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: file://na.cs.yale.edu/pub/mgnet/www/mgnet.html or http://www.cerfacs.fr Today's editor: Craig Douglas (douglas-craig@cs.yale.edu) Volume 4, Number 12 (approximately December 31, 1994) Today's topics: Copper Mountain Conference on Multigrid Methods '95 (CCMM95) 1995 Copper Mountain Multigrid Conference Preprints Multiscale Phenomena: Modelling and Computation Meeting Preprints from Z. Chen et al Travel Support Available for ICIAM 95 Some bibliography additions in mgnet/bib/mgnet.bib ------------------------------------------------------- Date: Sat, 24 Dec 1994 08:20:06 -0700 From stevem@boulder.colorado.edu Sat Dec 24 10:22 EST 1994 Subject: Copper Mountain Conference on Multigrid Methods '95 (CCMM95) If you are thinking of attending and giving a talk, we need your title and abstract ASAP... Editor's Note: This means by 1 January or return e-mail before the 10th. ------------- I forgot to bug people in the last issue. While I am at it, here are the other things people need to know: CONFERENCE DEADLINES Abstracts Jan. 1, 1995 Lodging Reservations Feb. 28, 1995 Early Registration Feb. 28, 1995 Papers for Proceedings Apr. 2, 1995 (at conference) LODGING RESERVATIONS Copper Mountain Resort (800) 458-8386 ... Thanks and have HAPPY HOLIDAYS! steve Editor's Note: You, too, Steve. Have a nice trip overseas. For those of ------------- you with offices only on one continent, telnet is a real thrill during certain hours of the day when you just have to log into one of your tinkertoys in your home country. Requests sent to Steve will not be answered in a timely fashion; please send reasonable requests to ccmm@boulder.colorado.edu but do not ask for funds or lodging information. _/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ _/ Steve McCormick _/ _/ Program in Applied Math _/ _/ Campus Box 526 _/ _/ The University of Colorado _/ _/ at Boulder _/ _/ Boulder, CO 80309-0526 _/ _/ (303) 492-0662 _/ _/ stevem@boulder.colorado.edu _/ _/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/ ------------------------------------------------------- Date: Thu, 29 Dec 1994 15:19:55 -0500 From: douglas-craig (Craig Douglas) Subject: 1995 Copper Mountain Multigrid Conference Preprints Once again, the proceedings will be published by NASA. As last time, the pre-proceedings will be available electronically through MGNet before the conference. Thus, you will not receive a tree trunk to take home. In fact, you can bring it on your laptop and preview the papers with ghostview, mosaic, or your favorite web browser. The directions on how to submit something to MGNet are kept in the file mgnet/How2Submit.mgnet (you can find this information using a web browser, too). Basically, all you need to do is the following: * * * * Thank you for submitting a paper to the 1995 Copper Mountain Conference on Multigrid Methods. This year, we are going to continue the tradition of putting the papers on MGNet [1]. NASA will be putting the informal proceedings out as a report at some point. In the meantime, the organizers would appreciate it if you would put your paper in the MGNet repository. This way, anyone can see what you plan on talking about before coming to Copper Mountain. There are 3 methods for getting your paper to MGNet. They are, in order of preference, 1. Download the paper using ftp on the Internet. 2. E-mail the source (some flavor of TeX or whatever) 3. Mail me a 3.5 inch DOS formatted floppy. The papers will be in the directory mgnet/Conferences/CopperMtn95 on the machine casper.cs.yale.edu (Internet machine 128.36.12.1). See the README file in that directory for more information. This repository is mirrored at ftp.cerfacs.fr (Internet machine 138.63.200.33), but does not have a world writable directory. Hopefully, this will all work. Please have a little patience if things seem to be going awry. If all else fails, call me or send e-mail. Regards, Craig Douglas December 23, 1994 REFERENCES [1] C. C. Douglas, MGNet: a multigrid and domain decomposition network, ACM SIGNUM Newsletter, 27 (1992), pp. 2-8. DIRECTIONS for Putting a Paper on MGNet 1. Instructions for downloading papers to MGNet: % ftp casper.cs.yale.edu => Begin (or ftp 128.36.12.1) User: anonymous => You type anonymous Password: dinner@nine.pm.est => You type your e-mail address ftp> cd mgnet/incoming => Change to the incoming directory ftp> mkdir your_name => Make a directory for yourself ftp> cd your_name => Change