talks will generally not be moved from the given day, but the times may be adjusted within that day. Participants and speakers should therefore monitor this page and the bulletin board at the conference. Speakers should plan their talks to be at most 20 minutes. Program Chairs will adhere strictly to this schedule. We will have a slide projector and an overhead projector for speaker use. We will also provide an LCD panel (ViewFrame Spectra), which plugs into a standard video outlet on a Mac or PC to project its image onto the screen. This equipment will also be available for the Circus and Workshop sessions. Wednesday night's cash bar and banquet will be held in the Pavillon. All other activities will take place in the Village Square conference facilities. Sunday, April 6 7:00-9:00 PM Reception Monday, April 7 SESSION I Chair: Seymour Parter 8:00am Hans-Joachim Bungartz A Multigrid Algorithm for Higher Order Finite Elements on Sparse Grids 8:25am Zhangxin Chen The Analysis of Intergrid Transfer Operators and Nonconforming Multigrid Methods 8:50am Nicholas Coult Multiresolution Reduction of Elliptic PDE's and Eigenvalue Problems 9:15am Joel Dendy Some Applications of Black Box Multigrid to Systems 9:40am COFFEE BREAK 10:10am Jonathan Dym Multilevel Inversion of the Radon Transform 10:35am David Gines A Wavelet-based Direct Multilevel Solver 11:00am Ralf Hiptmair Multigrid Method for H(div) in Three Dimensions 11:25am D.A. Knoll Multigrid Preconditioning of Newton-Krylov Methods 11:50am Steven M. McKay Solution of a Convolution Equation with Unbounded Domain via Multigrid SESSION II Chair: Kirk Jordan 4:40pm Tom Manteuffel First-Order System Least Squares (FOSLS) for PDEs: Part I 5:05pm Steve McCormick First-Order System Least Squares (FOSLS) for PDEs: Part II 5:30pm SNACK BREAK 6:00pm Markus Berndt Adaptive Mesh Refinement for First-Order System Least Squares (FOSLS) 6:25pm Pavel Bochev Negative Norm Least-squares for the Velocity-flux Navier-Stokes Equations 6:50pm Sang Dong Kim A FOSLS Approach for Three-Dimensional Pure Traction Linear Elasticity 7:15pm Barry Lee First-Order System Least-Squares: Numerical Experiments Tuesday, April 8 SESSION III Chair: Irad Yavneh 8:00am Zhiqiang Cai An Analytic Basis for Multigrid for Stabilized Finite Element Methods for Stokes 8:25am Boris Diskin Multigrid Algorithm with Conditional Coarsening for the Non-aligned Sonic Flow 8:50am Scott R. Fulton A Comparison of Multilevel Adaptive Methods for Hurricane Track Prediction 9:15am Jim E. Jones A Note on Multi-block Relaxation Schemes for Multigrid Solvers 9:40am COFFEE BREAK 10:10am Dimitri J. Mavriplis Directional Coarsening and Smoothing for Anisotropic Navier-Stokes Problems 10:35am A. J. Meir A Two-Level Discretization Method for the MHD Equations 11:00am Erik Sterner A Multigrid Smoother for High Reynolds Number Flows 11:25am Xavier Vasseur FMG-FAS for the Navier-Stokes Equations on Cell-Centered Colocated Grids 11:50am Achi Brandt Multiscale Methods: 1996 Review CIRCUS Chair: Craig Douglas Everyone is welcome to talk and/or listen. The program will be determined at the start by polling the 7:00pm participants. Contact Craig for suggestions and information, or just show up and be ready to talk, interact, or just listen. Wednesday, April 9 SESSION IV Chair: Jim Jones 8:00am Serguei Maliassov Multilevel Fictitious Space Preconditioner for Nonconforming Unstructured Grids 8:25am Joseph Pasciak Inexact Uzawa Algorithms for Nonsymmetric Saddle Point Problems 8:50am Marcus Sarkis Overlapping Non-matching Grids Mortar Element Methods for Elliptic Problems 9:15am Gordon Wade A Comparison of Multilevel Methods for Total Variation Regularization 9:40am COFFEE BREAK 10:10am Wing-Lok Wan An Energy-Minimizing Interpolation for Multigrid