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Current editor:  Craig Douglas douglas-craig@cs.yale.edu
 

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                 http://www.nchc.gov.tw/RESEARCH/Math/mgnet/www/mgnet.html

Today's editor:  Craig Douglas (douglas-craig@cs.yale.edu)

Volume 11, Number 5 (approximately May 31, 2001)

Today's topics:

     New Publication (LNCSE 18) 
     MG Bibliography Entries
     Summer School on FEM and Industrial Applications in Beijing (July)
     Help on Multigrids Method
     Copper Mountain Virtual Proceedings
       Advancing Analysis Capabilities in ANSYS through Solver Technology
       Large-Eddy Simulation and Multigrid Methods
       Parallel CFD Enhancements on SGI ccNUMA and Cluster Architectures
       On the Accuracy of Multigrid Truncation Error Estimates
       An Additive Schwarz Preconditioner for the Spectral Element Ocean Model
       Local Approximation Estimators for Algebraic Multigrid
       Solution of Radiation Transport Equations with Adaptive Finite Elements
       Multilevel Preconditioners for Lagrange Multipliers in Domain Imbedding

-------------------------------------------------------

Date: Thu, 17 May 2001 13:46:59 +0200
From: "LeThi, Thanh-Ha" 
Subject: New Publication (LNCSE 18) 

Lecture Notes in Comptational Science and Enginnering Vol. 18: U. van
Rienen, M. Guenther, D. Hecht (Eds.) "Scientific Computing in Electrical
Engineering - Proceedings of the 3rd International Workshop, August 20-23,
2000, Warnemuende, Germany"
2001  DM 149,90/Euro 76,64; Softcover   ISBN 3-540-42173-4

This book presents the proceedings of the 3rd International Workshop
"Scientific Computing in Electrical Engineering", held in Warnemuende,
Germany, August 20-23, 2000.  This workshop followed two earlier workshops
held in 1997 at the Darmstadt University of Technology and in 1998 at
Weierstrass Institute for Applied Analysis and Stochastics under the auspices
of the German Mathematical Society.  The main topics of SCEE-2000 were
computational electrodynamics, circuit simulation and coupled problems.  The
objective of the workshop, which was mainly directed at mathematicians and
electrical engineers, was to bring together scientists from universities and
industry with the goal of intensive discussions about modelling and numerical
simulation of electronic circuits and electromagnetic fields.  The book
contains contributions of six invited speakers, 30 contributed speakers and 17
poster presentations.

For further information, please contact

Dr. Martin Peters               
Senior Mathematics Editor    Phone: *49-6221-487 185 
Springer-Verlag              FAX:   *49-6221-487 355
Tiergartenstrasse 17         mailto:Peters@Springer.de
D-69121 Heidelberg, Germany  http://www.springer.de/math/peters.html

Visit our Web site at http://www.springer.de 
                   or http://www.springer-ny.com 

-------------------------------------------------------

Date: Mon, 21 May 2001 13:03:00 -0400 (EDT)
From: Scott Fulton 
Subject: MG Bibliography Entries

Here are two entries for the MG Bibliography:

@article{SRFulton_2001a,
  author =      "S. R. Fulton",
  title =       "An adaptive multigrid barotropic tropical cyclone
                 track model",
  journal =     "Mon. Wea. Rev.",
  volume =      "129",
  year =        "2001",
  pages =       "138--151",
  }
@article{PECiesielski_SRFulton_WHSchubert_1986a,
  author =      "P. E. Ciesielski and S. R. Fulton and W. H. Schubert",
  title =       "Multigrid solution of an elliptic boundary value problem
                 from tropical cyclone theory",
  journal =     "Mon. Wea. Rev.",
  volume =      "114",
  year =        "1986",
  pages =       "797--807",
  }

Also, a CORRECTION:  please DELETE the entry:  

@article{SRFulton_PECiesielski_WHSchubert_1985a,
  author =      "S. R. Fulton and P. E. Ciesielski and W. H. Schubert",
  title =       "Multigrid methods for elliptic problems",
  journal =     "Mon. Wea. Rev.",
  year =        "1985",
  }

