```Send mail to:  mgnet@cs.yale.edu             for the digests or bakeoff

Anonymous ftp repository:  www.mgnet.org (128.163.209.19)

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

World Wide Web:  http://www.mgnet.org or
http://casper.cs.yale.edu/mgnet/www/mgnet.html or
http://www.cerfacs.fr/~douglas/mgnet.html or
http://phase.etl.go.jp/mgnet or
http://www.nchc.gov.tw/RESEARCH/Math/mgnet/www/mgnet.html

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

Volume 10, Number 6 (approximately June 30, 2000)

Today's topics:

Mirror Reminder
Multigrid and Voronoi Cell Finite Element Method
Paper Submission (T.L. Beck)
AMG-WS at St. Wolfgang/Strobl
2001-02 NA Year at the Fields Institute in Toronto
LBNL-NERSC Workshop on ACTS
Conference on Inverse Problems
GAMM Seminar on Construction of Grid Generation Algorithms
GAMM Workshop on Computational Electromagnetics

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

Date: Fri, 30 Jun 2000 25:22:11 -0400
From: Craig C. Douglas
Subject: Mirror Reminder

I have been asked several times by people in Europe if there is some way to
speed up transmission speeds from Kentucky (where http://www.mgnet.org sits).
At the top of this newsletter is a list of alternate sites that mirror the
Kentucky site.  If you are having trouble with transmission speeds, please try
directly.

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

Date: Fri, 07 Jul 2000 13:30:36 -0400
From: "Paul M. Eder"
Subject: Multigrid and Voronoi Cell Finite Element Method

My name is Paul Eder.  I am a graduate student at The Ohio State University.
One of the problems that I am working on involves developing code in Fortran
90 to solve problems involving the deformation and damage of composite
materials using the Voronoi Cell Finite Element Method.  Currently, there is
code that solves the entire problem, but it takes around 2 hours for a simple
linear elasticity problem.  There are three levels of elements:

level 0 = basic quadrilateral elements
level 1 = level 0 elements that were adaptively refined around stress
concentrations (these are level 0 elements that are divided into
smaller            elements and represent a general repetition of the microstructure)
level 2 = Voronoi cell elements, adaptively created from level 1 elements
around stress concentrations, that represent the actual microstructure

There is the possibility that all three elements exist simultaneously on
different locations of the geometry.  My goal is to parallelize the code to
run on the SV1 at the Ohio Supercomputer Center and to implement multigrid to
solve the problem.  Ultimately, it is desired to solve level 2 elements only
between level 0 and level 2 wherever level 2 elements exist.

I would like to know if you have any suggestions on what multigrid algorithms
or multigrid packages would be useful in a situation like this.  I have
searched through a lot of web sites and am having difficulty with this.  Any
help that you could provide would be greatly appreciated.

Paul M. Eder
The Ohio State University
Department of Mechanical Engineering
(614)846-7779

Editor's Note: If you think that your multigrid code will help Mr. Eder,

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

Date: Sat, 24 Jun 2000 15:25:24 -0400
From: "Thomas L. Beck"
Subject: Paper Submission (T.L. Beck)

I am submitting a postscript file of a paper called "Real-Space Mesh
Techniques in Density Functional Theory" to MGNet.  This paper will appear in
the Jan. 1, 2001 issue of Reviews of Modern Physics.  It discusses grid
methods for electrostatics and electronic structure calculations (with
extensive discussion of multigrid).

Thomas L. Beck | http://bessie.che.uc.edu/tlb/
Department of Chemistry | becktl@uc.edu
University of Cincinnati | phone: 513-556-4886
Cincinnati, OH  45221-0172 | fax: 513-556-9239

* * * * *

Real-space mesh techniques in density functional theory

Thomas L. Beck
Department of Chemistry, University of Cincinnati, Cincinnati, OH 45221-0172

Abstract

This review discusses progress in efflcient solvers which have as their
foundation a representation in real space, either through finite-difference or
finite-element formulations.  The relationship of real-space approaches to
linear-scaling electrostatics and electronic structure methods is first
discussed.  Then the basic aspects of real-space representations are
presented.  Multigrid techniques for solving the discretized problems are
covered; these numerical schemes allow for highly efflcient solution of the
grid-based equations.  Applications to problems in electrostatics are
discussed, in particular numerical solutions of Poisson and Poisson-Boltzmann
equations.  Next, methods for solving self-consistent eigenvalue problems in
real space are presented; these techniques have been extensively applied to
solutions of the Hartree-Fock and Kohn-Sham equations of electronic structure,
and to eigenvalue problems arising in semiconductor and polymer physics.
Finally, real-space methods have found recent application in computations of
optical response and excited states in time-dependent density functional
theory, and these computational developments are summarized.  Multiscale
solvers are competitive with the most efflcient available plane-wave
techniques in terms of the number of self-consistency steps required to reach
the ground state, and they require less work in each self-consistency update
on a uniform grid.  Besides excellent efficiencies,the decided advantages of
the real-space multiscale approach are 1) the near-locality of each function
update, 2) the ability to handle global eigenfunction constraints and
potential updates on coarse levels, and 3) the ability to incorporate adaptive
local mesh refinements without loss of optimal multigrid efflciencies.