Methods 10:35am Takumi Washio Krylov Subspace Acceleration Method for Nonlinear Multigrid Schemes 11:00am Kristian Witsch Multilevel Evaluation of Point Forces 11:25am Irad Yavneh Stranger Than Fiction: On Smoothing Symmetric Nine-point Operators 11:50am Xuejun Zhang A Multigrid Analysis for an Anisotropic Problem SESSION V Chair: Joe Pasciak 4:40pm Michael Griebel An Adaptive Multilevel Method for Sparse Grid Finite Difference Discretizations 5:05pm Ulrich Ruede On the Efficient Implementation of Adaptive Multigrid Methods 5:30pm Yair Shapira Multigrid for Locally Refined Meshes 5:55pm Leonid Y. Zaslavsky Adaptive Multigrid for Evaluating Long-range Forces in Biomolecular Simulations 6:20pm Huilong Zhang Object Oriented Programming and FAC in Numerical Reservoir Simulation 7:30pm CASH BAR AND BANQUET Thursday, April 10 SESSION VI Chair: Van Henson 8:00am M.L Bittencourt Non-nested Multigrid Methods in Finite Element Linear Structural Analysis 8:25am Susanne C. Brenner Multigrid Methods for Stress Intensity Factors and Singular Solutions 8:50am Wenlong Dai Iterative Schemes for Nonlinear Heat Transfer in Systems of Multi-materials 9:15am Andrew Knyazev Uniform Wellposedness of a Mixed Formulation of Symmetric Problems 9:40am COFFEE BREAK 10:10am R. Kulke Multigrid for the Laplace Equation in 2D-Electrostatic Structures 10:35am Paul A. Farrell Multigrid Methods for the Solution of Singularly Perturbed Differential Equations 11:00am Jules Kouatchou Asymptotic Stability of 9-Point Multigrid for Convection-Diffusion 11:25am Marc Kuether Exponentially Fitted Hierarchical Bases Multigrid for Convection Diffusion 11:50am Gerhard Starke Multilevel Methods for Exponential Spline Discretizations of Convection Diffusion 7:00pm DINNER BREAK WORKSHOP Chair: Paul Frederickson 8:30pm Topics to be arranged. Contact Paul for suggestions and information. Friday, April 11 SESSION VII Chair: Joel Dendy 8:00am John Ruge Recent Developments in Algebraic Multigrid Methods 8:25am Van Emden Henson Towards a Fully-Parallelizable Algebraic Multigrid 8:50am Craig C. Douglas Cache Based Multigrid Algorithms 9:15am Laura C. Dutto An Algebraic Multilevel Parallelizable Preconditioner for Large-Scale Computations 9:40am COFFEE BREAK 10:10am Sachit Malhotra Accelerating ADI on Parallel Processors including Multigrid with an ADI Smoother 10:35am William F. Mitchell A Parallel Adaptive Multilevel Method Using the Full Domain Partition 11:00am Hubertus Oswald Parallel Multilevel Algorithms for Incompressible Navier-Stokes 11:25am Clemens-August Thole Fast Solution of MSC/Nastran Sparse Matrix Problems Via a Multilevel Approach 11:50am Dexuan Xie Parallel U-Cycle Multigrid Method SESSION VIII Chair: Tom Manteuffel 4:40pm Valery Il'in Three-grid Method for Solving Boundary Value Problems 5:05pm Ira Livshits Multigrid Methods for Standing Wave Equations 5:30pm Rudolph Lorentz Computationally Efficient Wavelets in Sobolev Spaces 5:55pm Steve Thomas GCR(k)-Multigrid for the Anelastic Equations of Atmospheric Flow ------------------------------------------------------- Date: Fri, 07 Feb 1997 19:41:56 MET From: David.Dureisseix@lmt.ens-cachan.fr (david dureisseix) Subject: MGNet Database Entries Here are some new entries related to our domain decomposition method for structural analysis (a mixed deplacement-effort at interfaces approach). @inproceedings{LChampaney_JYCognard_DDureisseix_PLadeveze_1995b, author = "L. Champaney and J.-Y. Cognard and D. Dureisseix and P. Ladev{\`e}ze", title = "Numerical experimentations of parallel strategies in structural non-linear analysis", booktitle = "Euro{PVM}'95", editor = "J. Dongarra and M. Gengler and B. Tourancheau and X. Vigouroux", publisher = "Herm{\`}es", serie = "Parall{\'e}lisme, r{\'e}seaux et r{\'e}partition", volume = 5, address = "Lyon", month = September, year = "1995", pages = "221--226", } @article{LChampaney_JYCognard_DDureisseix_PLadeveze_1996, author = "L. Champaney and J.