This article does NOT exist--the entry is an erroneous duplicate of 
@article{SRFulton_PECiesielski_WHSchubert_1986a)

(from mgnet-bib downloaded 05/21/01:  last modified on April 6, 2001)

Scott R. Fulton
Department of Mathematics and Computer Science
Clarkson University, Potsdam, NY    13699-5815
phone:   315-268-2379       FAX:  315-268-2371

    Editor's Note: The bibliography is now updated.  Jan Mandel also reported
    -------------  broken long lines on download from the Yale server, but not
                   from the Kentucky server.  The files are identical, so it is
                   an intervening server error that I cannot seem to reproduce.
                   Please let me know if you see this error.

-------------------------------------------------------

Date: Sat, 2 Jun 2001 10:15:23 -0500 (CDT)
From: zchen@post.cis.smu.edu (Zhangxin Chen)
Subject: Summer School on FEM and Industrial Applications in Beijing (July)

Summer School on Finite Elements and Their Applications in Industry

July 9 - 13, 2001

Institute of Applied Physics and Computational Mathematics
Academy of Sciences, Beijing, China

Speakers:
Hongsen Chen, University of Wyoming, USA
Zhangxin Chen, Southern Methodist University, USA
Richard E. Ewing, Texas A&M University, USA
Zhong-Ci Shi, Academy of Sciences, China
Zhimin Zhang, Wayne State University, USA
Dongming Wei, University of New Orleans, USA

For more information on the School, please contact
Dr. Xijun Yu at yuxj@mail.iapcm.ac.cn

-------------------------------------------------------

Date: Sun, 03 Jun 2001 09:36:32 +0800
From: Zhiwen Zhu 
Subject: Help on Multigrids Method

I am working on the simulation for incompressible flow around irregular body
using the projection method, because of rate of convergence for the pressure
Poisson equation is too much slow, multigrids method must be used to speed up
the solution, for the fluid flow around the irregular bodies, if you want to
avoid using too much sentence like "if---then---else", a easy and useful way
is to use the so-called "Block-off method (Partakar, 1980, Numerical Heat
Transfer and Fluid Flow, Hemisphere Publishing Corporation)", which means the
numerical simulation is performed on the domain including both the fluid and
the irregular bodies (using cartesian mesh), in order to solve the pressure
Poisson equation among the solid body (the value of pressure aomong the solid
body can be prescribled), a so large source term is added to the pressure
Poisson equation to get the precribled value of pressure among the solid
bodies, while, the sourece term equal to zero aomng the fluid field, when
solving the pressure equation on coaser grids, it means in a coaser cell, there
will be solid finer cell and fluid finer cell, so trouble appears when solving
the pressure equation.  

How to deal with this kind of cells?  How to perform the restriction and
interpolation?  Anyone with this experence will be appreciated.

Best Regards,
Zhu

-------------------------------------------------------

Date: Tue, 01 May 2001 17:35:37 -0400 (EDT)
From: Craig Douglas 
Subject: Copper Mountain Virtual Proceedings

This issue continues papers associated with the Tenth Copper Mountain
Conference on Multigrid Methods.  There are more that will appear in the next
issue.  Please refer to

    http://www.mgnet.org/mgnet-cm2001.html

for the complete virtual proceedings.

-------------------------------------------------------

Date: Thu, 17 May 2001 14:08:30 -0400
From: Gene Poole 
Subject: Advancing Analysis Capabilities in ANSYS through Solver Technology

      Advancing Analysis Capabilities in ANSYS through Solver Technology

                            G. Poole and Y.-C. Liu

                                 ANSYS, Inc.
                             275 Technology Drive
                             Canonsburg, PA 15317

                                  J. Mandel

                          Department of Mathematics
                       University of Colorado at Denver
                             Denver CO 80217-3364

