Send mail to: mgnet@cs.yale.edu for the digests mgnet-requests@cs.yale.edu for comments or help Anonymous ftp repository: casper.cs.yale.edu (128.36.12.1) ftp.cerfacs.fr (138.63.200.33) 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 (douglas-craig@cs.yale.edu) Volume 6, Number 8 (approximately August 31, 1996) Today's topics: Dissertation - Adaptive Iterative & Multigrid on Non-structured Meshes Four Preprints (Jun Zhang) Preprint for MGNet (Gjesdal and Lossius) Multigrid for Refined Triangle Meshes Paper MGNet Bib Entries (Vandewalle et al) Strobl Virtual Proceedings Updated 8th Copper Mountain Conference on Multigrid Methods ------------------------------------------------------- Date: Tue, 13 Aug 1996 11:03:42 -0300 From: Marco Lucio Bittencourt Subject: Dissertation - Adaptive Iterative & Multigrid on Non-structured Meshes Adaptive Iterative and Multigrid Methods Applied to Non-structured Meshes Marco Lucio Bittencourt Universidade Estadual de Campinas Faculdade de Engenharia Mecanica Dipartimento de Projecto Mecanico Campinas, S.P. - Brasil Abstract This work presents direct, iterative and multigrid methods for solving systems of equations obtained by means of the finite element method applied to linear elliptic problems, considering two and three dimensional elastic examples. Adaptive analysis aspects are also discussed by taking an error estimator and some stress recovery procedures. All the algorithms are implemented using the object-oriented model with the C++ language. Comparisons between direct and iterative methods concerned to the number of operations and memory space are presented. The superiority of the iterative techniques accelerated by multigrid strategies can be detected, mainly on three dimensional applications. The multigrid methods have been used at most with nested meshes. In such cases the treatment of engineering problems with complex boundaries becomes difficult. In this thesis, the meshes are non-structured and non-nested and they are generated by frontal and Delaunay techniques. By using adaptive procedures, it is possible to get an optimal sequence of meshes for solving a problem within a specified admissible error. The numerical procedures were linked with some other developed programs, using the object paradigm in C++. Two environments with tools for defining geometrical boundaries, automatic meshes generation, errors estimation, meshes refinement and visualization of results are also presented, considering two dimensional linear elastic problems. Editor's Note: now in mgnet/papers/Bittencourt/thesis.ps.gz ------------- ------------------------------------------------------- Date: Sat, 17 Aug 1996 12:24:26 -0400 From: Jun Zhang Subject: Four Preprints (Jun Zhang) I have uploaded four preprints to mgnet... Jun Zhang Department of Mathematics The George Washington University Washington, DC 20052, USA zhang@math.gwu.edu http://gwis2.circ.gwu.edu/~yaohan A Cost-Effective Multigrid Projection Operator (to appear in Journal of Computational and Applied Mathematics.) Abstract A novel heuristic residual analysis is proposed to derive a computationally cost-effective residual projection operator in multigrid with the five-point Red-Black Gauss-Seidel relaxation for solving the two dimensional Poisson equation. This optimal residual injection operator is as cheap as the trivial injection operator, but is more efficient than the costly full-weighting operator and achieves near-optimal convergence rate. 1991 Mathematical Subject Classification: 65F10, 65N06, 65N22, 65N55. Key words and phrases: Multigrid method, residual projection, Poisson equation, Red-Black Gauss-Seidel. Editor's Note: in mgnet/papers/Zhang/optimal.ps.gz ------------- Accelerated Multigrid High Accuracy Solution of the Convection-Diffusion Equation with High Reynolds Number (to appear in Numerical Methods for PDEs) Abstract A fourth-order compact finite difference scheme is employed with the multigrid algorithm to obtain highly accurate numerical solution of the convection-diffusion equation