NA Digest Sunday, July 19, 1998 Volume 98 : Issue 26

Today's Editor:
Cleve Moler
The MathWorks, Inc.

Submissions for NA Digest:

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Information about NA-NET:

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URL for the World Wide Web:

From: James Epperson <>
Date: Thu, 9 Jul 1998 14:37:35 -0500 (CDT)
Subject: History of Splines

Two weeks ago I posted a query here about the connections between the
development of spline approximations and automotive body design, and received
over 30 responses, all of them very informative. Since several of them asked
me to pass along what I learned, I decided to write up a brief summary and
post it to the digest. Hence this note.

It is commonly accepted that the first mathematical reference to splines is
Schoenberg's paper [S], which is probably the first place that the word
"spline" is used in connection with smooth, piecewise polynomial
approximation. However, the ideas have their roots in the aircraft and
ship-building industries. In the forward to [BBB], Robin Forrest describes
"lofting," a technique used in the British aircraft industry during World War
Two to construct templates for airplanes by passing thin wooden planks
through points laid out on the floor of a large design loft. The planks
would be held in place at discrete points (called "ducks" by Forrest;
Schoenberg used "dogs" or "rats") and between these points would assume
shapes of minimum strain energy. According to Forrest, one possible impetus
for a mathematical model for this process was the potential loss of the
critical design components for an entire aircraft should the loft be hit by
an enemy bomb. This gave rise to "conic lofting," which used conic sections
to model the position of the curve between the ducks. Conic lofting was
replaced by what we would call splines in the early 1960's based on work by
J. C. Ferguson at Boeing and (somewhat later) by M.A. Sabin at British

Interestingly, Forrest says that the word "spline" comes from an East Anglian

The use of splines for modeling automobile bodies seems to have several
independent beginnings. Credit is claimed on behalf of de Casteljau at
Citroen, Bezier at Renault, and Birkhoff, Garabedian, and de Boor at General
Motors, all for work occuring in the very early 1960's or late 1950's. At
least one of de Casteljau's papers was published, but not widely, in 1959.
De Boor's work at GM resulted in a number of papers being published in the
early 60's, including some of the fundamental work on B-splines.

Work was also being done at Pratt & Whitney Aircraft, where two of the
authors of [ANW] (the first book-length treatment of splines) were employed,
and the David Taylor Model Basin, by Feodor Theilheimer. The work at GM is
detailed nicely in the article [B] and the retrospective [Y]. I was also
pointed to the article [BdB] by several people, but our library does not have
that volume, so I have not been able to see it for myself. Paul Davis
summarized some of this material in SIAM News in 1996; see [D].

Again, my thanks to all who sent me messages and suggestions.


[ANW] Ahlberg, Nielson, and Walsh, The Theory of Splines and Their
Applications, 1967.

[B] Birkhoff, "Fluid dynamics, reactor computations, and surface
representation," in A History of Scientific Computation (Steve Nash,
editor), 1990.

[BBB] Bartels, Beatty, and Barsky, An Introduction to Splines for Use
in Computer Graphics and Geometric Modeling, 1987.

[BdB] Birkhoff and de Boor, "Piecewise polynomial interpolation and
approximation," Proc. General Motors Symposium of 1964, H. L. Garabedian,
ed., Elsevier, New York and Amsterdam, 1965, pp. 164-190.

[D] Davis, "B-splines and Geometric design," SIAM News, vol. 29, no. 5;
available at

[S] Schoenberg, "Contributions to the problem of approximation of
equidistant data by analytic functions," Quart. Appl. Math., vol. 4,
pp. 45-99 and 112-141.

[Y] Young, "Garrett Birkhoff and applied mathematics," Notices of the AMS,
vol. 44, no. 11, pp. 1446-1449.


