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) World Wide Web: http://na.cs.yale.edu/mgnet/www/mgnet.html or http://www.cerfacs.fr/~douglas/mgnet.html or http://www.ccs.uky.edu/mgnet Today's editor: Craig Douglas (douglas-craig@cs.yale.edu) Volume 7, Number 6 (approximately June 30, 1997) Today's topics: MGNet finally synchronized Benchmark mailing lists Mesh Coarsening Three Papers by Z. Chen New Paper on MGNet Multigrid Course ------------------------------------------------------- Date: Thu, 19 Jun 97 20:20:01 -0400 From: Craig Douglas Subject: MGNet finally synchronized After 6 years, I finally got all of the copies of MGNet synchronized today. By that, I mean that all 1818 files (roughly 85 Mb total) have identical file dates, sizes, and check sums. There are 5 copies of MGNet, including one behind a firewall. Hopefully, I did not break or lose anything in the process. All copies now look like the main site at Yale. For those of you interested in how the Internet is bearing up to the web, it took about 4 hours to ftp all of MGnet from Yale to Europe. It took about 8 hours to ftp it from Yale to Kentucky. ------------------------------------------------------- Date: Mon, 20 Jun 97 09:45:13 -0400 From: Craig Douglas Subject: Benchmark mailing lists The two mailing lists, mgnetb@ccs.uky.edu for discussions about multigrid benchmarks and model problems mgnetbc@ccs.uky.edu for people wanting to contribute multigrid applications for major benchmarks (like SPEC) are set up and ready for use. All they need now is some traffic. They will be moderated for the next few weeks. Those who indicated they wanted to be on one of these lists earlier (at Copper Mountain or by e-mail to me) need do nothing more. If you want on one of these lists, please send e-mail to mgnet@ccs.uky.edu. ------------------------------------------------------- Date: Sun, 22 Jun 97 23:48:35 -0400 From: Subject: Mesh Coarsening Short version: I am seeking help from multigrid practitioners, in evaluating our automatic mesh coarsening algorithm for 2D unstructured triangular meshes. Long version: I have worked, together with Gary Miller and Shang-Hua Teng, on the geometrical problem of automatic mesh coarsening of two dimensional, unstructured triangular meshes. Our algorithm comes with theoretical guarantees for the aspect-ratio and size of the meshes in the hierarchy, and is very simple and efficient in practice. I'd like to find a person willing to collaborate on testing our algorithm within a multigrid framework: using the unstructured coarsening hierarchy our algorithm produces with a multigrid solver, and seeing if the geometrically good sequence we produce results in improved convergence. I'd also appreciate pointers to other mesh coarsening programs or papers. We tried to address the mesh coarsening problem from a computational geometry point of view. We have developed an algorithm that is guaranteed to generate a coarsening sequence such that all the meshes in the sequence are of good aspect ratio, neighboring meshes approximate each other well, and the size of the meshes is as small as possible (up to a constant factor) under the above restrictions. This work is described in SODA 97. (look also in http://www.cs.cmu.edu/~tdafna/soda97.html) We also worked on a practical variant of the algorithm, and implemented it. This work is not yet published, and is currently described only in my thesis. The algorithm is very simple and efficient. As part of my thesis work, I tested it on a test suite of graded, unstructured meshes, and the algorithm produces high-quality coarsening sequences. The difficulty is, however, that our quality measures are only geometrical and combinatorial in nature: aspect ratio of the mesh elements, and number of elements. Ultimately, I'd like to verify that the coarsening sequences we produce improve convergence behavior of the multigrid method. For that, I'd like to find someone to work with, who has tried to solve a particular differential equation over a graded mesh, and would like to experiment with the coarsening sequences our program generates. I think the better quality of the coarsening sequences we produce is particularly noticeable over very graded, unstructured meshes. Quasi-uniform unstructured meshes are simpler to coarsen, for example by the MIS method. Therefore, I'd like to find someone trying to use the multigrid over very graded unstructured meshes. Please contact me at tdafna@cs.cmu.edu. I would greatly appreciate hearing from people willing to experiment with our coarsening sequences, and I hope that in turn, the coarsening sequences we produce will be helpful to the multigrid community. Thank you, Dafna Talmor tdafna@cs.cmu.edu http://www.cs.cmu.edu/~tdafna ------------------------------------------------------- Date: Sat, 21 Jun 1997 12:04:36 -0500 From: Zhang-xin CHEN Subject: Three Papers by Z. Chen I have