-Y. Cognard and D. Dureisseix and P. Ladev{\`e}ze", title = "Numerical experimentations of parallel strategies in structural non-linear analysis", journal = "Calculateurs Parall{\`e}les", volume = "8", number = "2", year = "1996", pages = "245--249", } @inproceedings{DDureisseix_PLadeveze_1996, author = "D. Dureisseix and P. Ladev{\`e}ze", title = "Parallel and multi-level strategies for structural analysis", editor = "J.-A. D{\'e}sid{\'e}ri", booktitle = "Proceedings of the Second European Conference on Numerical Methods in Engineering", organization = "ECCOMAS", publisher = "Wiley", month = September, year = "1996", pages = "599--604", } @phdthesis{DDureisseix_1997, author = "D. Dureisseix", title = "Une approche multi-{\'e}chelles pour des calculs de structures sur ordinateurs {\`a} architecture parall{\`e}le", school = "ENS de Cachan", type = "Th{\`e}se", address = "Cachan", month = January, year = 1997, } @inproceedings{JYCognard_DDureisseix_PLadeveze_PLorong_1995, author = "J.-Y. Cognard and D. Dureisseix and P. Ladev{\`e}ze and Ph. Lorong", title = "Une approche multi-{\'e}chelles en calcul des structures pour ordinateur {\`a} architecture parall{\`e}le", booktitle = "Actes du 12\`eme Congr\`es Fran\c{c}ais de M\'ecanique", organization = "{AUM}", address = "Strasbourg", month = September, year = "1995", pages = "101--104", } David DUREISSEIX LMT CACHAN fax : 01 47 40 27 85 61 Av du Pdt Wilson tel : 01 47 40 22 25 94235 CACHAN CEDEX e-mail : dureisse@lmt.ens-cachan.fr Editor's Note: will be entered almost immediately ------------- ------------------------------------------------------- Date: Fri, 28 Feb 1997 15:49:04 -0500 From: Jun Zhang Subject: MGNet Database Entries (J. Zhang) @article{JZhang_1997b, author = "J. Zhang", title = "On Convergence of Iterative Methods for a Fourth-Order Discretization Scheme", year = "1997", journal= "Appl. Math. Letters", month = "March", volume = "10", number = "2", pages = "49-55", } Editor's Note: will be entered almost immediately ------------- ------------------------------------------------------- Date: Fri, 28 Feb 1997 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. [1] P. Arbenz and W. Gander, Direct methods for banded linear systems on massively parallel processor computers, in Paral- lel Processing for Scientific Computing, SIAM Proceedings, Philadelphia, 1995, SIAM, pp. 506-507. [2] D. H. Bailey, P. E. Bjorstad, J. R. Gilbert, M. D. Mascagni, R. Schrieber, H. D. Simon, V. J. Torc- zon, and L. T. Watson, eds., Parallel Processing for Sci- entific Computing, SIAM Proceedings, Philadelphia, 1995, SIAM. [3] J. M. Beckers and F. Schmitz, The junction: a tool to par- allelise ocean models by a domain decomposition, to connect different kind of models and to impose open sea boundary conditions, in Parallel Processing for Scientific Computing, SIAM Proceedings, Philadelphia, 1995, SIAM, pp. 173-174. [4] E. Brakkee and A. Segal, A parallel domain decomposition algorithm for the incompressible Navier Stokes equations, in Proceedings of Massively Parallel Processing Applications and Development, Delft, The Netherlands, June 21-23, 1994, Amsterdam, 1994, Elsevier, pp. 743-752. [5] M. B. Davis and G. F. Carey, Parallel element by element spectral multilevel techniques for finite elements, in Paral- lel Processing for Scientific Computing, SIAM Proceedings, Philadelphia, 1995, SIAM, pp. 393-394. [6] F. Debae, Y. Jiang, J. M. Marchal, and P. Henriksen, A parallel version of Polyflow, in Proceedings of International Conference on High Performance Computing and Network- ing. HPCN '95 