CONTENTS
I. INTRODUCTION 2
II. DENSITY FUNCTIONAL THEORY 5
A. Kohn-Sham equations 5
B. Classical DFT 6
III. LINEAR-SCALING CALCULATIONS 7
A. Classical electrostatics 8
B. Electronic structure 9
IV. REAL-SPACE REPRESENT A TIONS 10
A. Finite differences 11
1. Basic finite-difference representation 11
2. Solution by iterative techniques 12
3. Generation of high-order finite-difference formulas 13
B. Finite elements 14
1. Variational formulation 14
2. Finite-element bases 15
V. MULTIGRID TECHNIQUES 16
A. Essential features of multigrid 16
B. Full approximation scheme multigrid V-cycle 17
C. Full multigrid 18
VI. ELECTROST A TICS CALCULA TIONS 18
A. Poisson solvers 19
1. Illustration of multigrid efficiency 19
2. Mesh-refinement techniques 20
B. Poisson-Boltzmann solvers 21
C. Computations of free energies 23
D. Biophysical applications 25
VII. SOLUTION OF SELF-CONSISTENT EIGENVALUE PROBLEMS 26
A. Fixed-potential eigenvalue problems in real-space 26
1. Algorithms 26
2. Applications 28
B. Finite-difference methods for self-consistent problems 29
C. Multigrid methods 31
D. Finite-difference mesh-refinement techniques 34
E. Finite-element solutions 35
F. Orbital-minimization methods 37
VIII. TIME-DEPENDENT DFT CALCULATIONS IN REAL SPACE 37
A. TDDFT in real time and optical response 38
B. TDDFT calculation of excited states 39
IX. SUMMARY 40
ACKNOWLEDGMENTS 41
Appendix A 41
References 42

Editor's Note: See http://www.mgnet.org/mgnet-papers.html or
-------------  http://www.mgnet.org/mgnet/papers/Beck/rmptb.ps.gz

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

Date: Wed, 28 Jun 2000 22:25:11 -0400
From: Craig C. Douglas
Subject: AMG-WS at St. Wolfgang/Strobl

A great two day workshop was held in Austria.  Below are the talks that were
given.  A virtual proceedings is being constructed by Gundolf Haase and me for
MGNet.  There will be many more details in the July newsletter.  Stay tuned.

* * * * *

Klaus Stueben
Some studies of the AMG performance in critical situations

Johannes Kraus
An Optimal Order Algebraic Multilevel Method

Jim E. Jones
Algebraic Multigrid for Finite Element Problems (AMGe)

Andreas Bollhoefer
AMG Preconditioners for Sparse Approximate Inverse Matrices

Craig C. Douglas
Using a Multilayer Ocean Model on Clusters versus a Traditional Supercomputer

Gundolf Haase
A principle for constructing parallel AMG and its realization:  part I

Michael Kuhn
A principle for constructing parallel AMG and its realization:  part II

Claus Bayreuther
Construction of homogenization based transfer operators

Christian Wagner
On the Algebraic Construction of Multilevel Transfer Operators

Van Emden Henson
AMGe and Element-free AMGe:  General algorithms for computing interpolation
weights

Ferdinand Kickinger
Algebraic Multigrid for Stokes Equation

Rudolf Beck
Algebraic Multigrid for Edge Elements by Component Splitting

Stefan Reitzinger
Algebraic Multigrid for 3D Magnetic Field Problems

Joseph E. Pasciak
Iterative techniques for mixed discretizations of Maxwell's equations

Participants without a presentation:  Ronald Hoppe, Barbara Kaltenbacher, Karl
Kunisch, Ulrich Langer, Volker Schulz

Editor's Note: See http://www.mgnet.org/mgnet-amg2000-strobl.html (it
-------------  may be a few days before this is really available).

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

Date: Tue, 6 Jun 2000 14:15:13 -0400
From: Ken Jackson
Subject: 2001-02 NA Year at the Fields Institute in Toronto

The Fields Institute in Toronto is sponsoring a Thematic Year on "Numerical
and Computational Challenges in Science and Engineering" (NCCSE) from August
2001 to July 2002.  The main point of this announcement is to inform the
in participating can include it in their plans for 2001-02.

A key to the success of this program will be the senior long-term visitors
that it attracts.  Their research interests will shape many of the events that
take place during the year and their participation in the program will attract
many junior colleagues, postdocs and graduate students.

We are now considering applications from senior researchers to visit the
Fields Institute for a month or more, possibly spread out over several shorter
visits, such as a couple of weeks around two or more workshops or one day each
week for a term.  We would particularly welcome visitors for one or both terms
of the year.

We have some funds to support travel and local expenses for senior
researchers, but not to pay their salaries.  If you are a senior researcher
interested in participating in the program, please e-mail Ken Jackson at
krj@cs.utoronto.ca.

Year in particular can be found at

http://www.fields.utoronto.ca
and
http://www.fields.utoronto.ca/numerical.html

respectively.

