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 (ccd@ms.uky.edu) Volume 6, Number 12 (approximately December 31, 1996) Today's topics: The Editor Is Moving 1995 Copper Mountain Multigrid Proceedings Mailed !!! A new paper on biharmonic equation Dissertation on multigrid methods Updated algebraic multigrid code Multigrid in Numerical Linear Algebra with Applications Assistant Professorship at Tufts 13th GAMM-Seminar Kiel Multiscale Phenomena, Modelling and Computation Workshop Various Conferences New bib entry (Jun Zhang) Some of the new entries in the bibliography (> 3,000 entries warning) ------------------------------------------------------- Date: Wed, 1 Jan 1996 00:00:01 -0500 From: Craig DouglasSubject: The Editor Is Moving There will be another MGNet site added in the next month. I have left IBM for University of Kentucky, where I am now a professor in both the mathematics and mechanical engineering departments, and am the associate directory of the center for computational sciences. I will still be at Yale one day a week and spending my weekends in Connecticut. Nine of the readers of this list wrote letters in support of my move. I know who several of you are, but do not have a clue who the rest are; many thanks to the all of you. As has been noted before in this digest, there are faculty positions open in mathematics and computer science (1 each) that are appropriate to the readers of MGNet. Applications are due in writing about 10 January. ------------------------------------------------------- Date: Thu, 19 Dec 1996 21:45:11 GMT From: Duane Melson Subject: 1995 Copper Mountain Multigrid Proceedings Mailed !!! The proceedings are back from the printers. Most of the copies have been mailed. Editor's Note: My copies arrived at my house on December 24th. ------------- ------------------------------------------------------- Date: Wed, 4 Dec 96 12:30:24 EST From: Murli Gupta Subject: A new paper on biharmonic equation I have placed in mgnet/incoming two files marked gupta.ps and gupta.txt containing .ps file of our new paper with abstract in gupta.txt. The abstract is given below. The paper will appear in SIAM J. Sci. Computing. Multigrid Solution of Automatically Generated High Order Discretizations for the Biharmonic Equation Irfan Altas School of Information Studies, Charles Sturt University, Wagga Wagga, NSW 2678 Australia ialtas@csu.edu.au; Jonathan Dym Department of Mathematics, University of Southern California, Los Angeles, CA 90089 jdym@cams.usc.edu; Murli M. Gupta Department of Mathematics, The George Washington University, Washington, DC 20052 mmg@math.gwu.edu; and Ram P. Manohar Department of Mathematics, University of Saskatchewan, Saskatchewan, S7N OWO Canada manohar@sask.usask.ca Abstract In this work, we use a symbolic algebra package to derive a family of finite difference approximations for the biharmonic equation on a 9 point compact stencil. The solution and its first derivatives are carried as unknowns at the grid points. Dirichlet boundary conditions are thus incorporated naturally. Since the approximations use the 9 point compact stencil, no special formulas are needed near the boundaries. Both second order and fourth order discretizations are derived. The fourth order approximations produce more accurate results than the 13 point classical stencil or the commonly used system of two second order equations coupled by the boundary condition. The method suffers from slow convergence when classical iteration methods such as Gauss-Seidel or SOR are employed. In order to alleviate this problem we propose several multigrid techniques which exhibit grid- independent convergence and solve the biharmonic equation in a small amount of computer time. Test results from three different problems, including Stokes flow in a driven cavity, are reported. Editor's Note: in mgnet/papers/Altas-Dym-Gupta-Manohar/high-order.ps.gz. ------------- ------------------------------------------------------- Date: Mon, 09 Dec 96 14:06:59 -0500 From: Sachit Malhotra Subject: Dissertation on multigrid methods Topics in Multigrid Methods Sachit Malhotra Computer Science Department Yale University Abstract Multigrid methods are often used for the solution of systems of equations arising from the discretization of elliptic partial differential equations. Such problems are often the compute intensive kernels for many numerical problems arising in science and engineering. The solution of three--dimensional problems, which lead to very large systems of equations, is particulary well suited to solution by multigrid methods. The large size of the problems to be solved has led to the increasing use of parallel computers, for example clusters or LANs of workstations. However, in practice, most workstations are