From: Stephen Vavasis <vavasis@CS.Cornell.EDU>
Date: Wed, 15 Jul 1998 16:48:46 -0400
Subject: Quadrature Over Tetrahedra

Colleagues here at Cornell who work on finite-element methods for
structural analysis asked me about high-order quadrature rules for
tetrahedra. The "classical" quadrature rule (e.g., A. Stroud and D.
Secrest, "Gaussian Quadrature Formulas", Prentice Hall, 1966) for the
tetrahedron is simply a product rule. For example, to extend the
k-point Gaussian quadrature formula to the tetrahedron, one uses k^3
quadrature points arranged in a distorted cube inside the tetrahedron
with appropriate polynomial weights. But this solution seems
inefficient because many quadrature points are clustered (apparently
needlessly) near one of the four vertices of the tetrahedron. So I'm
wondering whether more efficient rules have been developed for this

Steve Vavasis (


From: Sheri Martinelli <>
Date: Fri, 17 Jul 1998 09:39:38 -0400
Subject: Hankel Transform

We are students working on a project which requires us to take an accurate
Hankel transform of some data. We are wondering if anybody knows of a good
algorithm that is available (we're not so much concerned about speed as we
are accuracy). The Hankel transform is


Please email any suggestions to:

Sheri Martinelli, Dan Renzi, and Jaime Haletky

Thank you!


From: Peter Alfeld <>
Date: Tue, 7 Jul 1998 07:53:50 -0600 (MDT)
Subject: Bernstein-Bezier Applet

For my teaching and research I have written an applet that lets you
explore the Bernstein-Bezier Form of a bivariate polynomial, design
finite elements, and analyze spaces of splines defined on
triangulations. If you are interested check it out at

Peter Alfeld, Dept of Mathematics, University of Utah, Utah 84112,


From: Xiong Zhang <xzhang@me.UVic.CA>
Date: Fri, 10 Jul 1998 16:49:41 -0700
Subject: A Nonlinear Eigenproblem

I have a nonlinear eigenproblem:

( K(w)-w^2M)X=0

where K(w) is a nonlinear complex symmetric matrix and M is a real symmetric

The first eigen value can be obtained by using matrix iteration method.
Is there a way to obtain the first n eigen velues and eigen vectors ?


From: Armin Iske <>
Date: Tue, 7 Jul 1998 10:22:01 +0200
Subject: Change of Address for Armin Iske

I have moved to Munich University of Technology, Germany.
Effective since July 1st 1998, my new professional address
and related data are:

Dr. Armin Iske
Chair for Numerical Analysis
and Scientific Computing
Center of Mathematical Sciences
Munich University of Technology
Arcisstrasse 21
D-80290 Muenchen

Phone: +49-89-289-28 375
Fax : +49-89-289-28 689



From: Rob Owens <>
Date: Fri, 17 Jul 1998 14:13:14 +0100 (BST)
Subject: Change of address for Robert G. Owens

Dear all,

After 1 September 1998 my new contact details
will be as follows:

CH-1015 Lausanne,

Fax: +41 21 693 3646

Best wishes,

Rob Owens

Department of Mathematics,
Napier University,
219 Colinton Road,
Edinburgh EH14 1DJ,
Scotland, UK


From: Ashok Srinivasan <>
Date: Wed, 8 Jul 1998 10:22:23 -0500 (CDT)
Subject: Parallel Random Number Generator Library

Parallel Random Number Generator Library

We are happy to announce the release of SPRNG 1.0: a Scalable
Parallel Random Number Generator Library. (It can be used for the usual
serial random number generation too.)

These libraries are callable from C, C++, and FORTRAN programs. We
have ported the generator to the following machines: Cray T3E, Convex
Exemplar, SGI Power Challenge array, Origin 2000, IBM SP2, DEC, HP and SUN
workstations, and PC (Linux). It should be easy for users to port it to
other machines too.

We have also included a test suite. The six random number generators
included in our library have been subjected to some of the largest
random number tests ever performed, with up to 10^13 random numbers in
certain tests.

Please see our home page:
For further information.

