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 Today's editor: Craig Douglas (douglas-craig@cs.yale.edu) Volume 7, Number 1 (approximately January 31, 1997) Today's topics: Short Issue Deadlines for Copper Mountain Conference on Multigrid Methods Paper (Diskin) Paper (Kouatchou) Paper (Kuether) Paper (Oswald) Paper (Sterner) Paper (Vasseur) Paper (W. L. Wan) New bib entry (J. Zhang) 4 Conference/Workshop Announcements (Abridged) ------------------------------------------------------- Date: Fri, 31 Jan 1997 11:10:01 -0500 (EST) From: Craig Douglas Subject: Short Issue Due to my moving, this issue is shorter than normal. My apologies; next month I ought to be able to pester more people for material. Many papers were due today or shortly thanks to the European and Copper Mountain multigrid conferences recently held or soon to be held. As always, I am looking for more material. ------------------------------------------------------- From: Steve McCormick Date: Sun, 19 Jan 1997 22:29:38 -0700 (MST) Subject: Deadlines for Copper Mountain Conference on Multigrid Methods For the 8th Copper Mountain Conference on Multigrid Methods (April 6-11), we have extended the deadline for submission of abstracts to February 6th. This is also the deadline for early registration and guaranteed availability of lodging. Please access http://amath-www.colorado.edu/appm/faculty/copper/ for information on how to submit an abstract, register, or reserve a room. There you will also find a bulletin board for sharing rooms, and later in February you will find the schedule. 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/ ------------------------------------------------------- Date: Wed, 29 Jan 1997 11:59:57 +0200 From: Diskin Boris Subject: Paper (Diskin) Multigrid Algorithm with Conditional Coarsening for the Non-aligned Sonic Flow Boris Diskin Department of Applied Mathematics and Computer Science The Weizmann Institute of Science Rehovot, Israel Abstract A multigrid approach using conditional coarsening in constructing solvers for non-elliptic equations on a rectangular grid is presented. Such an approach permits to achieve a full multigrid efficiency even in the case where the equation characteristics do not align with the grid. The 2D sonic-flow equation linearized over a constant velocity field have been chosen as model problem. Efficient FMG solver for the problem is demonstrated. Editor's Note: in Conferences/CopperMtn97/diskin.ps.gz ------------- ------------------------------------------------------- Date: Wed, 29 Jan 1997 14:15:57 +0100 From: "Marc Kuether" Subject: Paper (Kuether) Exponentially fitted hierarchical bases multigrid for the convection-diffusion equation Abstract In this paper we construct hierarchical bases for an exponentially fitted finite element discretisation of the one-dimensional stationary convection-diffusion equation. Then we prove the approximation and smoothing property of the corresponding Hierarchical Bases twogrid method. Key words: Hierarchical Bases Multigrid method, exponentially fitted schemes, convection-diffusion equation. Editor's Note: in Conferences/CopperMtn97/kuether.ps.gz ------------- ------------------------------------------------------- Date: Wed, 29 Jan 1997 10:46:57 -0500 From: Jules Kouatchou Subject: Paper (Kouatchou) Asymptotic Stability of a 9-point Multigrid Algorithm for the Convection-Diffusion Equations Jules Kouatchou Department of Mathematics The George Washington University Washington, DC 20052 Abstract We consider the solution of the convection-diffusion equation in two dimension by a 9-point discretization formula combined with multigrid algorithm . We analytically prove the epsilon-asymptotic stability of the coarse-grid operators. Two strategies are examined. A method to compute the asymptotic convergence is described and applied to the multigrid algorithm. Editor's Note: in Conferences/CopperMtn97/kouatchou.ps.gz ------------- ------------------------------------------------------- From: Hubertus.Oswald Subject: Paper (Oswald) Parallel multilevel algorithms for solving the incompressible Navier-Stokes equations with nonconforming finite elements in three dimensions H. Oswald Institut fur Angewandte Mathematik Universitat Heidelberg Im Neuenheimer Feld 294 69120 Heidelberg, Germany Email: Hubertus.Oswald@IWR.uni-heidelberg.de Abstract This paper presents results of a numerical study for unsteady three- dimensional, incompressible flow. A finite element multigrid method is used in combination with a operator splitting techniqueand upwind discretization for the convective term. A nonconforming element pair, living on hexahedrons, which is of order O(h^2/h) for velocity and pressure, is used for the spatial discretization. The second order \theta fractional step scheme is employed for the time discretization. For this approach we present the parallel implementation of a multigrid code for MIMD computers with message passing and distributed memory . Multiplicative multigrid methods as stand-alone iterations are considered. We present a very efflcient implementation of Gauss-Seidel resp. SOR smoothers, which have the same amount of communication as a Jacobi smoother. Editor's Note: in