to your directory ftp> put paper.abs => Put an abstract file (ascii, please) ftp> binary => Binary transfer ftp> put paper.ps => Put the paper in some format ftp> quit => All done The abstract file should be the same one that you submitted in December, 1994. The paper.dvi file above can also be paper.tex or whatever. If you include a TeX file, please put a comment line at the top with directions on how to make the file (at least, please indicate which flavor of TeX you used -- LaTeX, AMSTeX, Plain TeX, etc.). PostScript files are preferred, but .dvi is also fine. If your paper includes PostScript figures in separate files, please download those as well (or indicate that you did not do this). Then mail mgnet-requests@casper.cs.yale.edu a message saying you downloaded a paper for the Copper Mountain meeting. I will send you an acknowledgment as soon as possible. 2. Just e-mail your paper and abstract files to mgnet-requests@casper.cs.yale.edu Include on the subject line that this is a Copper Mountain paper. It will help greatly if you do not have any lines longer than 80 characters (certainly not longer than 128). This is because certain machines (e.g., IBM mainframes) have the habit of trimming long lines in mail. I will try to determine that your files arrived intact. In any case, I will send you a note with a success or failure indication. 3. If all else fails, I will also accept 3.5 inch floppies formatted under DOS. Make certain you label your floppy with your name. If you want me to send you an acknowledgment, please include a return address (e-mail preferred). Mail your floppy to me at my home address: Dr. Craig Douglas 8 South Street Cos Cob, CT 06807-1618 USA This will get to me quicker than if you send it to my office (further, I will even get it this way). DIRECTIONS for Retrieving a Paper on MGNet Instructions for downloading papers from MGNet: % ftp casper.cs.yale.edu => Begin (or ftp 128.36.12.1) User: anonymous => You type anonymous Password: dinner@nine.pm.est => You type your e-mail address ftp> cd mgnet/Conferences/CopperMtn95 => Change directory (case counts) ftp> binary => Binary transfer ftp> prompt => So ftp will just grab files quietly ftp> mget paper1.* => Get the first paper ftp> mget paper2.* => Get the second paper ftp> mget * => Get everything ftp> quit => All done The "mget *" command should be used only if you want all the files in the directory. Use the "mget paper1.*" style of commands if you only want selected papers. ------------------------------------------------------- Date: Thu, 15 Dec 94 13:21:09 +0200 From: Carol WeintraubSubject: Multiscale Phenomena: Modelling and Computation Meeting Craig, Could you please announce the following? Thanks, Achi MULTISCALE PHENOMENA: MODELLING AND COMPUTATION February 20--24, 1995 Neptune Hotel -- Eilat, Israel Workshop Committee: ------------------- Achi Brandt, (organizer) Weizmann Institute, Rehovot, Israel Gerhard Mack, Hamburg University, Germany Sorin Solomon, Hebrew University, Jerusalem, Israel * Scientific background The nature of the interactions between different scales of phenomena in a complex system has recently become the focus of interest in an increasingly wider range of scientific fields. This interest originated independently in theoretical physics and in computational mathematics. The purpose of the Eilat workshop is to bring together different communities of researchers interested in the methodology, derivation, exploitation, and philosophical implications of multiscale interactions. The participants include theoretical physicists and computational mathematicians. The physicists are mainly from the field theory and statistical mechanics communities, especially in the theoretical and/or simulation aspects of renormalization group, criticality and universality. Many of them manifested lately a growing interest in the more general theory of dynamical and complex phenomena and/or in their computational aspects. The participating mathematicians will represent several research communities which have adopted different versions of multiscale scientific computation: multigrid, multipole, hierarchical bases, wavelets, and other relatives. * Further information and forms Further information about the workshop scientific background, organization and location, including details on travel, climate, prices and tours, with registration and accommodation forms, can be obtained by: 1. anonymous ftp: ------------- a) ftp ftp.wisdom.weizmann.ac.il