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 Today's editor: Craig Douglas (douglas-craig@cs.yale.edu) Volume 6, Number 1 (approximately January 31, 1996) Today's topics: If you got this issue twice... Important Date: February 8 Preprint from Jun Zhang Preprint from Craig Douglas 1995 Copper Mountain Proceedings Update MGNet Tutorials Update Some of the new entries in the bibliography ***** You could see your contribution listed here ***** ------------------------------------------------------- Date: Sat, 03 Feb 1996 13:52:10 -0500 From: Craig DouglasSubject: If you got this issue twice... If you received this twice, my apologies. When I first tried to send it out, every single message seems to have bounced with "host unknown" as the reason. Obviously, the local name server was not working. There are a lot of you on this list, as my mailbox can attest. ------------------------------------------------------- Date: Wed, 31 Jan 1996 10:32:26 -0500 From: Craig Douglas Subject: Important Date: February 8 February 8: Copper Mountain Conference on Iterative Methods (USA) Early registration due and hotel reservations must be made. Contact cm96@newton.colorado.edu February 8: 9th Domain Decomposition Symposium (Norway) Abstracts due (1-2 pages preferably in LaTeX). Send these to dd9@ii.uib.no ------------------------------------------------------- Date: Tue, 16 Jan 1996 15:35:26 -0500 From: Jun Zhang Subject: Preprint from Jun Zhang Minimal Residual Smoothing in Multi-Level Iterative Method JUN ZHANG Department of Mathematics, The George Washington University Washington, DC 20052, USA ABSTRACT A minimal residual smoothing (MRS) technique is employed to accelerate the convergence of the multi-level iterative method by smoothing the residuals of the original iterative sequence. The sequence with smoothed residuals is re-introduced into the multi-level iterative process. The new sequence generated by this acceleration procedure converges much faster than both the sequence generated by the original multi-level method and the sequence generated by MRS technique. The cost of this acceleration scheme is independent of the original operator and in many cases is negligible. The emphasis of this paper is on the practical implementation of MRS acceleration techniques in the multi-level method. The discussions are focused on the two-level method because the acceleration scheme is only applied on the finest level of the multi-level method. Numerical experiments using the proposed MRS acceleration scheme to accelerate both the two-level and multi-level methods are conducted to show the efficiency and the cost-effectiveness of this acceleration scheme. Editor's Note: in mgnet/papers/Zhang/mrs.ps.gz and .../mrs.abs. ------------- ------------------------------------------------------- Date: Wed, 31 Jan 1996 10:42:09 -0500 From: Craig Douglas Subject: Preprint from Craig Douglas Multigrid and Multilevel Methods in Science and Engineering Craig C. Douglas IBM T.J. Watson Research Center P.O. Box 218 Yorktown Heights, NY 10598-0218 USA and Yale University Department of Computer Science P.O. Box 208285 New Haven, CT 06520-8285 USA This is a survey article for the IEEE-Computational Science and Engineering magazine. It is aimed at scientists and engineers who know nothing about multigrid and multilevel methods. It provides some basic information, examples, algorithms (linear, nonlinear, and time dependent PDE's; single and multiple processors), and other sources of information available on the Internet and World Wide Web. ====> If you think your web site should be in <==== ====> this, let me know as soon as possible. <==== Editor's Note: in mgnet/papers/Douglas/cse.ps.gz and .../cse.abs. ------------- ------------------------------------------------------- Date: Wed, 31 Jan 1996 09:20:16 -0500 From: Craig Douglas Subject: 1995 Copper