Abstract

This paper describes substantial improvements in analysis capabilities in a
large scale commercial finite element program made possible by the
implementation of solver technology .  The ANSYS program is a commercial
finite element analysis program which has been in use for thirty years.  The
original code, developed around a direct frontal solver has been expanded over
the years to include full featured pre- and post- processing capabilities
which support a comprehensive list of analysis capabilities including linear
static analysis, multiple nonlinear analyses, modal analysis and many other
analysis types.  The finite element models on which these analyses are used
have continued to grow in size and complexity .  This growth in size and
complexity has been both enabled by and dependent on new solver technology
along with increased computer memory and CPU resources.  Beginning in 1994
ANSYS added a Jacobi preconditioned conjugate gradient solver (JCG) and
subsequently an Incomplete Cholesky Preconditioned Conjugate Gradient solver
(ICCG) to improve thermal analysis capabilities.  In recent years the addition
of the Boeing sparse matrix library for modal and static analysis, and a
proprietary preconditioned conjugate gradient solver as well as additional
iterative solvers to support new CFD capabilities have greatly increased the
number of solver options available in ANSYS.  Most recently , in version 5.7,
ANSYS has added a new domain solver for solving very large structural analysis
solutions on distributed MPI-based computer systems andthe newest iterative
solver option, an algebraic multi-grid iterative solver (AMG).

This paper will describe implementation considerations for the addition of new
solver technology to a large legacy code, compare resource requirements for
the various solver choices and present some comparative results from several
customer generated problems.  The AMG solver benefits, both in improved
robustness and parallel processing efflciency will be described.  The paper
will also discuss some of the implementation challenges that have been
overcome to add new solver technologyto a large existing code.  The role of
solver technologyin meeting current and future demands of large scale
commercial analysis codes will be discussed.

Keywords.  Finite Elements, elasticity , iterative solvers, Algebraic
multigrid

    Editor's Note: See http://www.mgnet.org/mgnet-cm2001.html#Poole-Liu-Mandel
    -------------

-------------------------------------------------------

Date: Fri, 18 May 2001 16:49:26 -0700
From: Sandra Kerstin Naegele 
Subject: Large-Eddy Simulation and Multigrid Methods

                 Large-Eddy Simulation and Multigrid Methods
                                       
                      Sandra Naegele and Gabriel Wittum

                          Technische Simulation, IfI
                           Universitaet Heidelberg
    sandra.naegele@iwr.uni-heidelberg.de and wittum@iwr.uni-heidelberg.de

                                   Abstract

A method to simulate turbulent flows with Large-Eddy Simulation on
unstructured grids is presented.  Two kinds of dynamic models are used to model
the unresolved scales of motion and are compared with each other on different
grids.  Thereby the behaviour of the models is shown and additionally the
feature of adaptive grid refinement is investigated.  Furthermore the
parallelization aspect is adressed.

Keywords. LES, turbulence, multigrid,parallelization
AMS subject classifications. 65N55, 65Y05, 76F65

This work was supported by the Deutsche Forschungsgemeinschaft, SFB 359 and
Center of Applied Scientific Computing at Lawrence Livermore National
Laboratories.

    Editor's Note: See http://www.mgnet.org/mgnet-cm2001.html#Naegele-Wittum
    -------------

-------------------------------------------------------

Date: Sun, 20 May 2001 11:59:08 -0700
From: "Stan Posey" 
Subject: Parallel CFD Enhancements on SGI ccNUMA and Cluster Architectures

                 Considerations for Parallel CFD Enhancements
                   on SGI ccNUMA and Cluster Architectures

                       Mark Kremenetsky and Stan Posey

                            Silicon Graphics Inc,
                            1600 Amphitheatre Pkwy
                            Mountain View CA, USA
                        mdk@sgi.com and sposey@sgi.com

                                 Tom Tysinger

                                  Fluent Inc
                              10 Cavendish Court
                               Lebanon, NH, USA
                                tlt@fluent.com

                                   Abstract

The maturity of Computational Fluid Dynamics (CFD) methods and the
increasing computational power of contemporary computers has enabled
industry to incorporate CFD technology into several stages of a design
process. As the application of CFD technology grows from component level
analysis to system level, the complexity and size of models are increasing
continuously. Successful simulation requires synergy between CAD, grid
generation and CFD solvers.

