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 4, Number 3 (March 31, 1994) Today's topics: MG Methods for acoustic wave propagation C++ MG codes Adaptive Grid MG Adaptive Finite Difference MG / Richardson Extrapolation Question pltmg7 GAMM Workshop on Multigrid Methods References / Bibliography ... ------------------------------------------------------- Date: Fri, 4 Mar 1994 18:49:55 -0500 (EST) From: Sylvia IslerSubject: MG Methods for acoustic wave propagation I am working on simulating ultrasound wave propagation through human tissue. Given an incident field, the simulation computes the scattered field that results from the incident wave encountering objects in a host medium that are more dense and less compressible than the medium. In the software that I've developed, the complex pressure amplitude is expressed in terms of a Kirchoff integral equation with a 3-D Green's function as the kernel. My advisor suggested looking into multigrid methods for improving the efficiency of the computation which is O(n^4) and takes hours. I would like to know if there is some literature on multigrid methods for solving this type of equation. Thanks in advance, Sylvia Isler ------------------------------------------------------- Date: Tue, 8 Mar 94 18:35:15 -0800 From: baden@cs.ucsd.edu (Scott B. Baden) Subject: C++ MG codes We have written a portable parallel implementation of multigrid in C++, using a software tool called LPAR-X, which has been developed in my research group. We will be distributing LPAR-X along with the multigrid codes in a few weeks. We are finishing a paper on LPAR-X; in the meatime, there is an extended abstract via anonymous ftp at cs.ucsd.edu, in directory pub/baden/LPARX Get the file shpccAbs.ps. LPAR-X runs on the CM-5, Intel Paragon, KSR-1, Cray C-90 (single processor in this release) and networks of workstations under PVM. The multigrid code will run on any of these machines and is is partially dimension-independent. Since LPAR-X simulates parallelism on a single processor, software can be developed on a workstation rather than on production hardware. We will announce the availablility of LPAR-X in a few weeks. Scott Baden CSE Department U. C. San Diego Editor's Note: Coming soon to MGNet, but it is not there yet. ------------- ------------------------------------------------------- Date: Thu, 10 Mar 1994 17:01:51 -0500 (EST) From: sara@msc.cornell.edu Subject: Adaptive Grid MG Hi, I am looking for an adaptive grid multigrid algorithm for solving non-linear partial differential equations using finite difference discretization. Is this available from someone or somewhere? Thanks a lot, Sara Perkovic Chem. Dept. Cornell University Ithaca, N.Y. 14850 (607) 255-0577 Editor's Note: Please cc mgnet@cs.yale.edu. ------------- ------------------------------------------------------- Date: Mon, 28 Mar 1994 08:49:07 -0600 (CST) From: scott@chpc.utexas.edu Subject: Adaptive Finite Difference MG / Richardson Extrapolation Question I have seen your multi grid digest, and I was wondering if you are someone you know can help me with a multigrid problem. The problem in some sense seems trivial, it is to get an adaptive multigrid code working, using finite differencing, to second order. Then, if the solution is precisely second order, it should be extrapolatable to fourth order via Richardson extrapolation. The example problem which I'm trying to solve is: $$ \frac{\partial^2 u}{x^} = f ~~ i = 2,\cdots n-1 $$ with the Dirichlet boundary conditions: $ u_1 = u1 $ , $u_n = un$ where the interior equations are finite differenced to $$ \frac { u_{i+1} + u_{i-1} - 2u_i }{h^2} = f_i . $$ Now I know that there are better methods to solve these equations, but I feel that whatever technique used in one dimension will work in multiple dimensions. My domain will look something like: lev 0 . . . 1 . . . . . 2 . . . . . . . . . 3 . . . . . . . . . 