with very high Reynolds number and variable coefficients. The multigrid solution process is accelerated by a minimal residual smoothing (MRS) technique. Numerical experiments are employed to show that the proposed multigrid solver is stable and yields accurate solution for high Reynolds number problems. We also show that the MRS acceleration procedure is efficient and the acceleration cost is negligible. Key words: Convection-diffusion equation, multigrid method, high-order compact discretization, minimal residual smoothing. Editor's Note: in mgnet/papers/Zhang/accel.ps.gz ------------- On Convergence of Iterative Methods for a Fourth-Order Discretization Scheme (to appear in Applied Mathematics Letters) Abstract We prove that, under certain conditions, some classical iterative methods converge for the linear system resulting from a fourth-order compact discretization of the convection-diffusion equation. Key words: Linear systems, iterative methods, fourth-order compact discretization scheme, convection-diffusion equation. Editor's Note: in mgnet/papers/Zhang/conv.ps.gz ------------- Residual Scaling Techniques in Multigrid, I: Equivalence Proof (to appear in Applied Mathematics and Computation) Abstract This paper addresses the residual scaling techniques (coarse-grid-correction optimization techniques) in multigrid methods. We survey recent developments in this area and prove the equivalence of the over-weighted residual technique and the over-correction technique. This leads to the proof of mathematical equivalence of the pre-scaling and post-scaling acceleration techniques. Two theorems have been proved to unify the concept of the residual scaling techniques. These theoretical results clear the way for developing efficient pre-scaling acceleration techniques for practical applications. Those practical pre-scaling acceleration techniques are discussed in a companion paper: Residual scaling techniques, II: practical applications. Key words and phrases: Multigrid method, residual scaling techniques, heuristic residual analysis. Editor's Note: in mgnet/papers/Zhang/scaling1.ps.gz ------------- ------------------------------------------------------- Date: Thu, 22 Aug 1996 16:26:11 +0200 From: Thor Gjesdal Subject: Preprint for MGNet Comparison of Pressure Correction Smoothers for Multigrid Solution of Incompressible Flow Thor Gjesdal and Magni El\'{e}n Hope Lossius Christian Michelsen Research as Fantoftvegen 38, PO Box 3, N-5036 Fantoft, Norway Phone (+47) 55 57 40 40, fax (+47) 55 57 40 41 e-mail: Thor.Gjesdal@cmr.no Abstract We compare the performance of different pressure correction algorithms used as basic solvers in a multigrid method for the solution of the incompressible Navier-Stokes equations on non-staggered grids. Numerical tests were performed on several cases of lid-driven cavity flow using four different pressure correction schemes, including the traditional SIMPLE and SIMPLEC methods as well as novel variants, and varying combinations of under-relaxation parameters. The results show that three of the four algorithms tested are robust smoothers for the multigrid solver, and that one of the new methods converges fastest in most of the tests. Keywords: Incompressible laminar flow, Navier-Stokes equations, Multigrid methods, Pressure correction methods. 1991 Mathematics Subject Classification: 76D05, 76M20, 65N55, 35A40 Editor's Note: in mgnet/papers/Gjesdal-Lossius/pcorr_mg.ps.gz ------------- ------------------------------------------------------- Date: Thu, 29 Aug 1996 18:04:04 -0600 (MDT) From: Yair Shapira Subject: Multigrid for Refined Triangle Meshes Paper Multigrid for Refined Triangle Meshes Yair Shapira * Abstract A two-level preconditioning method for the solution of (locally) refined finite element schemes using triangle meshes is introduced. In the isotropic SPD case, it is shown that the condition number of the preconditioned stiffness matrix is bounded uniformly for all sufflciently regular triangulations. This is also verified numerically for an isotropic diffusion problem with highly discontinuous coefflcients. * Computer Science Department, Technion, Haifa 32000, Israel. Now at Los Alamos National Laboratory, MS B-256, Los Alamos, NM 87545, e-mail: yairs@lanl.gov. Editor's Note: in mgnet/papers/Shapira/reftriangle.ps.gz ------------- ------------------------------------------------------- Date: Thu, 8 Aug 1996 10:17:41 +0200 From: Stefan Vandewalle Subject: MGNet Bib Entries @ARTICLE{vdw:vand:94, AUTHOR = {Vandewalle, S. and Van de Velde, E.