The requirement for shorter design cycles has put severe limitations on the
turnaround time of the numerical simulations. The time required for (1) mesh
generation for computational domains of complex geometry and (2) obtaining
numerical solutions for flows with complex physics has traditionally been
the pacing item for CFD applications. Unstructured grid generation
techniques and parallel algorithms have been instrumental in making such
calculations affordable. Availability of these algorithms in commercial
packages has grown in the last few years and parallel performance has become
a very important factor in the selection of such methods for production
work.

Although extensive research has been devoted in determining the optimum
parallel paradigm, in practice the best parallel performance can be obtained
only when algorithm and paradigms take into consideration the architectural
design of the target computer system they are intended for. This paper
addresses the issues related to efficient performance of the commercial CFD
software FLUENT on a cache coherent Non Uniform Memory Architecture, or
ccNUMA. Also presented are results from implementation of FLUENT on a
cluster of systems for both the Linux and SGI IRIX operating systems. Issues
related to performance of the message passing system and data placement are
investigated for efficient scalability of FLUENT when applied to a variety
of industrial problems.

Key words:  computational fluid dynamics, FLUENT, parallel performance

    Editor's Note: See http://www.mgnet.org/mgnet-cm2001.html#Kremenetsky-Posey-Tysinger
    -------------

-------------------------------------------------------

Date: Mon, 21 May 2001 12:58:15 -0400 (EDT)
From: Scott Fulton 
Subject: On the Accuracy of Multigrid Truncation Error Estimates

     On the Accuracy of Multigrid Truncation Error Estimates

                        Scott R. Fulton

           Department of Mathematics and Computer Science 
            Clarkson University, Potsdam, NY 13699-5815

                           Abstract

In solving boundary-value problems, multigrid methods can provide
computable estimates of the truncation error by comparing
discretizations on grids of different mesh sizes.  In the standard
formulation, such estimates are contaminated by errors larger than the
truncation error itself unless the residual transfer operator satisfies
a restrictive condition (typically valid for injection but not for full
weighting) or is itself high-order accurate.  This paper proves that a
simple generalization based on the work of Schaffer leads to accurate
truncation error estimates without these restrictions.  Numerical
results for several model problems illustrates the analysis.

    Editor's Note: See http://www.mgnet.org/mgnet-cm2001.html#Fulton
    -------------

-------------------------------------------------------

Date: Wed, 23 May 2001 09:03:31 -0400 (EDT)
From: Craig Douglas 
Subject: An Additive Schwarz Preconditioner for the Spectral Element Ocean Model

   An Additive Schwarz Preconditioner for the Spectral Element Ocean Model
                  Formulation of the Shallow Water Equations

                               Craig C. Douglas
                            University of Kentucky
                        Department of Computer Science
                             325 McVey Hall - CCS
                        Lexington, KY 40506-0045, USA
                             douglas@ccs.uky.edu

                                Gundolf Haase
                       Johannes Kepler University Linz
             Institute for Analysis and Computational Mathematics
           Department of Computational Mathematics and Optimization
                            Altenberger Strasse 69
                             A-4040 Linz, Austria
                          ghaase@numa.uni-linz.ac.at

                             Mohamed Iskandarani
             Rosenstiel School of Marine and Atmospheric Science
                          4600 Rickenbacker Causeway
                             Miami, FL 33149-1098
                         miskandarani@rsmas.miami.edu

                                   Abstract

We  discretize the shallow water equations with an Adams-Bashford scheme 
combined with the Crank-Nicholson scheme for the time derivatives and 
spectral elements for the discretization in space. 
The resulting coupled system of equations will be reduced to a Schur
complement system with a special structure of the Schur complement.  This
system can be solved with a preconditioned conjugate gradients, where the
matrix-vector product is only implicitly given.  We derive an overlapping
block preconditioner based on additive Schwarz methods for preconditioning the
reduced system.

Key words:  Shallow water equations, h-p finite elements, adaptive grids,
multigrid, parallel computing, conjugate gradients, additive Schwarz
preconditioner.