4 . . . . . . . . . i.e. finer grids will in general cover less of the entire the domain then then coarser grids. The algorithm must use finite differencing for arguements which need not be explained. I have searched literature for this and have not been able to come up with anything. And when I try to program this I get results that are not second order, i.e. when I run convergence tests where I keep on doubling the points on the coarsest level, I do not get errors ( u-uexact)/ (uexact), which are reduced by a factor of four, for each doubling. I am in some sense trying to use standard MLAT's. I would appreciate any help Thank you Scott Klasky scott@einstein.ph.utexas.edu (512)-471-4700 t,th (512)-471-2479 m,w,f ------------------------------------------------------- Date: Mon, 14 Mar 94 13:45:08 PST From: reb@sdna1.UCSD.EDU (Randolph E. Bank) To: douglas-craig Subject: pltmg7 I am happy to announce that a new version of the PLTMG package is now available. PLTMG edition 7.0 is a package for solving linear and nonlinear elliptic partial differential equations in general regions of the plane. It is based on continuous piecewise linear triangle finite element approximation, and features a damped Newton iteration, adaptive local mesh refinement, hierarchical basis multigrid iteration, and pseudo-arclength continuation for parameter dependencies. The package also includes an initial mesh generator, a skeleton generator, and several graphics routines. The source code is available by anonymous ftp from Netlib and Mgnet. Full documentation can be obtained in the PLTMG User's Guide, available from SIAM publications, 1400 Architects Building, 117 South 17th Street, Philadelphia PA 19103-5052. They can also be reached by email at pubs@siam.org. The title is: PLTMG: A Software Package for Solving Elliptic Partial Differential Equations (ISBN 0-89871-330-7). Randy Bank Editor's Note: in mgnet/pltmg/pltmg7.tar ------------- ------------------------------------------------------- Date: Mon, 21 Mar 1994 16:02:41 +0200 (MESZ) From: Friedhelm Schieweck Subject: GAMM Workshop on Multigrid Methods Dear colleagues, in the following I want to announce an international workshop on multilevel methods organized by our institute in September this year. If anybody is interested please contact me. Friedhelm Schieweck 1. Announcement The Institute for Analysis and Numerical Mathematics of the University Magdeburg in cooperation with the GAMM Committee "Efficient numerical methods for pde" organizes the GAMM - Workshop on Multilevel Methods Chairmanship: D.Braess (Bochum), U.Langer (Linz), L.Tobiska (Magdeburg) Date: September 26 to 28, 1994 Location: Parkhotel "Schloss Meisdorf", Meisdorf (Harz) Topics: theory and applications of multilevel methods, parallelization aspects, subspace correction methods, hierarchical basis techniques, adaptive refinement Conference fee: about 80 DM Invited Speakers (preliminary list): S.C.Brenner, W.Hackbusch, S.V.Nepomnyaschikh, A.Reusken, V.Shaidurov, J.Xu Registration: until April 15, 1994 Abstracts: 10-20 lines, deadline: May 15, 1994 Accommodation: you can be accommodated in the Parkhotel "Schloss Meisdorf". The price for single and double rooms ranges between 40 and 115 DM per night Contact address: F.Schieweck Department of Mathematics University Magdeburg PSF 4120 D-39016 Magdeburg Germany e-mail: Friedhelm.Schieweck@Mathematik.Uni-Magdeburg.d400.de Phone: +49-391 5592-2236 Fax: +49-391 5592-2758 ------------------------------------------------------- Date: Thur, 31 Mar 1994 13:27:31 -0500 From: douglas-craig (Craig Douglas) Subject: References / Bibliography The bibliography has been extensively updated in the last month. Special thanks to Frederic Lebon, Jeff Scroggs, and Nigel Wright for contributions. Jeff contributed numerous domain decomposition entries from his extensive files. What was added this month was a large number of papers that appeared in journals in 1993. As this digest is already too long, I will put these out later in future digests. ------------------------------------------------------- Date: Tue, 22 Mar 94 15:49:21 +0100 From: fred@lmgc.univ-montp2.fr (Frederic LEBON LMGC) Subject: References of Frederic Lebon I would like to add publications to the mg-net. 1 Lebon F , Raous M a Multigrid method for the Coulomb friction law. Application in reactor technology. Proceedings Femcad-88 Vol2 pp 292-301 Pergamon Press 1988 b Multigrid method for contact with friction in structure assembling problems. Proceedings Smirt 10 Vol B pp 197-202 AASMIRT 1989 c Fixed point and internal multigrid method for friction problems in structural mechanics. Proceedings Gamni 5 vol 1 pp 457-462 Springer-Verlag 1989 2 Lebon F Ledain MA Bellet M Chenot JL Raous M Introduction aux mithodes multigrilles en micanique des structures lineaires et non liniaires. (in french) Calcul des Structures et intelligence artificielle T3 pp 215-230 Pruralis 3 Lebon F Raous M Latil JC Grego L a Multigrid method in non linear structure mechanics New advances in computational structural mechanics