}, TITLE = {Space-time Concurrent Multigrid Waveform Relaxation}, YEAR = 1994, JOURNAL= {Annals of Num. Math.}, MONTH = apr, VOLUME = 1, NUMBER = {1-4}, PAGES = {347--363} } @ARTICLE {jans:vdw:96a, AUTHOR = "Janssen, J. and Vandewalle, S.", TITLE = "Multigrid waveform relaxation on spatial finite element meshes: the discrete-time case", MONTH = jan, JOURNAL= sisc, VOLUME = 17, NUMBER = 1, YEAR = 1996, Pages = {133--155} } @ARTICLE {jans:vdw:96b, AUTHOR = "Janssen, J. and Vandewalle, S.", TITLE = "Multigrid waveform relaxation on spatial finite element meshes: the continuous-time case", MONTH = apr, JOURNAL= sinum, VOLUME = 33, NUMBER = 2, YEAR = 1996, PAGES = {456--474} } Editor's Note: added to mgnet/bib/mgnet.bib in the MGNet format. ------------- ------------------------------------------------------- Date: Tue, 3 Sep 96 10:29:11 +0200 From: @mephisto.numa.uni-linz.ac.at:ghaase@mephisto (Dr. Gundolf Haase) Subject: Strobl Virtual Proceedings Updated Now, there are 28 contributions available in the V i r t u a l P r o c e e d i n g s of the N i n t h I n t . G A M M - W o r k s h o p on P a r a l l e l M u l t i g r i d M e t h o d s Editor's Note: These can be accessed through the MGNet virtual conference ------------- web page (or ftp) and through the web page at Linz, http://www.numa.uni-linz.ac.at/Workshops. The additions since last month's digest are the following: Carsten Carstensen: Domain Decomposition For A Non-smooth Convex Minimization Problem And Its Application To Plasticity. Michael Griebel, Thomas Grauschopf, and Hans Regler : Additive Multilievel Preconditioners based on Bilinear Interpolation, Matrix Dependent Geometric Coarsening and Algebraic Multigrid Coarsening for Second Order Elliptic PDEs. Bodo Heise and Michael Jung : Robust Parallel Newton-Multilevel Methods. Ferdinand Kickinger : Algebraic Multigrid Solver for Discrete Elliptic Second Order Problems. Michael Kuhn, M. Goppold, Bodo Heise, and Gundolf Haase : Preprocessing in FE/BE Domain Decomposition Methods. Joachim Schoeberl : Solving the Signorini Problem on the Basis of Domain Decomposition Techniques. Joachim Schoeberl : An Automatic Mesh Generator using Geometric Rules for Two and Three Space Dimensions. ------------------------------------------------------- Date: Wed, 28 Aug 1996 08:04:35 -0600 From: stevem@boulder.colorado.edu (steve mccormick) Subject: 8th Copper Mountain Conference on Multigrid Methods The 8th Copper Mountain Conference on Multigrid Methods is to be held at Copper Mountain, Colorado, April 9-13, 1997. We are seeking funds to support perhaps 10 or more students to attend the Conference and present their papers. The deadline for submission of student papers is December 15, 1996. The deadline for regular submission of author abstracts is January 15, 1997. Information is available on the web at: http://amath-www.colorado.edu/appm/faculty/copper/ Steve McCormick: Appl. Math, C.B. 526, U. of CO, Boulder, CO 80309-0526 (303)492-0662 stevem@newton.colorado.edu ftp://amath.colorado.edu/pub -4066 fax http://amath-www.colorado.edu/appm/faculty/stevem/ Editor's Note: Here is what I found at this address. There are many ------------- hyperlinks, so please look at the document directly. 