Milan, Italy, May 3-5, 1995, Berlin, 1995, Springer-Verlag, pp. 826-830. [7] A. Dickinson, P. Burton, J. Parker, and R. Baxter, Implementation and initial results from a parallel version of the meteorological office atmosphere prediction model, in Proceedings of the Sixth ECMWF Workshop on the Use of Parallel Processors in Meteorology, Reading, UK, Nov. 21- 25, 1994, Singapore, 1995, World Scientific, pp. 177-194. [8] C. C. Douglas, A review of numerous parallel multigrid meth- ods, in Applications on Advanced Architecture Computers, G. Astfalk, ed., SIAM, Philadelphia, 1996, pp. 187-202. [9] C. C. Douglas, A. Ern, and M. D. Smooke, Numerical simulation of laminar diffusion flames, in Applications on Advanced Architecture Computers, G. Astfalk, ed., SIAM, Philadelphia, 1996, pp. 243-254. [10] E. G. D'yakonov, Optimization in Solving Elliptic Problems, CRC Press, Inc., Boca Raton, 1996. [11] S. J. Fink and S. B. Baden, Run time data distribution for block structured applications on distributed memory comput- ers, in Parallel Processing for Scientific Computing, SIAM Proceedings, Philadelphia, 1995, SIAM, pp. 762-767. [12] M. Fruscione, F. Guindani, S. Punzi, and P. Stofella, Parallel application development with parallel computational frames, in Proceedings of Massively Parallel Processing Ap- plications and Development, Delft, The Netherlands, June 21-23, 1994, Amsterdam, 1994, Elsevier, pp. 269-276. [13] H. G. Galbas and O. Kolp, A parallel program for computer- ized tomography, in Proceedings of ParCo93. Parallel Com- puting 93, Grenoble, France, September 7-10, 1993, Amster- dam, 1994, Elsevier, pp. 509-512. [14] E. Galligani and V. Ruggiero, A parallel preconditioner for block tridiagonal matrices, in Proceedings of ParCo93. Parallel Computing 93, Grenoble, France, September 7-10, 1993, Amsterdam, 1994, Elsevier, pp. 113-120. [15] G. Gazzaniga and G. Sacchi, Parallel implementation of domain decomposition methods for the solution of elliptic boundary value problems, in Parallel Processing for Scientific Computing, SIAM Proceedings, Philadelphia, 1995, SIAM, pp. 395-396. [16] M. van Gijzen, Parallel iterative solution methods for linear finite element computations on the CRAY T3D, in Proceed- ings of International Conference on High Performance Com- puting and Networking. HPCN '95 Milan, Italy, May 3-5, 1995, Berlin, 1995, Springer-Verlag, pp. 723-728. [17] P. Grisvard, Singularities in Boundary Value Problems, vol. 22 of Research Notes in Applied Mathematics, Masson, Paris, 1992. [18] C. S. Ierotheou, C. R. Forsey, and U. Block, Paralleli- sation of a novel 3D hybrid structured unstructured grid cfd production code, in Proceedings of International Conference on High Performance Computing and Networking. HPCN '95 Milan, Italy, May 3-5, 1995, Berlin, 1995, Springer- Verlag, pp. 831-836. [19] T. Kioustelidis and H. Herold, Bpx on Convex's MPP: an astrophysical application, in Parallel Processing for Scientific Computing, SIAM Proceedings, Philadelphia, 1995, SIAM, pp. 361-366. [20] M. Kischinhevsky, A direct domain decomposition procedure for elliptic problems, in Parallel Processing for Scientific Computing, SIAM Proceedings, Philadelphia, 1995, SIAM, pp. 405-406. [21] I. Lie and R. Skalin, Parallelism in semi Lagrangian trans- port, in Proceedings of the Sixth ECMWF Workshop on the Use of Parallel Processors in Meteorology, Reading, UK, Nov. 21-25, 1994, Singapore, 1995, World Scientific, pp. 455- 471. [22] A. Liegmann and W. Fichtner, Solving large sparse linear systems in a distributed computing environment, in Paral- lel Processing for Scientific Computing, SIAM Proceedings, Philadelphia, 1995, SIAM, pp. 496-497. [23] E. Loli Piccolomini, F. Zama, and V. Ruggiero, A do- main decomposition method for scattered