b) userid: [userid = anonymous] c) pw: [type minus sign with your userid@your_node_site example: -john@cs.mit.edu] d) cd /pub/carol [to get into public access directory] e) ls [to see list of file names] f) binaryt Digest g) get geninfo.ps [to get info file placed into your home directory] h) get registr.ps [to get registration forms " " " " "] i) quit [to exit anonymous ftp sesion] 2. Secretary: --------- Carol Weintraub Dept. of Applied Mathematics & Computer Science Weizmann Institute of Science Rehovot 76100, Israel Tel: 972-8-343545 Fax: 972-8-344122 Email: carol@wisdom.weizmann.ac.il ------------------------------------------------------- Date: Thu, 22 Dec 1994 13:25:53 -0600 From: zhangxin Chen Subject: Preprints from Z. Chen et al EQUIVALENCE BETWEEN AND MULTIGRID ALGORITHMS FOR MIXED AND NONCONFORMING METHODS FOR SECOND ORDER ELLIPTIC PROBLEMS Zhangxin Chen Department of Mathematics and the Institute for Scientific Computation, Texas A&M University, College Station, TX 77843 ABSTRACT The purpose of this paper is to establish an equivalence between mixed and nonconforming finite element methods for second order elliptic problems on both triangular and rectangular finite elements, and to provide an analysis of multigrid methods for both methods based on the equivalence. We first show that the linear system arising from the mixed method can be algebraically condensed to a symmetric and positive definite system for Lagrange multipliers using features of mixed finite element spaces and that the system for the Lagrange multipliers is identical to the system arising from the nonconforming method. Then we prove that optimal order multigrid algorithms can be developed for both methods. Two types of multigrid methods are considered in this paper. The first one makes use of the coarse-grid correction on nonconforming finite element spaces, while the second one has the coarse-grid correction step established on conforming finite element spaces. Finally, numerical examples are given to illustrate the present theory. Editor's Note: in mgnet/papers/ChenZ-et-al/mult.*. ------------- DOMAIN DECOMPOSITION ALGORITHMS FOR MIXED METHODS FOR SECOND ORDER ELLIPTIC PROBLEMS Zhangxin Chen, Richard E. Ewing, and Raytcho Lazarov Department of Mathematics and the Institute for Scientific Computation, Texas A&M University, College Station, TX 77843 ABSTRACT In this paper domain decomposition algorithms for mixed finite element methods for linear and quasilinear second order elliptic problems are developed. A convergence theory for two-level and multilevel Schwarz methods applied to the algorithms under consideration is given, and its extension to other substructuring methods such as vertex space and balancing domain decomposition methods is considered. It is shown that the condition number of these iterative methods is bounded uniformly from above in the same manner as in the theory of domain decomposition methods for conforming and nonconforming finite element methods for the same differential problems. Numerical experiments are presented to illustrate the present techniques. Editor's Note: in mgnet/papers/ChenZ-et-al/dd.*. ------------- MULTILEVEL PRECONDITIONERS FOR MIXED METHODS FOR SECOND ORDER ELLIPTIC PROBLEMS Zhangxin Chen, Richard E. Ewing, and Raytcho Lazarov Department of Mathematics and the Institute for Scientific Computation, Texas A&M University, College Station, TX 77843 Yuri A. Kuznetsov Institute of Numerical Mathematics, Russian Academy of Sciences, 32-a Leninski Prospect, 117334 Moscow, Russia ABSTRACT A new approach of constructing algebraic multilevel preconditioners for mixed finite element methods for second order elliptic problems with tensor coefficients on general geometry is proposed. The linear system arising from the mixed methods is first algebraically condensed to a symmetric, positive definite system for Lagrange multipliers, which corresponds to a linear system generated by standard nonconforming finite element methods. Algebraic multilevel preconditioners are then constructed for this system based on a triangulation of parallelepipeds into tetrahedral substructures. Explicit estimates of condition numbers and simple computational schemes are established for the constructed preconditioners. Finally, numerical results for the mixed finite element methods are presented to illustrate the present theory. Editor's Note: in mgnet/papers/ChenZ-et-al/mixprc.