8th COPPER MOUNTAIN CONFERENCE ON MULTIGRID METHODS APRIL 6-11, 1997 INDEX * Conference Chairs * Program Committee * Circus Chair * Workshop Chair * Special Features * Format * Conference Deadlines * Submission of Abstracts * Where to Submit * Virtual Pre-Proceedings * NASA Proceedings * Special Issue of ETNA * Student Papers * Workshops and Circus Sessions * Location * Conference Registration * Accommodations at Copper Mountain * Transportation * Tentative Schedule (subject to change) * Registration Form CONFERENCE CHAIRS Tom Manteuffel, University of Colorado Steve McCormick, University of Colorado PROGRAM COMMITTEE Joel Dendy , Los Alamos Van Henson , Naval Postgraduate School Jim Jones , ICASE Kirk Jordan, IBM Jan Mandel, CU-Denver Duane Melson, NASA Langley Seymour Parter, Univ. Wisconsin Joseph Pasciak, Brookhaven John Ruge, CU-Denver Klaus Stueben, GMD, Germany Ulrich Trottenberg, GMD, Germany Pieter Wesseling , Univ. of Delft Olof Widlund , Courant Institute Irad Yavneh , Technion CIRCUS CHAIR Craig Douglas , Yale/IBM WORKSHOP CHAIR Paul Frederickson, MathCube SPECIAL FEATURES * Circus--Forum for Late-Breaking Results * Workshops--Informal Topical Discussions * Student Papers and Travel Support * MGNet Virtual Proceedings * NASA Publication of Proceedings * Special Issue of ETNA FORMAT Morning and afternoon sessions will consist of individual talks of approximately 25 minutes each. Workshop and Circus sessions will be held in the evenings. CONFERENCE DEADLINES Student Papers December 15, 1996 Author Abstracts January 15, 1997 Papers for NASA Proceedings March 15, 1997 Guaranteed Availibility of Lodging February 6, 1997 Early Registration February 6, 1997 SUBMISSION OF ABSTRACTS In order to guarantee a spot in the program, each speaker will be asked to submit an abstract by January 15, 1997. Abstracts will only be accepted from the intended speaker. In the list of papers that we will eventually post, we will include the name of the person who submitted the abstract as the speaker along with a link to the email address used in the submission. This year we are asking authors to submit html versions of their abstracts, so symbols should not be used, or at least they should be kept to a minimum. You will find the form for html abstract submission below. Also, anyone who wants to expand on their abstract is encouraged to submit a ps file to the Virtual Proceedings described below. WHERE TO SUBMIT Potential contributors should submit an abstract by email to cm97@boulder.colorado.edu . Click here to display the html form for submitting your abstract. Then please download or copy it, fill in the information, and submit it to us by e-mail. Please do not send a ps, TeX, or LaTeX file. It will be returned if you do. Your abstract submission must be in html format, but you are also welcome to submit a ps file of an extended abstract or paper to the Virtual Proceedings described below. Student papers should be submitted in ps format, but students whose papers are accepted will be asked to submit abstracts in html format in due time. Deadline for submission of abstracts is January 15, 1997. VIRTUAL PRE-PROCEEDINGS A tradition of these conferences is a pre-proceedings, available before the conference. As with the 1993 and 1995 conferences, this will only be available electronically on MGNet. There will be no multiple volume set of papers to take home from Copper Mountain. Instead of having to cram your paper into a few pages, you have as many pages as you wish, preferably in an easy to read font. Please submit a PostScript file using the directions for a MGNet preprint submission. Then send e-mail with a message that you submitted a pre-proceedings paper. NASA PROCEEEDINGS Each speaker will be invited to submit a paper to NASA for publication in the final proceedings, which will be published in NASA's Conference Proceedings series. SPECIAL ISSUE OF ETNA We are planning to have a special issue of ENTA (Electronic Transactions on Numerical Analysis) dedicated to this conference. The tentative time-table for submission to ETNA is May 15, 1997. Final versions of all papers (including changes determined in the refereeing process) must be in the hands of ENTA by Dec. 15, 1997. Expected publication (posting) as an ETNA volume: February 15, 1998. Click here to access the ETNA journal and author instructions. STUDENT PAPERS Travel and