connected by relatively slow connections such as ethernet. In this dissertation, we investigate some of the issues involved in the solution of elliptic problems using multigrid methods. We shall focus on the solution of these problems on clusters of workstations. We shall define a class of algorithms to accelerate the multigrid smoother on such clusters. These methods subsume the latency inherent in the communication by using redundant computation to combine a large number of small messages. Alternating direction methods, which are often used as smoothers in the serial case, suffer from a high parallel overhead because of the need to transpose data in each smoothing iteration. We suggest modifications of these methods which are parallelizable and maintain the rate of convergence. These modifications are also applicable to alternating direction line SOR iterative methods. Lastly, we shall deal with the theoretical issues involved in transferring the error in multigrid algorithms from one grid to another, possibly unrelated, grid. We derive sharp upper and lower bounds on the condition number of this procedure. Editor's Note: in mgnet/papers/Malhotra. ------------- ------------------------------------------------------- Date: Sun, 8 Dec 1996 21:44:00 -0700 From: pvanek@tiger.cudenver.edu (Petr Vanek) Subject: Updated algebraic multigrid code I am just releasing the new version of the amg code. Differences compare to the older one are: 1. It is significantly more robust 2. It runs in parallel on SGI-PC. For the sake of portability, the only parallel construct which has been used is the C$DOACROSS directive, so the code can be ported to other shared-memory machines very easily. The diasadvantage of the new version is sligtly lower performance in the case of very simple problems. Editor's Note: in mgnet/codes/vanek. ------------- ------------------------------------------------------- Date: Fri, 06 Dec 1996 14:57:28 +0100 From neytchev@sci.kun.nl Fri Dec 6 09:00 EST 1996 Subject: Multigrid in Numerical Linear Algebra with Applications Volume 3, Issue 4, 1996 P. Vanek and J. Krizkova Two-Level Method with Small Coarse Grid Appropriate for Unstructured Meshes (255--274) P. Amestoy, I.S. Duff and C. Puglisi Multifrontal QR Factorization in a Multiprocessor Environment (275--300) M. Berry and R. Fierro Low-rank Orthogonal Decompositions for Information Retrieval Applications (301--327) Y. Saad and K. Wu DQGMRES: A Direct Quasi-minimal Residual Algorithm Based on Incomplete Orthogonalization (329--343) Volume 3, Issue 5, 1996 Speciall issue on Algebraic Multilevel Iteration Methods G. Starke (351--367) Multilevel Minimal Residual Methods for Nonsymmetric Elliptic Problems A. Reusken A Multigrid Method Based on Incomplete Gaussian Elimination (369--390) P.J. Ferket The Finite Difference Based Fast Adaptive Composite Grid Method (391--411) V. Migallon, J. Penades and D. Szyld Block Two-stage Methods for Singular Systems and Markov Chains (413--426) Z. Chen, R. Ewing, R. Lazarov, S. Malyasov and Y.A. Kuznetsov Multilevel Preconditioners for Mixed Methods for Second (427--453) Order Elliptic Problems Maya Neytcheva Faculty of Mathematics and Informatics, University of Nijmegen Toernooiveld, 6525 ED Nijmegen, The Netherlands tel: +31-24-3652485 e-mail: neytchev@sci.kun.nl ------------------------------------------------------- Date: Tue, 3 Dec 1996 13:08:31 -0500 From: borgers@math.tufts.edu (Christoph Borgers) Subject: Assistant Professorship at Tufts Tufts University Department of Mathematics Medford, MA 02155 Applications are invited for an Assistant Professorship to begin September 1, 1997. Initial one-year contract, renewable to a maximum of three years. Ph.D., promise of strong research and evidence of strong teaching ability required. Research interests preferred: numerical linear algebra or numerical elliptic PDE's or mathematical biology. Candidates with the ability to be successful at teaching students from underrepresented groups are encouraged to apply. Send application and three letters of recommendation to Christoph Borgers, Hiring Committee Chair. Review of applications will begin January 31, 1997 and continue until the position is filled. Tufts University is an Equal Opportunity/Affirmative Action employer. Members of underrepresented groups (including people of color, persons with disabilities, Vietnam veterans and women) are strongly encouraged to apply. ------------------------------------------------------- Date: Mon, 23 Dec 1996 11:00:38 +0100 (MET) From: Jens Burmeister Subject: 13th GAMM-Seminar Kiel The prelimanary programme of the 13th GAMM-Seminar Kiel on Numerical Treatment of Multi-Scale Problems January 24th to 26th, 1997. Kiel, Germany is now available on the web. Please visit our webpage