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 2, Number 1 (January 16, 1992) Today's topics: New book on fast solver for large sparse systems Book Announcement Multigrid 6 (2 messages) Movements ------------------------------------------------------- Date: Tue, 17 Dec 91 17:59:47 +0100 From: wittum@iwr1.iwr.uni-heidelberg.de (Gabriel Wittum) Subject: New book on fast solver for large sparse systems My book Filternde Zerlegungen Schnelle Loeser fuer grosse Gleichungssysteme Teubner Skripten zur Numerik, Bd. 1 Teubner Verlag Stuttgart, 1992, DM 29.- (in German) is avilable now. It presents Frequency Filtering Decompositions, a new class of solvers for large systems of equations. These merely algebraic solvers are based on a special kind of incomplete decompositions. The basic idea is very similar to multigrid, but the method needs only one single grid. It is very efficient and is suited for symmetric, unsymmetric, and nonlinear problems. The decompositions may also be used as preconditioner or smoother within usual accelerating methods. Besides the description of the algorithms and some model problem analysis, the book includes a convergence theory for these methods. A large section further concentrates on the numerical application. Results of numerical tests are given for several scalar pde such as linear and nonlinear diffusion type equations with varying coeficients, linear and nonlinear convection-diffusion equations with dominating convection, interface problems etc. The results are compared to known methods, showing that frequency filtering is able to compete with standard solvers. ------------------------------------------------------- Date: Fri, 10 Jan 92 15:54:37 MET From: Piet Wesseling(NW)Subject: Book Announcement I am pleased to announce the publication of the following book: An Introduction to Multigrid Methods by P.Wesseling John Wiley & Sons, Chichester, 1992. ISBN 0 471 93083 0 284 pages. Price: $105 Table of contents: 1. Introduction 2. The Essential Principle of Multigrid Methods for Partial Differential Equations 1. Introduction 2. The Essential Principle 3. The Two-Grid Algorithm 4. Two-Grid Analysis 3. Finite Difference and Finite Volume Discretization 1. Introduction 2. An Elliptic Equation 3. A One-Dimensional Example 4. Vertex-Centered Discretization 5. Cell-Centered Discretization 6. Upwind Discretization 7. A Hyperbolic System 4. Basic Iterative Methods 1. Introduction 2. Convergenc of Basic Iterative Methods 3. Examples of Basic Iterative Methods: Jacobi and Gauss-Seidel 4. Examples of Basic Iterative Methods: Incomplete Point LU Factorization 5. Examples of Basic Iterative Methods: Incomplete Block LU Factorization 6. Some Methods for Non-M-Matrices 5. Prolongation and Restriction 1. Introduction 2. Stencil Notation 3. Interpolating Transfer Operators 4. Operator-Dependent Transfer Operators 6. Coarse Grid Approximation and Two-Grid Convergence 1. Introduction 2. Computation of the Coarse Grid Matrix with Galerkin Approximation 3. Some Examples of Coarse Grid Operators 4. Singular Equations 5. Two-Grid Analysis; Smoothing and Approximation Properties 6. A Numerical Illustration 7. Smoothing Analysis 1. Introduction 2. The Smoothing Property 3. Elements of Fourier Analysis in Grid-Function Space 4. The Fourier Smoothing Factor 5. Fourier Smoothing Analysis 6. Jacobi Smoothing 7. Gauss-Seidel Smoothing 8. Incomplete Point LU Smoothing 9. Incomplete Block Factorization Smoothing 10. Fourier Analysis of White-Black and Zebra Gauss-Seidel Smoothing 11. Multistage Smoothing Methods 12. Concluding Remarks 8. Multigrid Algorithms 1. Introduction 2. The Basic Two-Grid Algorithm 3. The Basic Multigrid Algorithm 4. Nested Iteration 5. Rate of Convergence of the Multigrid Algorithm 6. Convergence of Nested Iteration 7. Non-Recursive Formulation of the Basic Multigrid Algorithm 8. Remarks on software 9. Comparison with conjugate gradient methods 9. Applications of Multigrid Methods in Computational Fluid Dynamics 1. Introduction 2. The Governing Equations 3. Grid Generation 4. The Full Potential Equation 5. The Euler Equations of Gasdynamics 6. The Compressible Navier-Stokes Equations 7. The Incompressible Navier-Stokes and Boussinesq Equations 8. Final Remarks ------------------------------------------------------- Date: Tue, 17 Dec 91 16:50:52 -0700 From: smccormi@copper.Denver.Colorado.EDU (McCormick Steve) Subject: Sixth Copper Mountain Conference on Multigrid Methods This is in response to the request by Pat Collins about the next Copper Mountain Conference on Multigrid Methods. Continuing the tradition of having it every two years in the first full week of April, the Sixth conference will be held April 4-10, 1993. The rationale for this timing is that it's the beginning of off-peak season as defined by the Copper Mountain Ski Association, so all prices are much lower, but it's almost always great ski conditions. The conference format has always been with intense morning and evening sessions. I think that this works best in an environment that allows for afternoon recreation to clear the mind and renew energy. Most of you seem to agree. I was just getting ready to write the proposal for funding (Thanks, Craig! Argh!!!) when I read Pat's request for information. This brings me to a request for help: Does anyone out there have any suggestions of (almost) any kind that the organizing committee (which I will soon activate) should consider for the next meeting? We'd love to consider new ideas, or critique of the old ones. You can send them directly to me at: smccormi@copper.denver.colorado.edu As most of you know, the multigrid conferences now alternate with the Copper Mountain Conferences on Iterative Methods, the second of which will be held April 9-14, 1992. It will have a multigrid component to it as before. For more information on that conference, send a message by e-mail (content is irrelevant) to: cm-info@copper.denver.colorado.edu Thanks, Steve McCormick ------------------------------------------------------- Date: Fri, 20 Dec 91 19:52:22 -0500 From: bells (Craig Douglas) Subject: Copper Mountain 6 Steve, I would like to organize a session on trying to define what components should go into a differential equations' library. By this, I do not mean including routines to model underground contaminants or semiconductor devices at the molecular level, but rather, what would these modeling software need in order to construct high level solvers more easily. If you are interested in this, and want to include something in the grant proposal, let me know and I will send you a few pages of LaTeX on this. I spent a lot of time thinking about this during the summer of 1990 and I think I know exactly what not to propose. This could be thought of as a BDES (ala BLAS), but I do not think the field is that well defined. This cannot be a multigrid only library. In fact, it should not even be serial computer only. I am not sure it should be in Fortran, C, C++, or something entirely new. I have an opinion on this, too. (I know, someday I should learn to keep my mouth shut.) Cheers, Craig ------------------------------------------------------- From: Various_People Subject: Movements George ABE Sony Corporation, Research Center Yokohama, Japan. jabe@src.sony.co.jp Dongming Hwang xkx@flyer.ncsc.org Hubert Ritzdorf Institute I1.T GMD 5205 St. Augustin Germany gmap21@f1euler.gmd.de ------------------------------------------------------- End of MGNet Digest **************************