put three papers chen I, II, and III (abstracts and PS-files) under mgnet/incoming/ chen. You may announce them in the mgnet news letter. Expanded Mixed Finite Element Methods for Linear Second-Order Elliptic Problems, I Zhangxin Chen Department of Mathematics, Box 156 Southern Methodist University Dallas, Texas 75275--0156, USA. Abstract We develop a new mixed formulation for the numerical solution of second-order elliptic problems. This new formulation expands the standard mixed formulation in the sense that three variables are explicitly treated: the scalar unknown, its gradient, and its flux (the coefficient times the gradient). Based on this formulation, mixed finite element approximations of the second-order elliptic problems are considered. Optimal order error estimates in the Lp- and H-s-norms are obtained for the mixed approximations. Various implementation techniques for solving the systems of algebraic equations are discussed. A postprocessing method for improving the scalar variable is analyzed, and superconvergent estimates in the Lp-norm are derived. The mixed formulation is suitable for the case where the coefficient of differential equations is a small tensor and does not need to be inverted. This paper will appear in RAIRO Mod\`el. Math. Anal. Num\'er. Editor's Note: in mgnet/papers/ChenZ/chenI.ps.gz ------------- Expanded Mixed Finite Element Methods for Quasilinear Second-Order Elliptic Problems, II Zhangxin Chen Department of Mathematics, Box 156 Southern Methodist University Dallas, Texas 75275--0156, USA. Abstract A new mixed formulation recently proposed for linear problems is extended to quasilinear second-order elliptic problems. This new formulation expands the standard mixed formulation in the sense that three variables are explicitly treated; i.e., the scalar unknown, its gradient, and its flux (the coefficient times the gradient). Based on this formulation, mixed finite element approximations of the quasilinear problems are established. Existence and uniqueness of the solution of the mixed formulation and its discretization are demonstrated. Optimal order error estimates in Lp and H-s are obtained for the mixed approximations. A postprocessing method for improving the scalar variable is analyzed, and superconvergent estimates are derived. Implementation techniques for solving the systems of algebraic equations are discussed. Comparisons between the standard and expanded mixed formulations are given both theoretically and experimentally. The mixed formulation proposed here is suitable for the case where the coefficient of differential equations is a small tensor and does not need to be inverted. This paper will appear in RAIRO Mod\`el. Math. Anal. Num\'er. Editor's Note: in mgnet/papers/ChenZ/chenII.ps.gz ------------- Analysis of Expanded Mixed Methods for Fourth-Order Elliptic Problems, III Zhangxin Chen Department of Mathematics, Box 156 Southern Methodist University Dallas, Texas 75275--0156, USA. Abstract The recently proposed expanded mixed formulation for numerical solution of second order elliptic problems is here extended to fourth order elliptic problems. This expanded formulation for the differential problems under consideration differs from the classical formulation in that three variables are treated, i.e., the displacement and the stress and moment tensors. It works for the case where the coefficient of the differential equations is small and does not need to be inverted, or for the case in which the stress tensor of the equations does not need to be symmetric. Based on this new formulation, various mixed finite elements for fourth order problems are considered; error estimates of quasi-optimal or optimal order depending upon the mixed elements are derived. Implementation techniques for solving the linear system arising from these expanded mixed methods are discussed, and numerical results are presented. This paper will appear in Numerical Methods for PDE. Editor's Note: in mgnet/papers/ChenZ/chenIII.ps.gz ------------- ------------------------------------------------------- Date: Sun, 29 Jun 97 10:28:55 -0400 From: Craig Douglas Subject: New Paper on MGNet This was added to mgnet/Conferences/CopperMtn97 and can be found through the conference web page. Craig C. Douglas Minimizing memory cache usage for multigrid algorithms in two dimensions For those of you at the conference dinner, I hope you see the humor in this being the last paper added (so far). ------------------------------------------------------- Date: Mon, 30 Jun 1997 12:45:26 +0200 From: Wolfgang.Joppich@gmd.de (Wolfgang Joppich) Subject: Multigrid Course Dear Ladies and Gentlemen, dear colleagues and friends! I am sorry to disturb you. But this broadcast message is the easiest and cheapest way to attract your attention to a MULTIGRID COURSE at the GMD from Friday 10.10.97 to Sunday 12.10.1997. For more information contact