http://www.numerik.uni-kiel.de/gamm.html With best regards Jens Burmeister ------------------------------------------------------- Date: Thu, 2 Jan 1997 11:26:17 +0200 From: Weintraub Carol Subject: Multiscale Phenomena, Modelling and Computation Workshop Research Workshop of the Israel Science Foundation MULTISCALE PHENOMENA, MODELLING AND COMPUTATION March 2-7, 1997. Neptune Hotel, Eilat, Israel Workshop Organizers: Secretary: -------------------- ---------- Achi Brandt, Weizmann Institute Carol Weintraub Gerhard Mack, Hamburg University Office: 972-8-9343545 Sorin Solomon, Hebrew University Fax: 972-8-9344122 WWW: http://shum.cc.huji.ac.il/~sol/eilat/eilatcon.html The nature of the interactions between different scales of phenomena in a complex system is the focus of interest in an increasingly wider range of scientific fields. This interest originated independently in theoretical physics and in computational mathematics. Like the first Eilat workshop (February, 1995) the purpose of this second one is to bring together different communities of researchers having the common interest of studying the different ways in which inter-scale interactions occur in nature and can be devised and exploited in calculations. This time, computational chemistry will be added as one of the main themes. The participants include computational physicists, chemists and 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, with interest in the more general theory of dynamical and complex phenomena and/or in their computational aspects. The chemists bring special interest in ab initio quantum calculation and in large scale molecular dynamics. 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. More information about the workshop, its scientific background, mode of organization and location, including details on travel, climate, prices, accommodations, services, social program, etc. is available at the above Web site, together with registration, accommodation and travel forms. This information can also be received via email, fax or regular mail by request from the conference secretary: Carol Weintraub, Department of Applied Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Email: carol@wisdom.weizmann.ac.il, Tel: +972-8-9343545, Fax: +972-8-9344122. Because time is short, hearing soon from anybody who intends to participate would be appreciated. The number of rooms in the hotels at the conference rate is, unfortunately, limited, so it is advisable to complete the accommodation forms as soon as possible. ------------------------------------------------------- Date: Sat, 28 Dec 1996 11:53:16 -0500 From: Craig Douglas Subject: Various Conferences I have received long announcements of a number of conferences for MGNet. I will put a link in the MGNet conferences' web page to each of the followinge with the entire text sent to me. Here is a very short summary: 1. From: Jiangping Zhu Third Mississippi State Conference on DIFFERENTIAL EQUATIONS & COMPUTATIONAL SIMULATIONS Preliminary Announcement and Call for Papers May 16-17, 1997 Mississippi State University URL: http://www.msstate.edu/Dept/Math/conf.html MGNet: mgnet/conferences/msu-difeq.0597 2. From: Guido Kanschat Charles University Prague, Czech Technical University Prague, and Ruprecht-Karls-Universitaet Heidelberg First Announcement NUMERICAL MODELLING IN CONTINUUM MECHANICS Theory, Algorithms, Applications The Third Summer Conference Prague (Czech Republic), September 8 - 11, 1997 Prof. Dr. Miloslav Feistauer, DrSc. Charles University Prague Faculty of Mathematics and Physics Institute of Numerical Mathematics Malostranske nam. 25 118 00 Praha 1 Czech Republic E-mail: nmicm97@ms.mff.cuni.cz Phone: +42 2 21914223, +42 2 535229 Fax: +42 2 535229 URL: none listed MGNet: mgnet/conferences/prague-nummodel.0997 3. From: ENUMATH Guido Kanschat 2nd Announcement - Call for Papers ENUMATH 97 Second European Conference on Numerical Mathematics and Advanced Applications September 29 - October 3, 1997 New University Heidelberg, Germany URL: http:gaia.iwr.uni-heidelberg.de/ENUMATH.html MGNet: mgnet/conferences/enumath.0997 ------------------------------------------------------- Date: Mon, 30 Dec 1996 19:30:58 -0500 From: Jun Zhang Subject: New bib entry (Jun Zhang) @ARTICLE{JZHANG_1997a, AUTHOR = {J. Zhang}, TITLE = {Accelerated multigrid high accuracy solution of the convection-diffusion equation with high Reynolds number}, YEAR = 1997, JOURNAL= {Numerical Methods for Partial Differential Equations}, MONTH = January, VOLUME = 13, NUMBER = {1}, PAGES = {77-92} } Editor's Note: will be in the bibliography shortly ------------- ------------------------------------------------------- Date: Sat, 28 Dec 1996 11:53:16 -0500 From: Craig Douglas Subject: Some of the new entries in the