*. ------------- ------------------------------------------------------- From: bdilisi@siam.org Date: Mon, 12 Dec 94 14:46:52 EST Subject: Travel Support Available for ICIAM 95 SIAM is administering a travel grant program for ICIAM 95 to be held in Hamburg, Germany, July 3--7. The grants, which are funded by the National Science Foundation and the Department of Energy, will provide partial travel support to qualified applicants. Typical anticipated awards will range from $800 to $1000. Travel costs will be reimbursed up to the amount of the award on submission of a signed travel expense form to SIAM. The awards are intended primarily for young researchers and graduate students; women and minorities are especially encouraged to apply. Awards will be based on merit. Preference will be given to participants in the ICIAM 95 program and to applicants who do not have other travel support for the meeting. Additional information and application forms can be accessed through the SIAM home page on the World Wide Web (http://www.siam.org) or the SIAM gopher server (gopher.siam.org). Application materials can also be obtained from the SIAM office (ICIAM 95 Coordinator, SIAM, 3600 University City Science Center, Philadelphia, PA 19104-2688; 215-382-9800; 215-386-7999 (fax); meetings@siam.org). The cutoff date for applications is March 15, and final decisions will be made no later than April 15. Early submission of applications is encouraged; whenever possible, SIAM will make decisions and notify applicants as the applications are received. Editor's Note: I usually do not run this type of submission since it is ------------- also run in the NA Digest. Also, the vast majority of MGNet members do not qualify for a variety of reasons. If you feel strongly that I should or should not not include this type of message in MGNet, please send me e-mail at mgnet-requests@cs.yale.edu. ------------------------------------------------------- Date: Thu, 29 Dec 1994 15:19:55 -0500 From: douglas-craig (Craig Douglas) Subject: Some bibliography additions in mgnet/bib/mgnet.bib These will be in by the first of the year along with some more that I will list next time. Corrections and additions are always welcome. Does anyone happen to know if there are any editors for the first one of these? @inproceedings{GAgrawal_ASussman_JSSaltz_1993a, author = "G. Agrawal and A. Sussman and J. S. Saltz", title = "Compiler and runtime support for structuredd and block structured applications", booktitle = "Proceedings of the Supercomputing Conference 1993", editors = "", series = "", volume = "", publisher = "IEEE, Computer Society Press", address = "Los Alamitos", year = "1993", pages = "578--587", } @article{XAi_HSCheng_1994a, author = "X. Ai and H. S. Cheng", title = "Influence of moving dent on point {EHL} contacts", journal = "STLE Tribology Trans.", volume = "37", year = "1994", pages = "323--335", } @article{XAi_HSCheng_1994b, author = "X. Ai and H. S. Cheng", title = "Transient {EHL} analysis for line contacts with measured surface roughness using multigrid technique", journal = "Journal of Tribology, Transactions of the ASME", volume = "116", year = "1994", pages = "549--558", } @article{MAlef_1994a, author = "M. Alef", title = "Implementation of a multigrid algorithm on {SUPRENUM} and other systems", journal = "Parallel Comput.", volume = "20", year = "1994", pages = "1547--1557", } @inproceedings{AAmin_PSadayappan_MGudavalli_1994a, author = "A. Amin and P. Sadayappan and M. Gudavalli", title = "Clustered reduced communication element by element preconditioned conjugate gradient algorithm for finite element computations", booktitle = "Proceedings of the International Conference on Parallel Processing 1994", editors = "", series = "", volume = "", publisher = "IEEE", address = "IEEE Service Center, Piscataway", year = "1994", pages = "509--516", } @article{AArnone_1994a, author = "A. Arnone", title = "Viscous analysis of three-dimensional rotor flow using a multigrid method", journal = "J. Turbomachinery, Trans. ASME", volume = "116", year = "1994", pages = "435--445", } @article{IAtlas_KBurrage_1994a, author = "I. Atlas and K. Burrage", title = "A high accuracy defect correction multigrid method for the steady incompressible {N}avier {S}tokes equations", journal = "J. Comput. Phys.", volume = "114", year = "1994", pages = "227--233", } @article{NBaaziz_CLabit_1994a, author = "N. Baaziz and C. Labit", title = "Multiconstraint Wiener based motion compensation using wavelet pyramids", journal = "IEEE Trans. Image Process", volume = "3", year = "1994", pages = "688--692", } @article{DBrown_JHRClarke_MOkuda_TYamazaki_1994a, author = "D. Brown and J. H. R. Clarke and M. Okuda and T. Yamazaki", title = "A domain decomposition parallel processing algorithm for molecular dynamics simulations of polymers", journal = "Comput. Phys. Commun.", volume = "83", year = "1994", pages = "1--13", } @article{ABBurshtej_1994a, author = "A. B. Burshtejn", title = "A semi-Lagrangian scheme utilizing the multigrid method", journal = "Meteorologiya i Gidrologiya", volume = "5", year = "1994", pages = "21--31", } @article{PGCiarletJr_1994a, author = "P. G. Ciarle{t,~Jr.}", title = "Implementation of a domain decomposition method well suited for (massively) parallel architectures", journal = "Int. J. High Speed Comput.", volume = "6", year = "1994", pages = "P157--182", } @article{SDConnel_DGHolmes_1994a, author = "S. D. Connell and D. G. Holmes", title = "Three dimensional unstructured adaptive multigrid scheme for the {E}uler equations", journal = "AIAA J.", volume = "32", year = "1994", pages = "1626--1632", } @inproceedings{LDagum_1993a, author = "L. Dagum", title = "Automatic partitioning of unstructured grids into connected components", booktitle = "Proceedings of the Supercomputing Conference 1993", editors = "", series = "", volume = "", publisher = "IEEE, Computer Society Press", address = "Los Alamitos", year = "1993", pages = "94--101", } @article{RDas_DJMavriplis_JSSaltz_SGupta_RPonnusamy_1994a, author = "R. Das and D. J. Mavriplis and J. S. Saltz and S. Gupta and R. Ponnusamy", title = "Design and implementation of a parallel unstructured {E}uler solver using software primitives", journal = "AIAA J.", volume = "32", year = "1994", pages = "489--496", } @article{CNDawson_TFDupont_1994a, author = "C. N. Dawson and T. F. Dupont", title = "Explicit/implicit, conservative domain decomposition procedures for parabolic problems based on block-centered finite differences", journal = "SIAM J. Numer. Anal.", volume = "31", year = "1994", pages = "1045--1061", } @article{GPDemetre_SMFarouqAli_1994a, author = "G. P. Demetre and S. M. Farou{q~A}li", title = "Review of analytical well models used in reservoir simulation", journal = "SPE of AIME", volume = "SPE28179", year = "1994", pages = "1--9", } @article{EDick_KRiemslagh_1994a, author = "E. Dick and K. Riemslagh", title = "Multi staging of {J}acobi relaxation to improve smoothing properties of multigrid methods for steady {E}uler equations", journal = "J. Comput. Appl. Math.", volume = "50", year = "1994", pages = "241--254", } @article{LDieci_GBader_1994a, author = "L. Dieci and G. Bader", title = "Solution of the systems associated with invariant tori approximation. {II}. {M}ultigrid methods", journal = "SIAM J. Sci. Comput.", volume = "15", year = "1994", pages = "1375--1400", } @article{MEMElSayed_CKHsiung_1994a, author = "M. E. M. El~{S}ayed and C. K. Hsiung", title = "Comparison between two decomposition approaches for parallel computation of structural optimization", journal = "Comput. Struct.", volume = "52", year = "1994", pages = "719--722", } @article{CFarhat_LCrivelli_FXRoux_1994a, author = "C. Farhat and L. Crivelli and F.-X. Roux", title = "Extending substructure based iterative solvers to multiple load and repeated analyses", journal = "Computer Meth. Appl. Mech. Engng.", volume = "117", year = "1994", pages = "195--209", } @article{CFarhat_LCrivelli_FXRoux_1994b, author = "C. Farhat and L. Crivelli and F.-X. Roux", title = "Transient {FETI} methodology for large-scale parallel implicit computations in structural mechanics", journal = "Int. J. Numer. Meth. Engng.", volume = "37", year = "1994", pages = "1945--1975", } @article{MGarbey_1994a, author = "M. Garbey", title = "Domain decomposition to solve transition layers and asymptotics", journal = "SIAM J. Sci. Comput.", volume = "15", year = "1994", pages = "866--891", } @article{FGruttmann_WWagner_1994a, author = "F. Gruttmann and W. Wagner", title = "On the numerical analysis of local effects in composite structures", journal = "Compos. Struct.", volume = "29", year = "1994", pages = "1--12", } @article{YRHakopian_YAKuznetsov_1994a, author = "Yu. R. Hakopian and Yu. A. Kuznetsov", title = "Algebraic multigrid/fictitious domain preconditioners on quasihierarchical triangular grids", journal = "Russian J. Numer. Anal. Math. Modelling", volume = "9", year = "1994", pages = "201--222", } @article{JHe_LKang_1993a, author = "J. He and L. Kang", title = "Parallel multigrid algorithms based on wavelet multiresolution approximations", journal = "Neural Parallel Sci. Comput.", volume = "1", year = "1993", pages = "421--430", } @article{WHeinrichs_1994a, author = "W. Heinrichs", title = "Spectral methods for singular perturbation problems", journal = "Appl. Math.", volume = "39", year = "1994", pages = "161--188", } @article{FHeitz_PPerez_PBouthemy_1994a, author = "F. Heitz and P. Perez and P. Bouthemy", title = "Multiscale minimization of global energy functions in some visual recovery problems", journal = "CVGIP: Image Understanding", volume = "59", year = "1994", pages = "125--134", } @article{GHorton_STLeutenegger_1994a, author = "G. Horton and S. T. Leutenegger", title = "Multi-level solution algorithm for steady-state {M}arkov chains", journal = "Perform. Eval. Rev.", volume = "22", year = "1994", pages = "191--200", } @article{RAIndik_JHIndik_1994a, author = "R. A. Indik and J. H. Indik", title = "A new computer method to quickly and accurately compute steady state temperatures from ferromagnetic seed heating", journal = "Med. Phys.", volume = "21", year = "1994", pages = "1135--1144", } @article{VMKadyshnikov_VMLosev_1994a, author = "V. M. Kadyshnikov and V. M. Losev", title = "Performance evaluation of multigrid variants of a relaxation method for integrating prognostic equations by implicit schemes", journal = "Meteorologiya i Gidrologiya", volume = "3", year = "1994", pages = "29--38", } @article{TKalkreuter_1994b, author = "T. Kalkreuter", title = "Multigrid methods for the computation of propagators in gauge fields", journal = "Int. J. Mod. Phys. C, Phys. Comput.", volume = "5", year = "1994", pages = "629--700", } @article{TKauranne_1994a, author = "T. Kauranne", title = "Summary of {GENESIS} work at the {E}uropean {C}entre for {M}edium range {W}eather {F}orecasts {(ECMWF)}", journal = "Parallel Comput.", volume = "20", year = "1994", pages = "1685--1688", } @article{BLafaurie_CNardone_RScardovelli_SZaleski_GZanetti_1994a, author = "B. Lafaurie and C. Nardone and R. Scardovelli and S. Zaleski and G. Zanetti", title = "Modelling merging and fragmentation in multiphase flows with {SURFER}", journal = "J. Comput. Phys.", volume = "113", year = "1994", pages = "134--147", } @article{FSLien_MALeschziner_1994b, author = "F. S. Lien and M. A. Leschziner", title = "Multigrid acceleration for recirculating laminar and turbulent flows computed with a non orthogonal, collocated finite volume scheme", journal = "Comput. Methods Appl. Mech. Eng.", volume = "118", year = "1994", pages = "351--371", } @article{JLinden_GLonsdale_HRitzdorf_ASchuller_1994a, author = "J. Linden and G. Lonsdale and H. Ritzdorf and A. Schuller", title = "Scalability aspects of parallel multigrid ", journal = "Future Gener. Comput. Syst.", volume = "10", year = "1994", pages = "429--439", } @article{ZLiu_CLiu_1994a, author = "Z. Liu and C. Liu", title = "Fourth order finite difference and multigrid methods for modeling instabilities in flat plate boundary layers 2-{D} and 3-{D} approaches", journal = "Comput. Fluids", volume = "23", year = "1994", pages = "955--982", } @article{ZLiu_CLiu_SFMcCormick_1994a, author = "Z. Liu and C. Liu and S. F. McCormick", title = "Multilevel methods for temporal and spatial flow transition simulation in a rough channel", journal = "Int. J. Numer. Methods Fluids", volume = "19", year = "1994", pages = "23--40", } @article{CALong_PGTucker_1994a, author = "C. A. Long and P. G. Tucker", title = "Numerical computation of laminar flow in a heated rotating cavity with an axial throughflow of air", journal = "Int. J. Numer. Methods Heat Fluid Flow", volume = "4", year = "1994", pages = "347--365", } @article{MLouterNool_1994a, author = "M. Loute{r~N}ool", title = "A parallel multigrid code with a fast vectorized {ILU} relaxation", journal = "Future Gener. Comput. Syst.", volume = "10", year = "1994", pages = "309--313", } @article{DJMavriplis_LMatinelli_1994a, author = "D. J. Mavriplis and L. Matinelli", title = "Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model", journal = "Int. J. Numer. Meth. Fluids", volume = "18", year = "1994", pages = "887--914", } @article{PMichielse_1994a, author = "P. Michielse", title = "Parallel multigrid using {PVM}", journal = "Supercomputer", volume = "10", year = "1994", pages = "10--23", } ------------------------------ End of MGNet Digest **************************