joppich@gmd.de or look at the GMD web-pages http://www.gmd.de and go to News, upcoming events. You may also view directly http://www.gmd.de/SCAI/scicomp/multigrid-course.html If you know about persons which might be interested in such a course, please inform them. Thank you for your help. With kind regards Wolfgang Joppich, GMD-SCAI Editor's Note: This is the information available on the web... ------------- Multigrid Course - Introduction to Standard Methods 10 - 12 October 1997 The Course: This course results from several lecture series Algorithms I/II at the Fachhochschule of Cologne. At the end of the course even beginners without numerical experience will be able to write standard MG programs for model problems. This is possible by an appropriate mixture of heuristics and exactness combined with theory and practice. This concept proved to be successful by the previous course in 1996. Target Group: Everybody who is interested in numerical methods may use this course to start with multilevel algorithms. Students with mathematical or technical interest from universities and Fachhochschulen are encouraged to visit the course. Mathematical Prerequisite: A basic knowledge of numerical analysis is helpful, including standard discretization techniques for partial differential equations (finite differences and similar approaches on cartesian grids), and a general familiarity with iterative solvers for large systems of equations. W. Joppich, GMD-SCAI Program: Friday 10.10.97 14:00 - 14:45 Registration 14:45 - 15:00 Welcome, History and Development of Multigrid Methods 15:00 - 16:30 Basic Principles - Analysis of Relaxation Methods, Course Grid Correction, Correction Scheme 16:30 - 17:00 Coffee Break 17:00 - 18:30 Components of the Multigrid Method - Discretization and Grids, Relaxation (Smoothing), Coarsening Strategies, Coarse Grid Operators, Cycles, Grid Transfer 18:30 - open Programming Saturday 11.10.97 9:00 - 10:30 Full Approximation Scheme (FAS), Full Multigrid (FMG) 10:30 - 11:00 Coffee Break 11:00 - 12:30 Local Refinements (MLAT) - Adaptive Grids, Refinement Criteria, Estimation of the Discretization Error 12:30 - 14:00 Lunch Break 14:00 - 15:30 Parabolic Problems - Implicit Time Discretization, Direct and Indirekt MG 15:30 - 16:00 Coffee Break 16:00 - 17:30 Local Analysis - Smoothing Analysis, Two Grid Analysis 17:30 - 19:00 Programming Sunday 12.10.97 9:00 - 10:30 Presentation of selected Multigrid Programs 10:30 - 11:00 Coffee Break 11:00 - 12:30 Programming, Discussion 12:30 End of the Course Secretariat: Conference and Software Consulting, Ms Karin Joppich, Weilbergstrassee 16, D-53639 oenigswinter, Phone +49 (0) 2244 80098 Location: GMD, Sankt Augustin; C3-T26. Accomodation: Rooms have been reserved for participants in Hotels close to the GMD. The reservation in these hotels will be organized if the subscription has been received before end of August 1997. The price per night, including breakfast, is approximately 90 - 105 DM for a single room. Further information after course subscription. Number of Participants: The maximum number of participants is about 15. The sequence of subscription decides on participation. Course Fee: 350 DM, includes course material (copies of transparencies, preprints, recent publications, if asked for Grundlagen der Mehrgittermethode - eine Einfahrung in die Standardverfahren), refreshments during coffee breaks, lunch on Saturday and sandwiches at Saturday evening. On receiving your subscription form you will get a confirmation, additional information and an invoice. The amount due is to reach us two weeks before the first day of the course. Subscription: Use the attached form and give the requested additional information, if possible. For further information please contact the secretariat or joppich@gmd.de. Cancellation: Cancellations received earlier than two weeks before the first day of the course will be reimbursed less 50 DM administration charge. No reimbursement of the subscription fee will be made for cancellations received later, unless the participant provides a replacement. If for any reason the course will not take place, the subscription fee will be returned in full. Further claims for compensation are excluded. Subscription form - Multigrid Course, 10. - 12. Oktober 1997, please return to Conference and Software Consulting Ms Karin Joppich Weilbergstrasse 16 D-53639 Koenigswinter Germany Ms. / Mr. : Last name : First name : Affiliation: Department : Adress : Postal code: City : Country : Phone/Fax : E-mail : Arrange accomodation ( ) no ( ) yes Arrival : Departure: ( ) special requirement: Place Date Signature Registration implies acceptance of the above conditions of participation. ---------------------------------------------------------------------------- Wolfgang Joppich Tue May 27 13:30:53 MDT 1997 ------------------------------ End of MGNet Digest **************************