    Editor's Note: See http://www.mgnet.org/mgnet-cm2001.html#Douglas-Haase-Iskandarani
    -------------

-------------------------------------------------------

Date: Wed, 23 May 2001 09:07:03 -0600 (MDT)
From: Jan Mandel 
Subject: Local Approximation Estimators for Algebraic Multigrid

            Local Approximation Estimators for Algebraic Multigrid

                                  Jan Mandel
                          Department of Mathematics
                       University of Colorado at Denver
                             Denver CO 80217-3364

                                   Abstract

In Smoothed Aggregation Algebraic Multigrid, the prolongator is defined by
smoothing of the output of a simpler tentative prolongator.  The weak
approximation property for the tentative prolongator is known to give a bound
on the convergence factor of the two-level and even multilevel method.  It is
known how to bound the constants in the weak approximation property when the
system matrix is given as the sum of positive semidefinite local matrices.  In
practice, however, the local matrices are often not known to the solver, or
the problem is given in terms of local matrices and additional constraints.
We characterize the matrices that can be decomposed in a sum of local positive
semidefinite matrices with only given rows and columns allowed to be nonzero,
and we show that such a decomposition may not always exist.  We then propose a
construction of approximate local matrices that may be used for local
estimates.  Finally , we show how eliminating the constraints from the local
matrices can be used to obtain rigorous bounds.

    Editor's Note: See http://www.mgnet.org/mgnet-cm2001.html#Mandel
    -------------

-------------------------------------------------------

Date: Thu, 24 May 2001 09:35:50 -0400 (EDT)
From: Linda Stals 
Subject: Solution of Radiation Transport Equations with Adaptive Finite Elements

The Solution of Radiation Transport Equations with Adaptive Finite Elements

Linda Stals

Department of Computer Science
Old Dominion University
Norfolk, VA 23529-0162, USA
and
ICASE
NASA Langley Res. Ctr
Hampton, VA 23681-2199, USA

Abstract

We compare the performance of an inexact Newton-multigrid method and Full
Approximation Scheme when solving radiation transport equations.  We also
present an adaptive refinement algorithm and explore its impact on the
solution of such equations.

Keywords:  FAS, Multigrid, NewtonMethod, Radiation Transport

AMS subject classifications:  35K55, 65M55, 65M60, 49M15

    Editor's Note: See http://www.mgnet.org/mgnet-cm2001.html#Stals
    -------------

-------------------------------------------------------

Date: Fri, 25 May 2001 15:37:01 +0300 (EETDST)
From: Jari Toivanen 
Subject: Multilevel Preconditioners for Lagrange Multipliers in Domain Imbedding

Multilevel Preconditioners for Lagrange Multipliers in Domain Imbedding

Janne Martikainen, Tuomo Rossi, and Jari Toivanen

Department of Mathematical Information Technology
University of Jyvaskyla
P.O. Box 35 (Agora)
FIN-40351 Jyvaskyla
Finland
Janne.Martikainen@mit.jyu.fi, Tuomo.Rossi@mit.jyu.fi, Jari.Toivanen@mit.jyu.fi

Abstract

A domain imbedding method where the Dirichlet boundary conditions are treated
using boundary supported Lagrange multipliers isconsidered.  The
discretization leads to a saddle-point problem which is solved iteratively by
using either the PMINRES method with a block-diagonal preconditioner or the
PCG method in an Uzawa type approach.  In both cases, the preconditioning of
the Schur complement related to Lagrange multipliers is based on a special
sparse implementationof BPX/MDS method.  The developed preconditioning
technique is well-suited even for three-dimensional problems in domains with
complicated shapes.  Several numerical experiments for two-dimensional and
three-dimensional problems demonstrate the efflciency and the applicability of
the proposed method.

Key words.  domain imbedding method, Lagrange multipliers, multilevel methods,
preconditioning

AMS subject classifications. 65F10, 65N22, 65N55

    Editor's Note: See http://www.mgnet.org/mgnet-cm2001.html#Martikainen-Rossi-Toivanen
    -------------

------------------------------

End of MGNet Digest
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