Mountain Proceedings Update For those of you wondering what ever happened to the last proceedings... This is expected to be completed and mailed to the participants and anyone else who requests a copy (more on this later) sometime in the next 2 months. NASA is publishing the proceedings. NASA does not have a real budget for this fiscal year (October-September), so things slowed down considerably (particularly during the US government shutdowns). If you want a printed copy of the proceedings, send e-mail to Duane Melson at melson@cfd356.larc.nasa.gov. He can tell you what is needed to get one. The editing process is nearly done. I have received several updates this month which are in the electronic version of the proceedings. If you have updated the printed version and not the electronic one, please put an update in mgnet/incoming/YourLastName on casper.cs.yale.edu and send me e-mail. ------------------------------------------------------- Date: Wed, 31 Jan 1996 09:20:16 -0500 From: Craig Douglas Subject: MGNet Tutorials Update The first tutorials are now accessible from the MGNet web pages. An effort will be made to provide a PostScript file of each one put here, but that will not be instantaneous, nor will it always be possible. ------------------------------------------------------- Date: Wed, 31 Jan 1995 15:52:59 -0500 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] R. Arina and C. Canuto, A self adaptive domain decompo- sition for the viscous/inviscid coupling. I. Burgers equation, J. Comput. Phys., 105 (1993), pp. 290-300. [2] L. Badea, On the Schwarz alternating method with more than two subdomains for nonlinear monotone problems, SIAM J. Numer. Anal., 28 (1991), pp. 179-204. [3] N. S. Bakhvalov and A. V. Knyazev, A new iterative algo- rithm for solving problems of the fictitious flow method for elliptic equations, Soviet Math. Doklady, 41 (1990), pp. 57- 62. [4] ______, Fictitious domain methods and computation of homoge- nized properties of composites with a periodic structure of essentially different components, in Numerical Methods and Applications, CRC Press, Boca Raton, 1994, pp. 221-276. [5] R. E. Bank and L. R. Scott, On the conditioning of finite element equations with highly refined meshes, SIAM J. Nu- mer. Anal., 26 (1989), pp. 1383-1394. [6] R. E. Bank and K. Smith, A posteriori estimates based on hi- erarchical basis, SIAM J. Numer. Anal., 30 (1993), pp. 921- 935. [7] S. T. Barnard and H. D. Simon, A fast multilevel implemen- tation of recursive spectral bisection, in Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, 1993, pp. 711-718. [8] C. B"orgers and O. B. Widllund, On finite element do- main imbedding methods, SIAM J. Numer. Anal., 27 (1990), pp. 963-978. [9] F. Bornemann, B. Erdmann, and R. Kornhuber, Adap- tive multilevel-methods in three space dimensions, Int. J. Numer. Methods Engng., 36 (1993), pp. 3187-3203. [10] X.-C. Cai, An optimal two-level overlapping domain decompo- sition method for elliptic problems in two and three dimen- sions, SIAM J. Sci. Stat. Comput., 14 (1989), pp. 239-247. [11] J. C. Cavendish, Automatic triangulation of arbitrary planar domains for the finit element method, Int. J. Numer. Meth. Engng., 8 (1974), pp. 679-696. [12] T. W. Clark, R. v. Hanxleden, J. A. McCammon, and L. R. Scott, Parallelizing molecular dynamics using spa- tial decomposition, in Proceedings of the Scalable High- Performance Computing Conference, IEEE Computer Soc. Press, 1994, pp. 95-102. [13] R. K. Coomer, Parallel Iterative Methods in Semiconductor Device Modelling, PhD thesis, University of Bath, Bath, 1994. [14] L. Demkowicz, J. T. Oden, W. Rachowicz, and O. Hardy, Toward a univeral hp adaptive finite element strategy, part 1. Constrained approxiamation and data struc- ture, Comput. Meth. Appl. Mech. Engrg., 77 (1989), pp. 79- 112. [15] V. Eijkhout and P. S. Vassilevski, The role of the strength- ened Cauchy-Buniakowskii-Schwarz inequality in multilevel methods, SIAM Review, 33 (1991), pp. 405-419. [16] R. E. Ewing, R. D. Lazarov, and P. S. Vassilevski, Local refinement techniques for elliptic problems on cell-centered grids. I: Error analysis, Math. Comp., 56 (1991), pp. 437- 461. [17] C. Farhat and F.