Elsevier 1991 b Multigrid method for non linear structure mechanics problems Publications du LMA n0 124 ISSN 0750-7356 pp 127-138 1991 4 Lebon F Remarks on multigrid methods for frictional elastostatics Proceedings of 1st Internatioanl symposium on contact mechanics p 504 1992 5 Alart P Lebon F Multigrid method applied to mixed formulation for frictional contact problem Contact mechanics pp 227-234 Computational mechanics publications 1993 Not yet published in a journal or book 1 Lebon F Two-grid method for regularized frictional elastostatics problem December 1993 2 Grego L Latil JC Lebon F Raous M Multigrid method for unilateral problems with friction February 1994 3 Alart P Lebon F Solution of frictional contact problems using performing preconditioners 4 Lebon F Alart P Doudet P Friction and preconditioners Frederic Lebon Universite Montpellier 2 Laboratoire de Micanique et Ginie Civil Pl. E. Bataillon CC048 34095 Montpellier Cedex 5 France ------------------------------------------------------- Date: 3 Mar 94 09:35:37 GMT From: NIGEL WRIGHT Subject: bibliography @INPROCEEDINGS{Ga87a, author = {P.H. Gaskell and N.G. Wright}, title = {A Multigrid Algorithm for the Investigation of Thermal, Recirculating Fluid Flow Problems}, year = 1987, booktitle = {Numerical Methods in Thermal Problems, Proceedings of The Fifth International Conference}, publisher = {Pineridge Press} } @INPROCEEDINGS{Ga87b, author = {P.H. Gaskell and A.K.C. Lau and N.G. Wright}, title = {Two Efficient Solution Strategies for Use with Higher Order Discretisation Schemes, in the Simulation of Fluid Flow Problems}, year = 1987, booktitle = {Numerical Methods in Laminar and Turbulent Problems, Proceedings of The Fifth International Conference}, publisher = {Pineridge Press} } @ARTICLE{Ga88, author = {P.H. Gaskell and A.K.C. Lau and N.G. Wright}, title = {Comparison of Two Strategies for Use with Higher Order Discretisation Schemes in Fluid Flow Simulation}, year = 1988, journal = {International Journal for Numerical Methods in Fluids}, volume = 8, pages = {1203-1215} } @INPROCEEDINGS{Ga88a, author = {P.H. Gaskell and N.G. Wright}, editor = {A.J. Osiadacz}, title = {Multigrids Applied to a Solution Technique for Recirculating Fluid Flow Problems}, year = 1988, pages = {51-55}, booktitle = {The Proceedings of the IMA Conference on Simulation and Optimisation of Large Systems}, address = {Reading} } @INPROCEEDINGS{Ga88d, author = {P.H. Gaskell and A.K.C. Lau and N.G. Wright}, editor = {Morton {\&} Baines}, title = {The accurate approximation and economic solution of steady-state convection dominated flows}, year = 1988, pages = 425, booktitle = {Numerical Methods for Fluid Dynamics III}, publisher = {Clarendon Press}, address = {Oxford}, series = {IMA Conference series} } @TECHREPORT{Ga88e, author = {P.H. Gaskell and N.G. Wright}, title = {An Improved Multigrid Strategy for the Investigation of Highly Recirculating Fluid Flows}, year = 1988, number = {AIAA 88-3651}, institution = {AIAA} } @INCOLLECTION{Ga90, author = {P.H. Gaskell and P.A. Sleigh and N.G. Wright}, title = {Multigrids and their Role in the Solution of Practical {CFD} Problems}, year = 1990, booktitle = {Multigrid Methods: Special Topics and Applications II}, publisher = {Gesellschaft f\"{u}r Mathematik und Datenverarbeitung}, address = {Sankt Augustin} } @INPROCEEDINGS{ga93, author = {P.H. Gaskell and P.A. Sleigh and N.G. Wright}, title = {Buoyancy driven flow in a uniformly heated cavity: Multigrid benchmark solutions}, year = 1993, pages = 144, booktitle = {Proceedings of the 8th International Conference on Numerical Methods for Thermal Problems}, address = {Swansea} } @INPROCEEDINGS{sl91, author = {P.A. Sleigh and P.H. Gaskell and N.G. Wright}, title = {Non-linear coupled multigrid solutions to thermal problems, employing different nodal grid arrangements and convective transport approximations}, year = 1991, booktitle = {Numerical Methods in Laminar and Turbulent Problems, Proceedings of The Seventh International Conference}, publisher = {Pineridge Press} } @INPROCEEDINGS{wr93a, author = {N.G. Wright and P.A. Sleigh and P.H. Gaskell}, title = {Application of numerical methods to convection in a differentially heated cavity at high aspect ratio}, year = 1993, pages = 443, booktitle = {Proceedings of the 8th International Conference on Numerical Methods for Thermal Problems}, address = {Swansea} } ------------------------------ End of MGNet Digest **************************