lodging assistance will be awarded to student authors judged to have the best research papers. Papers containing original research due mainly to the student must be received before Dec. 15, 1995. They must be singly authored and may be no more than 10 pages in length. Sending only an abstract is unacceptable. A panel of judges will determine the best papers. Authors of the best papers will be given a travel stipend, free lodging, and registration, and each will be expected to present their paper in one of the regular conference sessions. We are hoping to support 10 or more students who submit acceptable papers, but this is contingent on funding we are currently seeking. Student papers should be submitted as ps files by e-mail. If this is not possible, a hard copy of the paper may be submitted by regular post to: CMCMM97 UNIVERSITY OF COLORADO PROGRAM IN APPLIED MATH CAMPUS BOX 526 BOULDER CO 80309-0526 Postdocs are not considered "students" for this competition--nor are they eligible for student registration fees. WORKSHOPS AND CIRCUS SESSIONS The program will include special time set aside for Workshops and Circuses. The Workshop Chairman will encourage and support informal workshops on special topics of interest. The Circus Chairman, for each of the three planned circus sessions, will encourage participation and contributions and will organize, set the schedule, and oversee its progress. LOCATION The conference will be held at Copper Mountain, Colorado, located 75 miles west of Denver. They have a current weather picture that you might want to view as the conference approaches! Condominium accommodations and adjacent meeting rooms are located in the Mountain Plaza Conference Center located at the base of the Copper Mountain ski lifts. CONFERENCE REGISTRATION Conference registration is available on line. If you use the on-line registration, your payment must still be received by Feb. 6th, 1997 in order to receive the discounted rates. Sending your name by using the on-line registration will get you on the registeration list, but your fee depends on whether or not you make the early registration deadline of Feb. 6th, 1997. At the bottom of this message are instructions for accessing and sending your registration form. If you are paying by credit card, your form must include the card number and expiration date. If you are paying by check, please mail it with your form. You will receive a discounted rate if your payment is postmarked before February 6, 1997. The only types of payments accepted will be VISA, MASTER CARD, or CHECK (money order). We DO NOT accept American Express. Registration fees include a registration packet, a reception on Sunday evening, coffee breaks each day, and a banquet on Wednesday evening. The fee schedule is stated on the form. Please check the appropriate rate. If paying with a Eurocheque, please add $6.00 for processing. SEND REGISTRATION FORMS TO: CMCMM97 UNIVERSITY OF COLORADO PROGRAM IN APPLIED MATH CAMPUS BOX 526 BOULDER CO 80309-0526 or fax it to CMCMM97 Attn: Steve McCormick at 303-492-4066. No refunds will be given for cancellations after March 6. Full refunds less a $50 service charge will be given if notified before March 6, 1997. ACCOMMODATIONS AT COPPER MOUNTAIN A lodge room has one or two queen beds, and a two-bedroom condominium has one or two queen beds in each bedroom, two baths, a kitchen, a dining area, and fireplace. Please be sure to verify the number of beds with your reservationist. Per night rates are as follows: Lodge Room $92/night Deluxe Studio $107/night One Bedroom Condo $120/night Two Bedroom Condo $183/night Make your room reservation directly with Copper Mountain before February 6, 1997. Availability of rooms cannot be guaranteed after February 6--Copper Mountain reserves the right to release part of our room block if 50% of our block is not reserved at this time. After March 6, all remaining unreserved rooms will be released from our group. Please reserve your lodging as soon as possible: State and local taxes (5.5%) will be added