Conferences/CopperMtn97/oswald.ps.gz ------------- ------------------------------------------------------- Date: Wed, 29 Jan 1997 14:04:04 +0100 (MET) From: Erik Sterner Subject: Paper (Sterner) A multigrid smoother for high Reynolds number flows Abstract The linearized Navier-Stokes equations are solved in 2D using a multigrid method where a semi-implicit Runge-Kutta scheme is the smoother. With this smoother the stiffness of the equations due to the disparate scales in the boundary layer is removed and Reynolds number independent convergence is obtained. Editor's Note: in Conferences/CopperMtn97/sterner.ps.gz ------------- ------------------------------------------------------- Date: Wed, 29 Jan 1997 10:43:35 +0000 From: "VASSEUR" Subject: Paper (Vasseur) A FMG-FAS procedure for the fully coupled resolution of the Navier-Stokes equations on cell-centered colocated grids X. Vasseur Ecole Centrale de Nantes CFD Group, LMF UA1217 CNRS 1, rue de la No\"e, B.P. 92101 F-44321 Nantes cedex 3, FRANCE Abstract These last twenty years, the search of robust and efficient strategies for the numerical resolution of the steady or unsteady incompressible Navier-Stokes equations has been a crucial task giving rise to numerous methods. The major obstacle of these equations lies in the absence of pressure terms in the incompressibility constraint. Several ways have been suggested to overcome this difficulty. The first trend is represented by pressure correction methods like SIMPLE or PISO procedures. The main drawback of such techniques lies in the slowing down of convergence when the number of grid points or the clustering ratios over curvilinear grids increase. A possible cure consists in using non-linear multigrid with sequential pressure correction methods as basis solvers (or smoothers). The second trend is to solve the incompressible Navier-Stokes equations in a locally or fully coupled manner, where momentum and continuity equations are solved simultaneously. Coupled strategies for the resolution of the Navier-Stokes equations in primitive variables allow to develop robust solvers and subsequently to understand the limitations of segregated methods. A fully coupled method for the resolution of the incompressible Navier-Stokes equations is presented. This method previously used by Deng et al. (1991) employs a cell-centered colocated grid, standard linearization of convection terms, central difference discretization for both convective and diffusive terms and a pressure Poisson equation approach, leading to deduce from the incompressibility constraint an equation for the pressure variable. The originality of this present work is to introduce auxiliary variables --the so-called pseudo-velocities-- to make easier the flux reconstruction step. The resulting structure of the nodal unknowns matrix consists in seven or nineteen bands of sparse blocks. Direct solvers have been used to solve coupled systems but their use for three-dimensional applications is penalized by strong storage limitations. In order to improve the global efficiency of the algorithm by seeking grid independent convergence rates, a non-linear multigrid approach is chosen by implementing a FMG-FAS (Full Multigrid-Full Approximation Scheme) procedure for the resolution of the coupled system. Numerical treatments and implementation aspects of this non-linear procedure are detailed. Steady laminar lid-driven cavity flows calculations have been performed on three-dimensional geometries to discuss the performances of this approach. The retained test-problems were the three-dimensional versions of the ones investigated by Demirdzic et al. (1992) and Oosterlee et al. (1993) : regular, skewed and L-shaped lid-driven cavities. The non-linear multigrid approach (MGC) is compared with the single grid coupled method (SGC) and decoupled methods based on the sequential PISO algorithm (DC, DC-MG) with different pressure linear solvers respectively Krylov subspace solver and a linear multigrid solver. Computations were performed on cartesian, orthogonal and stretched grids for the regular cubic cavity, cartesian and non-orthogonal grids for the skewed lid-driven cavity (skewness angle : 30 degrees) and finally curvilinear grids for the L-shaped cavity. The chosen Reynolds numbers (Re) are equal to 100 or 400. From the whole numerical results, the main conclusion is that the non-linear multigrid approach seems quite powerful, at least more efficient than decoupled or single grid coupled methods. Editor's Note: in Conferences/CopperMtn97/vasseur.ps.gz ------------- ------------------------------------------------------- Date: Wed, 29 Jan 1997 17:21:19 -0800 (PST) From: Wing-Lok Wan Subject: Paper (W. L. Wan) An Energy-Minimizing Interpolation for Multigrid Methods We shall study multigrid methods from energy minimizations and approximations. Through the analysis of an multigrid method in 1D, we introduce the concepts of stability and the approximation property in the classical theory. Based on them, we derive an energy-minimizing interpolation and present a two level analysis for it. Issues on coarsening are also addressed. Finally, we demonstrate the effectiveness of the multigrid method by applying it to