bibliography (> 3,000 entries warning) The bibliography passed 3,000 entries and 69,000 fields this month. Both are fixed limits inside of the version of the bibtex program that I use. I had to get the web-6.1 and web2c-6.1 distributions, build bibtex.c, and modify all instances of 3000 and 69000L (I changed them to 6000 and 140000L respectively). After recompiling bibtex, I could produce a new mgbib.bbl file again. Here are some recent new entries. As usual, please send additions and corrections. REFERENCES [1] L. M. Adams, A multigrid algorithm for immersed interface problems, in Seventh Copper Mountain Conference on Multi- grid Methods, N. D. Melson, T. A. Manteuffel, S. F. Mc- Cormick, and C. C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA, pp. 1-14. [2] E. Arian and S. Ta'asan, Smoothers for optimization prob- lems, 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, pp. 15-30. [3] M. Berndt and K. Witsch, Multigrid with overlapping patches, in Seventh Copper Mountain Conference on Multi- grid Methods, N. D. Melson, T. A. Manteuffel, S. F. Mc- Cormick, and C. C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA, pp. 31-40. [4] P. Bochev, Z. Cai, T. A. Manteuffel, and S. F. Mc- Cormick, First-order system least squares for the Navier- Stokes equations, 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, Hamp- ton, VA, 1996, NASA, pp. 41-55. [5] J. Bordner and F. Saied, MGLab: An interactive multigrid environment, 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, Hamp- ton, VA, 1996, NASA, pp. 57-71. [6] A. Borz`i, K. W. Morton, E. S"uli, and M. Vanmaele, A full multi-grid method for the solution of the cell vertex finite volume Cauchy-Riemann equations, 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, pp. 73-86. [7] 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. [8] A. Brandt and L. Yu. Zaslavsky, Multilevel algorithm for atmospheric assimilation, in Seventh Copper Mountain Con- ference on Multigrid Methods, N. D. Melson, T. A. Manteuf- fel, S. F. McCormick, and C. C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA, pp. 87-96. [9] J. Broeze, B. Geurts, H. Kuerten, and M. Streng, Multigrid acceleration of time-accurate DNS of compressible turbulent flow, 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, Hamp- ton, VA, 1996, NASA, pp. 109-121. [10] Z. Cai, T. A. Manteuffel, and S. F. McCormick, First- order system least squares for the Stokes equations, with ap- plications to linear elasticity, 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. 133-145. [11] ______, First-order system least squares for velocity-vorticity- pressure form of the Stokes equations, with applications to linear elasticity, 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, Hamp- ton, VA, 1996, NASA, pp. 123-132. [12] D. Canright and V. E. Henson, Towards an FVE-FAC method for determining thermocapillary effects on weld pool shape, 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, pp. 147-166. [13] M. Casarin, Quasi-optimal Schwarz methods for the conform- ing spectral element discretization, in Seventh Copper Moun- tain 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, pp. 167-182. [14] Z. Chen and R. E. Ewing, Recent development of multigrid algorithms for mixed and nonconforming methods for second order elliptic problems, in Seventh Copper Mountain Confer- ence on Multigrid Methods, N. D. Melson, T. A. Manteuffel, S. F. McCormick, and C. C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA, pp. 183-197. [15] M. B. Davis and G. F. Carey, A parallel multilevel spectral element scheme, 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, Hamp- ton, VA, 1996, NASA, pp. 213-225. [16] J. E. Dendy, Revenge of the semicoarsening frequency de- composition multigrid method, 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. 227-239. [17] Q. Deng, An optimal order nonnested mixed multigrid method for generalized Stokes problems, 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. 241-253. [18] C. C. Douglas, J. Douglas, and D. E. Fyfe, A note on multigrid theory for non-nested grids and/or quadrature, 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, pp. 255-264. [19] E. G. D'yakonov, Effective numerical methods for solving el- liptic problems in strengthened Sobolev spaces, 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, pp. 199-212. [20] P. Eliasson and B. Engquist, The effects of dissipation and coarse grid resolution for multigrid in flow problems, in Sev- enth 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, pp. 265-281. [21] H. C. Elman, Multigrid and Krylov subspace methods for the discrete Stokes equations, in Seventh Copper Mountain Con- ference on Multigrid Methods, N. D. Melson, T. A. Manteuf- fel, S. F. McCormick, and