to the cost of the room. Rates prior to April 6 are higher. If available, group rates will be given 2 days before and after the conference. Identify yourself with the CU Math Dept. Conference to get group rates. At time of reservation, a credit card number can hold the room, or you will be asked to send in 1 night's deposit within 14 days. Copper Mountain Resort Reservations North America Toll Free Phone Number: 1-800-458-8386 Direct Phone #: 970-968-2882 & Fax Number: 970-968-6227 Room sharing bulletin board If you are interested in sharing a room (the two bedroom condos are especially nice for that because they sleep up to two per room and they have kitchens and livingrooms), you may scan current contents and/or post your own message. TRANSPORTATION Copper Mountain is located 75 miles west of Denver via Interstate 70, at exit 195. Please make your airline reservation destination Denver International Airport. All major car rental agencies have counters at the airport. We will be arranging for group discounted rates with Resort Express shuttle service. You must identify yourself as attending the "CU Multigrid Methods" conference to receive whatever group rates are arranged. Reservations should be made by calling: 1-800-334-7433 or direct 970-468-7600, or fax: 970-468-0364. Resort Express is located on level 5, the baggage claim level, in the center of the main terminal. In order to receive a full refund for a cancellation, cancellations must be received more than 24 hours in advance of scheduled trip. TENTATIVE SCHEDULE (subject to change) Sunday, April 6 Registration 7:00 - 9:00 p.m. Reception Monday, April 7 8:00 - 12:00 Session 1 4:30 - 6:30 p.m. Session 2 7:30 - 9:30 p.m. Workshops & Circus Tuesday, April 8 8:00 - 12:00 Session 3 4:30 - 6:30 p.m. Session 4 7:30 - 9:30 p.m. Workshops & Circus Wednesday, April 9 8:00 - 12:00 Session 5 4:30 - 6:30 p.m. Session 6 7:30 - 9:30 p.m. Banquet Thursday, April 10 8:00 - 12:00 Session 7 4:30 - 6:30 p.m. Session 8 7:30 - 9:30 p.m. Workshops & Circus Friday, April 11 8:00 - 12:00 Session 9 4:30 - 6:30 p.m. Session 10 The preliminary program will be available by mid to late February by e-mail to: cm97info@boulder.colorado.edu or on the net. For further information e-mail to cm97@boulder.colorado.edu or Steve McCormick (303) 492-0662 stevem@boulder.colorado.edu or Cat Rachwalski (303) 980-8522 phone & fax number Duplication of messages is not necessary! REGISTRATION FORM * On line registration. * Registration form LaTeX file Register by mail by downloading the file. Make hard copy and mail with your fee to: CMCMM97 UNIVERSITY OF COLORADO PROGRAM IN APPLIED MATH; CB 526 BOULDER CO 80309-0526 or Fax to: (303) 492 - 4066. Sample Form Copper Mountain Conference on Iterative Methods Copper Mountain, Colorado, April 6th - April 11, 1997 please use the address you want on the attendee list. Name _________________________________________________ Affiliation _________________________________________ Street Address ______________________________________ _____________________________________________________ _____________________________________________________ Country ______________________________________ e-mail address ______________________________________ phone # ______________________________________ Advanced Registration Fee postmarked before February 6, 1997 ( ) SIAM Member $225.00 ( ) Non-SIAM Member $255.00 ( ) Student $50.00 Registration Fee postmarked 2/6/97 and after or paid at conference ( ) SIAM Member $265.00 ( ) Non-SIAM Member $295.00 ( ) Student $50.00 Method of Payment ( ) Check or money order enclosed Checks written to: Copper Mountain Conference Must be in U.S. funds drawn on a U.S. bank. If paying with a EuroCheque please add $6 to your fee for bank processing. ( ) VISA or MASTERCARD only (No Am.Ex) Card # _______________________________________ Exp. Date _____________________ Signature__________________________________ (if sending by e-mail no signature necessary) ------------------------------ End of MGNet Digest **************************