-X. Roux, An unconventional domain decomposition method for an efficient parallel solution of large-scle finite element systems, SIAM J. Sci. Stat. Com- put., 13 (1992), pp. 379-396. [18] T. Furnike, Computerized multiple level substructuring analy- sis, Comput. Struct., 2 (1972), pp. 1063-1073. [19] R. Glowinski, Viscous flow simulation by finite element meth- ods and related numerical techniques, in Progress and Super- computing in Computational Fluid Dynamics, Birkhauser, Boston, 1985, pp. 173-210. [20] R. Glowinski, T. W. Pan, and J. P'eriaux, A fictitious do- main method for Dirichlet problem and applications, Comp. Meth. Appl. Mech. Engng., 111 (1994), pp. 283-303. [21] ______, A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations, Comp. Meth. Appl. Mech. Engng., 112 (1994), pp. 133-148. [22] D. Gottlieb and R. S. Hirsh, Parallel pseudo-spectral do- main decompostion techniques, J. Sci. Comput., 4 (1989), pp. 309-325. [23] M. Griebel, Grid- and point-oriented multilevel algorithms, in Notes on Numerical Fluid Mechanics, vol. 41, Vieweg, Braunschweig, 1993, pp. 32-46. [24] M. Griebel, M. Schneider, and C. Zenger, A combina- tion technique for the solution of sparse grid problems, in Proceedings of the IMACS International Symposium on It- erative Methods in Linear Algebra, Amsterdam, 1992, Else- vier, pp. 263-281. [25] W. Hackbusch and G. Wittum, Incomplete Decomposition Algorithms, Theory and Applications, vol. 41 of Notes on Numerical Fluid Mechanics, Vieweg, Braunschweig, 1993. [26] T. Hagstrom, R. P. Tewarson, and A. Jazcilevich, Nu- merical experiments on a domain decomposition algorithm for nonlinear elliptic boundary value problems, Appl. Math. Lett., 1 (1988), pp. 299-302. [27] K.-H. Hoffmann and J. Zou, Parallel algorithms of Schwarz variant for variational inequalities, Num. Funct. Anal. Opt., 13 (1992), pp. 449-462. [28] M. J. Holst, Multilevel methods for the Poisson-Boltzmann equation, PhD thesis, University of Illnois, Urbana- Champaign, 1993. [29] M. J. Holst, R. Kozack, F. Saied, and S. Subramaniam, Treatment of electrostatic effects in protein: Multigrid- based-Newton iterative method for solution of the full non- linear Poisson-Boltzmann equation, Protein: Structure, Function, and Genetics, 18 (1994), pp. 231-245. [30] R. H. W. Hoppe and R. Kornhuber, Adaptive multilevel- methods for obstacle problems, SIAM J. Numer. Anal., 31 (1994), pp. 301-323. [31] G. C. Hsiao and W. L. Wendland, Domain decomposition via boundary element methods, in Numerical Methods in En- gineering and Applied Sciences Part I, CIMNE, Barcelona, 1992, pp. 198-207. [32] E. Katzer, A subspace decomposition twogrid method for hy- perbolic equations, PhD thesis, Universit"at Kiel, Kiel, Ger- many, 1992. [33] B. N. Khoromskij and W. L. Wendland, Spectally equiva- lent preconditioners for boundary equations in substructur- ing techniques, East-West J. Numer. Math., 1 (1992), pp. 1- 25. [34] U. Langer, Parallel iterative solution of symmetric coupled FE/BE- equations via domain decomposition, Contemp. Math., 157 (1994), pp. 335-344. [35] W. Layton and P. Rabier, Domain decomposition via opera- tor splitting for highly nonsymmetric problems, Appl. Math. Lett., 5 (1992), pp. 67-70. [36] P. LeTallec, Y-H. deRoeck, and M. Vidrascu, Domain- decomposition methods for large linearly elliptic three dimen- sional problems, J. Comput. Appl. Math., 34 (1991), pp. 93- 117. [37] A. M. Matsokin and S. V. Nepomnyaschikh, Method of fictitious space and explicit extension operators, Z. Vycisl. Mat. i. Mat. Fiz., 