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

Date: Thu, 29 Jun 2000 15:19:56 -0700
From: "Tony Drummond-Lewis"
Subject: LBNL-NERSC Workshop on ACTS

The US Department of Energy's National Energy Research Scientific Computing
Center (NERSC) is now taking applications from graduate students and
postdoctoral fellows to participate in a 3-day workshop on the ACTS toolkit,
September 28-30 of the current year.  The theme of this workshop is:  How can
ACTS work for you?  ACTS stands for Advanced Computational Testing and
Simulation, and it is a Department of Energy (DOE) funded project that
comprises a set tools developed mainly at DOE laboratories for the support of
large scientific and industrial software.  These tools deliver solutions for
numerical problems, scientific data representations, data manipulation,
visualization, program execution and distributed computing (for more
information visit the ACTS website at http://acts.nersc.gov).

Applicants from any scientific field are encouraged to submit a short abstract
describing their work and current or future computational needs.  DOE will
fully sponsor students and qualified postdoctoral fellows to attend this
workshop at Lawrence Berkeley National Laboratory.  The deadline for
applications is Tuesday, August 1st, 2000, and must be sent to
acts-workshop@nersc.gov.  Students must submit a short abstract of the current
work.  A letter of recommendation from the student's advisor with the
student's name in the subject line must also be received before the deadline.
Others applicants must submit a letter outlining their current work and future
plans and needs for computational resources with a list of publications.  For
or contact Tony Drummond at (510) 486-7624 or Osni Marques at (510) 486-5290

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

Date: Thu, 15 Jun 2000 09:50:13 -0400 (EDT)
From: Lothar Reichel
Subject: Conference on Inverse Problems

Preliminary announcement for conference on

Applied Inverse Problems: Theoretical and Computational Aspects

to be held June 18-22, 2001, at Montecatini Terme, Italy.

The scope of the meeting is to bring together scientists and engineers who are
working on theoretical and computational aspects of inverse problems.  The
meeting will consist of longer invited lectures, minisymposia and contributed
talks.

The following speakers have agreed to present invited lectures:

S. Arridge
A. Bjorck
T. F. Chan
L. Elden
H. W. Engl
G. H. Golub
P. C. Hansen
J. Nagy
Z. Nashed
F. Natterer
R. J. Plemmons
F. Santosa
E. Somersalo

Organizing and Scientific Committee:

M. Bertero, D. Calvetti, T.F. Chan, G.H. Golub, G. Inglese, A. Murli,
R.J. Plemmons, L. Reichel, S. Seatzu, F. Sgallari, G. Talenti

the conference can be sent to aip2001@mcs.kent.edu.

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

From: Jens Burmeister
Date: Tue, 27 Jun 2000 08:37:27 +0200
Subject: GAMM Seminar on Construction of Grid Generation Algorithms

Dear colleagues,

I'm very pleased to announce the

17th GAMM-Seminar Leipzig on
Construction of Grid Generation Algorithms
February 1st to 3rd, 2001.

Chairmanship: Wolfgang Hackbusch (Leipzig)
Ulrich Langer (Linz)
Location:     Max-Planck-Institute
for Mathematics in the Sciences,
Leipzig, Germany.

The first fifteen GAMM-Seminars were held in 1984, 1986-1999 at
the Christian-Albrechts-University to Kiel under the title
Annual GAMM-Seminar Kiel. In 2000, the sixteenth seminar took place at
the Max-Planck-Institute for Mathematics in the Sciences in Leipzig.

http://www.mis.mpg.de/conferences/gamm/

With best regards
Jens Burmeister

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

Date: Tue, 4 Jul 2000 13:04:47 +0200 (MET DST)
From: Stefan Funken
Subject: GAMM Workshop on Computational Electromagnetics

GAMM-WORKSHOP ON COMPUTATIONAL ELECTROMAGNETICS
Mathematisches Seminar,
Christian-Albrechts-University of Kiel, Germany,
January 26th to 28th, 2001

Organizers:
C. Carstensen  (Kiel)
S.A. Funken (Kiel)
W. Hackbusch (Kiel/Leipzig)
R.H.W. Hoppe (Augsburg)
P. Monk (Newark, Delaware, U.S.A.)

This workshop is intended to reflect the state-of-the-art of the foundations,
methods, and algorithmic tools of computational electromagnetics.  The
spectrum of the topics to be presented and discussed ranges from the
mathematical analysis of Maxwell's equations, different discretization schemes
and their efficient numerical realizations to the application of optimization
and optimal control methods as well as the appropriate treatment of inverse
problems.

Topics of interest include the following:

o Mathematical analysis of Maxwell's equations
in the low- and high-frequency range,
o Numerical analysis of discretization methods,
o Applications of multigrid/multilevel
and domain decomposition techniques,
o Multipole methods,
o A posteriori error analysis,
o Optimal control, structural optimization,
o Inverse modeling/parameter identification.

Call for papers:  Participants wanting to give a talk (20 min) should submit
an abstract before September 30, 2000.
Notification of acceptance will be given in October, 2000.

All correspondence in connection with the workshop, including registration and