C. C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA, pp. 283-299. [22] C. Farhat and D. Rixen, A new coarsening operator for the optimal preconditioning of the dual and primal domain de- composition methods: Application to problems with severe coefficient jumps, 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, Hamp- ton, VA, 1996, NASA, pp. 301-316. [23] P. O. Frederickson, High performance parallel multigrid al- gorithms for unstructured grids, in Seventh Copper Moun- tain 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, pp. 317-326. [24] T. Gjesdal, A cell-centered multigrid for all grid sizes, in Sev- enth 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, pp. 327-338. [25] W. L. Golik, Numerical study of multigrid methods with var- ious smoothers for the elliptic grid generation equations, 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, pp. 339-346. [26] H. Guillard and N. Marco, Some aspects of multigrid meth- ods on non-structured meshes, 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. 347-362. [27] M. J. Holst and S. Vanderwalle, Schwarz methods: To symmetrize or not to symmetrize, in Seventh Copper Moun- tain 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, pp. 363-378. [28] J. E. Jones, A mixed finite volume element method for flow calculations in porous media, 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. 379-391. [29] M. Jung and U. R"ude, Implicit extrapolation methods for various coefficient problems, 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. 393-408. [30] R. Jyotsna and S. P. Vanka, A pressure based multigrid procedure for the Navier-Stokes equations on unstructured grids, 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, pp. 409-424. [31] H.-C. Ku and A. S. Popel, The multigrid-mask numerical method for solution of incompressible Navier-Stokes eqau- tions, 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, pp. 425-437. [32] C.-Y. G. Lai, Implementation of hybrid V-cycle multilevel methods for mixied finite element systems with penalty, 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, pp. 439-453. [33] C.-O. Lee, A conforming multigrid method for the pure trac- tion problem of linear elasticity: Mixed formulation, in Sev- enth 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, pp. 455-471. [34] C. Liu and Z. Liu, Multiple scale simulation for transitional and turbulent flow, 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, Hamp- ton, VA, 1996, NASA, pp. 473-487. [35] S. Maliassov, A note on substructuring preconditioning for nonconforming finite element approximations of second or- der elliptic problems, in Seventh Copper Mountain Confer- ence on Multigrid Methods, N. D. Melson, T. A. Manteuffel, S. F. McCormick, and C. C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA, pp. 489-501. [36] J. Mandel and R. Tezaur, Convergence of a substructur- ing method with Lagrange multipliers, 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, pp. 503-518. [37] T. A. Manteuffel, S. F. McCormick, and G. Starke, First-order system least-squares for second order elliptic problems with discontinuous coefficients, 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, pp. 535-550. [38] T. A. Manteuffel and K. J. Ressel, A systematic solution approach for neutron transport problems in diffusive regimes, in Seventh Copper Mountain Conference on Multigrid Meth- ods, N. D. Melson, T. A. Manteuffel, S. F. McCormick, and C. C. Douglas, eds., vol. CP 3339, Hampton, VA, 1996, NASA, pp. 519-534. [39] A. J. Meir, On DGS relaxation: The Stokes problem, in Sev- enth 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, pp. 551-563. [40] N. D. Melson, T. A. Manteuffel, S. F. McCormick, and C. C. Douglas, eds., Seventh Copper Mountain Con- ference on Multigrid Methods, vol. CP 3339, Hampton, VA, 1996, NASA. [41] N. D. Melson and M. D. Sanetrik, Multigrid acceleration of time-accurate Navier-Stokes calculations, 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, pp. 565-579. [42] J. Molenaar, Multigrid methods for fully implicit oil reser- voir simulation, 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, Hamp- ton, VA, 1996, NASA, pp. 581-590. [43] E. Morano, D. J. Mavriplis, and V. Venkatakrishnan, Coarsening strategies for unstructured multigrid techniques with application to anisotropic problems, 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, pp. 591-606. [44] S. V. Nepomnyaschikh, Preconditioning operators on un- structired grids, 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, Hamp- ton, VA, 1996, NASA, pp. 607-621. [45] E. Nurgat and M. Berzins, Multigrid methods for EHL prob- lems, 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, pp. 623-636. [46] S. 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