unstructured grids computations and discontinuous coefficient problems. Editor's Note: in Conferences/CopperMtn97/wan.ps.gz ------------- ------------------------------------------------------- Date: Fri, 17 Jan 1997 21:09:51 -0500 From: Jun Zhang Subject: New bib entry (J. Zhang) @article{JZhang_1996b, author = "J. Zhang", title = "A cost-effective multigrid projection operator", year = "1996", journal= "J. Comput. Appl. Math.", month = "December", volume = "76", number = "1", pages = "325-333", } ------------------------------------------------------- Date: Fri, 31 Jan 1997 10:23:01 -0500 (EST) From: Craig Douglas Subject: 4 Conference/Workshop Announcements (Abridged) I condensed these radically. The full texts are on the indicated web pages and MGNet's conference page. From: Maya Neytcheva Date: Thu, 23 Jan 1997 08:41:45 +0100 (MET) Subject: PRISM'97 CONFERENCE on Preconditioned Iterative Solution Methods for Large Scale Problems in Scientific Computations PRISM'97 May 27-29, 1997, University of Nijmegen, The Netherlands SCOPE: The purpose of the conference is to provide a forum for the presentation and the discussion of recent progress in the analysis and implementation of of preconditioned iterative solution methods. This includes their implementation on parallel computer architectures. A stress will be put on applications in various fields where a strong demand of efficient solution of large scale problems exists. FURTHER INFORMATION CAN BE OBTAINED FROM: PRISM'97 attn. O. Axelsson or M. Neytcheva Department of Mathematics Toernooiveld 1, NL-6525 ED Nijmegen, The Netherlands e-mail: summer97@sci.kun.nl fax: +31 (0)24 3652140 http://www-math.sci.kun.nl/math/summer97 * * * * * Date: Thu, 23 Jan 1997 08:42:53 +0100 (MET) From: Maya Neytcheva Subject: Summer school SUMMER SCHOOL on Multilevel preconditioning methods with parallel implementation aspects and applications in Scientific Computing May 19--26, 1997, University of Nijmegen, The Netherlands The summer school will concentrate on methods, concepts, techniques for solving large scale Scientific Computation problems. The methods in focus are iterative methods with multilevel preconditioning, which offer rates of convergence, (almost) independent of the size of the problems (a crucial issue for very large scale real-life applications) and optimal computational complexity. Two important issues are specially emphasized: - efficient parallel implementations of methods of the above type, and - applicability of the methods to practical problems in which large scale linear and nonlinear systems have to be solved, especially for problems originating from material sciences, biomedical computations, and computational mechanics. FURTHER INFORMATION CAN BE OBTAINED FROM: Summer School'97 Attn. Maya Neytcheva Department of Mathematics Toernooiveld 1, NL-6525 ED Nijmegen, The Netherlands e-mail: summer97@sci.kun.nl fax: +31 (0)24 3652140 http://www-math.sci.kun.nl/math/summer97 * * * * * Date: Sun, 26 Jan 1997 21:46:12 -0800 (PST) From: "Scott B. Baden" Subject: Structured Adaptive mesh refinement workshop Workshop on Structured Adaptive Mesh Refinement Grid Methods March 12-13, 1997 Institute for Mathematics and Its Applications University of Minnesota Workshop Goals: This workshop will bring together experts in applications, numerical methods, and software development from academia, the national labs, and industry. The goal of the workshop is to identify common ground in the application and implementation of SAMR, as well as issues requiring specialization. The specific objectives of the workshop are: (i) to improve the general understanding of the application of SAMR to practical problems, (ii) to identify issues critical to efficient and effective implementation on high performance computers, (iii) to stimulate the development of a community code repository for software including benchmarks to assist in the evaluation of software and compiler technologies. Logistics: Further information on registration, accommodations, and travel is available at the following Web site: http://www.cse.nd.edu/amr/wshop.html * * * * * Date: Sun, 19 Jan 1997 20:56:38 GMT From: Chaoqun Liu FIRST AFOSR INTERNATIONAL CONFERENCE ON DIRECT NUMERICAL SIMULATION AND LARGE EDDY SIMULATION (DNS/LES) August 4-8, 1997 Louisiana Tech University, Ruston, Louisiana, USA The FIRST AFOSR INTERNATIONAL CONFERENCE ON DNS/LES (FAICDL), sponsored by the US Air Force Office of Scientific Research (AFOSR), will be hosted by Louisiana Tech University, Ruston, Louisiana, USA on August 4-8, 1997. As computers become more powerful, direct numerical simulation (DNS) and large eddy simulation (LES) become more viable for the prediction and control of transitional and turbulent flows on complex configurations. The conference encourages participants to make presentations on any topics related to DNS and LES. FURTHER INFORMATION Prof. Chaoqun Liu, FAICDL Chairman Department of Mathematics and Statistics Louisiana Tech University P.O. Box 3189 Ruston, LA 71272-0001, USA Tel : (318) 257-2257 Fax : (318) 257-2437 email : cliu@math.latech.edu http://www.math.latech.edu/\~cliu ------------------------------ End of MGNet Digest **************************