33 (1993), pp. 52-68. [38] G. A. Meurant, Domain decomposition methods for partial differential equations on parallel computers, Int. J. Super- computer Appl., 2 (1988), pp. 5-12. [39] F. Nataf, M'ethodes de Schur g'en'eralis'ees pour l'equation d'advection-diffusion (generalized Schur methods for the advection-diffusion equation, C. R. Acad. Sci. Paris, t. 314, S'erie I (1992), pp. 419-422. [40] J. T. Oden, A. Patra, and Y. S. Feng, An hp adaptive strategy, in Adaptive, Multilevel and Hierarchical Computa- tiona Strategies, AMD-Vol. 157, 1992, pp. 23-46. [41] P. Oswald, On discrete norm estimates related to multilevel preconditioners int the finite element method, in Construc- tive Theory of Functions, Proc. Int. Conf. Varna 1991, Sofia, 1992, Bulg. Acad. Sci., pp. 203-214. [42] ______, On the convergence rate of SOR: a worst case estimate, Comput., 52 (1994), pp. 245-255. [43] Jr. P. G. Ciarlet, Etude de pr'econditionnements parall`eles pour la r'esolution d''equations aux d'eriv'ees partielles ellip- tiques. Une d'ecomposition de l'espace L2( ), PhD thesis, University of Paris, Paris, 1992. [44] V. Pereyra, W. Proskurowski, and O. B. Widlund, High order fast Laplace solvers for the Dirichlet problem on gen- eral regions, Math. Comput., 31 (1977), pp. 1-16. [45] R. Peyret, The Chebyshev multidomain approach to stiff prob- lems in fluid mechanics, Comp. Meth. Appl. Mech. Engrg., 80 (1990), pp. 129-145. [46] W. Proskurowski and O. B. Widlund, On the numerical solution of Helmholtz's equation by the capacitance matrix method, Math. Comp., 30 (1976), pp. 433-468. [47] ______, A finite element - capacitance matrix method for the Neu- mann problem for Laplace's equation, SIAM J. Sci. Stat. Comput., 1 (1980), pp. 410-425. [48] J. P. Pulicani, A spectral multidomain method for the solu- tion of 1D-Helmholtz and Stokes-type equations, Comput. Fluids, 16 (1988), pp. 207-215. [49] A. Quarteroni, Domain decomposition and parallel processing for the numerical solution of partial differential equations, Surv. Math. Industry, 1 (1991), pp. 75-118. [50] M. F. Rubinstein, Combined analysis by substructures and recursion, ASCE J. Structural Division, 93 (ST2) (1967), pp. 231-235. [51] H. D. Simon, Partitioning of unstructured problems for parallel processing, Comput. Syst. Eng., 2 (1991), pp. 135-148. [52] M. D. Skogen, Schwarz methods and parallelism, PhD thesis, University of Bergen, Bergen, Norway, 1992. [53] B. F. Smith, A domain decomposition algorithm for elliptic problems in three dimensions, Numer. Math., 60 (1991), pp. 219-234. [54] B. F. Smith and O. Widlund, A domain decomposition algo- rithm using a hierarchical basis, SIAM J. Sci. Stat. Comput., 11 (1990), pp. 1212-1226. [55] M. Sun, Domain decomposition algorithms for solving Hamilton- Jacobi-Bellman equations, Numerical Functional Analysis and Optimization, 14 (1993), pp. 145-166. [56] R. A. Sweet, A cyclic reduction algorithm for solving block tridiagonal systems of arbitrary dimension, SIAM J. Numer. Anal., 14 (1977), pp. 706-720. [57] W.-P. Tang, Generalized Schwarz splittings, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 573-595. [58] P. S. Vassilevski, S. I. Petrova, and R. D. Lazarov, Finite difference schemes on triangular cell-centered grids with local refinement, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 1287-1313. [59] H. Wang, T. Lin, and R. E. Ewing, ELLAM with domain decomposition and local refinement techniques for advection- reaction problems with discontinuous coefficients, in Compu- tational Methods in Water Resources IX, vol. 1, Computa- tional Mechanics Publications and Elsevier Applied Science, London, 1992, pp. 17-24. [60] L. Zhou and H. F. Walker, Residual smoothing techniques for iterative methods, SIAM J. Sci. Comput., 15 (1994), pp. 297-312. ------------------------------ End of MGNet Digest **************************