data approximation on a multiprocessor system, in Proceedings of ParCo93. Par- allel Computing 93, Grenoble, France, September 7-10, 1993, Amsterdam, 1994, Elsevier, pp. 193-200. [24] J. Z. Lou, A parallel incompressible Navier Stokes solver with multigrid iterations, in Parallel Processing for Scientific Computing, SIAM Proceedings, Philadelphia, 1995, SIAM, pp. 167-168. [25] J. Michalakes, T. Canfield, R. Nanjundiah, S. Ham- mond, and G. Grell, Parallel implementation, valida- tion, and performance of cm5, in Proceedings of the Sixth ECMWF Workshop on the Use of Parallel Processors in Me- teorology, Reading, UK, Nov. 21-25, 1994, Singapore, 1995, World Scientific, pp. 266-276. [26] B. Moon, G. Patnaik, R. Bennett, D. E. Fyfe, A. Suss- man, C. C. Douglas, J. H. Saltz, , and K. Kailas- anth, Runtime support and dynamic load balancing strate- gies for structured adaptive applications, in Parallel Process- ing for Scientific Computing, SIAM Proceedings, Philadel- phia, 1995, SIAM, pp. 575-580. [27] J. Nieplocha and T. Z. Mai, Performance improvement of asynchronous iterations by non uniform load distribution, in Parallel Processing for Scientific Computing, SIAM Pro- ceedings, Philadelphia, 1995, SIAM, pp. 508-509. [28] J. M. Oberhuber and K. Ketelsen, Parallelization of an OGCM on the CRAY T3D, in Proceedings of the Sixth ECMWF Workshop on the Use of Parallel Processors in Me- teorology, Reading, UK, Nov. 21-25, 1994, Singapore, 1995, World Scientific, pp. 494-504. [29] C. Olmsted, D. Covey, and A. Otto, Boundary condi- tions and domain decomposition for a three dimensional fi- nite difference time domain code on a Cray T3D, in Paral- lel Processing for Scientific Computing, SIAM Proceedings, Philadelphia, 1995, SIAM, pp. 399-400. [30] E. Piault, F. Willien, and F.-X. Roux, Parallel solvers for reservoir simulation on MIMD computers, in Paral- lel Processing for Scientific Computing, SIAM Proceedings, Philadelphia, 1995, SIAM, pp. 478-483. [31] R. Pozo and K. Remington, Fast three dimensional ellip- tic solvers on distributed network clusters, in Proceedings of ParCo93. Parallel Computing 93, Grenoble, France, Septem- ber 7-10, 1993, Amsterdam, 1994, Elsevier, pp. 201-208. [32] C. Ronchi, R. Iacono, and P. S. Paolucci, Finite dif- ference approximation to the shallow water equations on a quasi uniform spherical grid, in Proceedings of International Conference on High Performance Computing and Network- ing. HPCN '95 Milan, Italy, May 3-5, 1995, Berlin, 1995, Springer-Verlag, pp. 741-747. [33] U. Schattler and E. Krenzien, Experiences on plotting the Deutschland Modell of DWD to parallel platforms and first results, in Proceedings of the Sixth ECMWF Workshop on the Use of Parallel Processors in Meteorology, Reading, UK, Nov. 21-25, 1994, Singapore, 1995, World Scientific, pp. 223- 239. [34] J. C. H. Wang, H. Lung, Y. Katsumata, and T. Ishigai, Using domain decomposition in the multigrid NAS parallel benchmark on the Fujitsu VPP500, in Parallel Processing for Scientific Computing, SIAM Proceedings, Philadelphia, 1995, SIAM, pp. 397-398. [35] M. F. Wehner, A. J. Bourgeois, P. G. Eltgroth, P. B. Duffy, and W. P. Dannevik, A parallel coupled oceanic atmospheric general circulation model, in Proceedings of the Sixth ECMWF Workshop on the Use of Parallel Processors in Meteorology, Reading, UK, Nov. 21-25, 1994, Singapore, 1995, World Scientific, pp. 512-522. [36] F. Willien, E. Piault, and F.-X. Roux, Parallel precondi- tioners on MIMD computers applied to petroleum industry, in Proceedings of International Conference on High Perfor- mance Computing and Networking. HPCN '95 Milan, Italy, May 3-5, 1995, Berlin, 1995, Springer-Verlag, pp. 287-292. ------------------------------ End of MGNet Digest **************************