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) Today's editor: Craig Douglas (douglas-craig@cs.yale.edu) Volume 3, Number 10 (October 31, 1993) Today's topics: Convergence Rates of Multigrid Methods for Poisson Equations Paper about Gauss adaptive relaxation Hackbusch's Iterative Method Book The bibliography database on MGNet Multigrid solvers for problems with complex data Eighth Domain Decomposition Meeting ------------------------------------------------------- Date: Tue, 05 Oct 93 15:10:53 EDT From: "Shang-Hong Lai"Subject: Convergence Rates of Multigrid Methods for Poisson Equations In the following paper "The convergence rate of a multigrid method with Gauss-Seidel relaxation for the Poisson equation" by Dietrich Braess in Mathematics of Computation, vol.42, no.166, pp.505-519, 1984, it said that the convergence rates of multigrid methods are bounded away from 1 for the Poisson equation independent of the size of the problem as long as the domain is convex or the boundary of the domain is smooth. I would like to know if there is any further results which can relax the conditions of convex domain or smooth boundary and retain the convergence rate of the multigrid method bounded away from 1. Any references or comments related to this question will be greatly appreciated. Shang-Hong Lai e-mail: hong@mosquito.cis.ufl.edu Editor's Note: In a paper in the Feb. 1993 issue of SINUM (pp. 136-158) ------------- is a very different approach to multigrid theory. There are 2 theorems in there that may be useful to you. One is quite simple and at a first glance appears to only say that the convergence rate is bounded by 1. However, one of the parameters (delta) in the theorem can be approximated almost exactly on each correction iteration. Normally this is << 1, which says that the multigrid convergence rate is also << 1 (see the example on pp. 146-147). The other theorem uses an affine space decomposition to get a sharper bound. While much more complicated, it could be used to relax the conditions you are interested in and get a useful bound. I would guess that several readers of this digest will have suggestions, too. Please copy me. Thanks. ------------------------------------------------------- Date: Wed, 20 Oct 1993 17:38:58 +0100 From: Christoph Pflaum Subject: Paper about Gauss adaptive relaxation Our paper Gauss adaptive relaxation for the multilevel solution of partial differential equations on sparse grids has just been downloaded to the mgnet ftp repository. The full paper is available in a compressed postscrip format, the abstract is also available as a plain ascii file. The paper will be published in "J. of Computing and Information". We gave a talk about this topic at the 2nd Gauss Symposium in Munich. Abstract: Gauss adaptive relaxation for the multilevel solution of partial differential equations on sparse grids C. Pflaum U. Ruede Institut fuer Informatik, Technische Universitaet D-80290 Muenchen, Germany e-mail: pflaum/ ruede@informatik.tu-muenchen.de In combination with the multilevel principle, relaxation methods are among the most efficient numerical solution techniques for elliptic partial differential equations. Typical methods used today are derivations of the Gauss -Seidel or Gauss -Jacobi method. Recently it has been recognized that in the context of multilevel algorithms, the original method suggested by Gauss has specific advantages. For this method the iteration is concentrated on unknowns where fast convergence can be obtained by intelligently monitoring the residuals. We will present this algorithm in the context of a sparse grid multigrid algorithm. Using sparse grids the dimension of the discrete approximation space can be reduced additionally. Keywords: adaptivity, multilevel techniques, elliptic PDE, finite elements AMS Classifications: 65N22, 65N30, 65N50, 65N55 Editor's Note: in mgnet/papers/Pflaum-Ruede/gauss.abstract and ------------- mgnet/papers/Pflaum-Ruede/gauss.ps. ------------------------------------------------------- Date: Wed, 20 Oct 1993 16:31:12 PDT From: (Tony Chan) Subject: Hackbusch's Iterative Methods Book ... I recall that you announced Hackbusch's book in a digest a while ago. Could you send me the information again, please? Editor's Note: Actually, I did not announce it. I saw it listed in a ------------- mailing a few months ago, but I do not recall from which publisher. I also do not know if the English translation is out, yet. It was not the last time I asked Hackbusch about it, but it was threatening to be. Could someone please e-mail Tony this information and copy me, please? I will add it to the bibliography database. Thanks. ------------------------------------------------------- Date: Sun, 31 Oct 1993 07:14:32 -0400 From: douglas-craig@cs.yale.edu (Craig Douglas) Subject: The bibliography database on MGNet The BibTeX oriented bibliography database on MGNet has received a very large infusion of citations lately. This is in part because someone else has been entering many hundreds of entries (soon to be thousands) in the multigrid and domain decomposition fields. The relevant files are on casper.cs.yale.edu in the directory mgnet/bib: mg.bib All of the entries sorted (hopefully) in alphabetical order by authors and years. mgbib.tex The LaTeX file to generate the bibliography in paper form. mgbib.dvi The paper form of the bibliography. mgbib.ps The PostScript form of the .dvi file. siam.bst A modified form of SIAM's BibTeX style file that does not convert van's to V.'s. You need this if you plan on using When this was first started, several people asked for a particular change in the keys used for each entry. Recently, another change was requested that I have implemented today. I will now guarantee that any entry in the database will never get a new key again. Period. The final scheme is For example, my dissertation's key from 1982 is CCDouglas_1982a The key for a book by Braess, Hackbusch, and Trottenberg from 1984 is DBraess_WHackbusch_UTrottenberg_1984a The change today was to include the century and to put a letter after every year, not just when I happen to know about multiple ones in a year already. You can help keep this accurate and up to date by spending a few seconds of your time now. Just send me by e-mail or by your postal system your own publication list in these areas (bibtex, ascii, plain paper, vitae style, etc.). Your naming convention will be changed for you; please just send the entries in now. E-mail to douglas-craig@cs.yale.edu or via the post office to me at 8 South Street, Cos Cob, CT 06807-1618, USA. Thanks! ------------------------------------------------------- Date: Wed, 26 Oct 1993 13:09:01 -0400 From: douglas-craig@cs.yale.edu (Craig Douglas) Subject: Multigrid solvers for problems with complex data I am looking for people who are solving (or trying to solve) problems with complex data. I am trying to determine how well the latest abstract multilevel solver I inspired to be written works on such problems. (The code works on real data, too.) ------------------------------------------------------- Date: Sun, 31 Oct 1993 07:20:01 -0400 From: douglas-craig@cs.yale.edu (Craig Douglas) Subject: Eighth Domain Decomposition Meeting At the recent 7th Domain Decomposition Meeting at Penn State, it was announced that the next one will be in Beijing, May 15-19, 1995. This is a tentative date still. ------------------------------ End of MGNet Digest **************************