Ashok Srinivasan

National Center for Supercomputing Applications (NCSA)
University of Illinois at Urbana-Champaign


From: Pete Stewart <>
Date: Fri, 10 Jul 1998 13:11:41 -0400 (EDT)
Subject: Householder Symposium


The Householder Symposium on Numerical Linear Algebra will be
held June 14-18, 1999 at the Chateau Whistler, Whistler B.C., Canada,
about 2 hours drive north of Vancouver. This meeting is the
fourteenth in a series, previously called the Gatlinburg Symposia.
The name honors Alston S. Householder, one of the pioneers in
numerical linear algebra and organizer of the first four meetings.
The meeting has traditionally been held in an isolated location and is
very informal in style. Each attendee is given the opportunity to
present a talk, but a talk is not mandatory. The format of the
meeting includes scheduled presentations during the day and more
informal evening sessions that are organized electronically shortly
before the meeting. Spirited discussion is encouraged.

At the meeting, the tenth Householder prize will be awarded for the
best thesis in numerical algebra written since 1 January 1996.

We hope that the meeting will be attended by recent entrants into
numerical algebra as well as more experienced researchers. We
encourage attendance by core numerical linear algebra researchers,
matrix theoreticians, and people in applications such as optimization,
signal processing, control, etc.

The Program Committee welcomes your contribution. The meeting
facility holds only 125 people, however, so attendance may need to be
limited. We are seeking funding to provide financial assistance to
recent Ph.Ds and others who might need it.

For full consideration, the committee must receive your abstract by 11
December 1998. Information concerning the application process may be
found at the URL listed above. Please use the format provided at the
Website. The committee expects to complete the list of attendees and
scheduled presentations by 1 February 1999.

After reading the files in the Website, if you have any questions
about local arrangements, please contact Jim Varah
(|}). Other questions can be directed to

The Program Committee:

A. Bjorck,
A. Bunse-Gerstner,
T. Chan,
C. Davis,
A. George,
N. Higham,
D. O'Leary,
G. W. Stewart (Chair),
P. Van Dooren,
C. Van Loan,
J. Varah (ex officio)


From: Pete Stewart <>
Date: Fri, 10 Jul 1998 13:11:41 -0400 (EDT)
Subject: Householder Prize


Nominations are solicited for the Alston S. Householder Award X
(1999). The award will be presented to the author of the best
dissertation in numerical algebra submitted by the recipient of a
Ph.D. earned between January 1, 1996, and December 31, 1998.

The term numerical algebra is intended to describe those parts of
mathematical research that have both algebraic aspects and numerical
content or implications. Thus, for example, the term covers linear
algebra that has numerical applications and the algebraic aspects of
ordinary differential, partial differential, integral, and nonlinear
equations. To qualify, the dissertation must have been submitted to
fulfill requirements for a degree at the level of a United States
Ph.D. Candidates from countries in which a formal dissertation is not
normally written at that level may submit an equivalent piece of work.

The Householder Award, given every three years, was established at the
1969 Gatlinburg Symposium (now renamed the Householder Symposium) to
recognize the outstanding contributions of Alston S. Householder,
1904--1993, to numerical analysis and linear algebra.

Entries will be assessed by an international committee consisting of
James Demmel (University of California, Berkeley), Ludwig Elsner
(University of Bielefeld), Paul Van Dooren (Catholic University of
Louvain), Charles Van Loan (Cornell University), and Olof Widlund
(Courant Institute, New York University).

The candidate's sponsor (the supervisor of the candidate's research)
should submit five copies of the dissertation (or qualifying work),
together with an appraisal by February 15, 1999, to

Professor Paul Van Dooren
Catholic University of Louvain
Centre for Systems Engineering and Applied Mechanics (CESAME)
Batiment Euler (Rm A.119), 4, avenue Georges Lemaitre
B-1348 Louvain la Neuve

The award will be presented at the Householder Symposium XIV, to be
held June 14--18, 1999, at Whistler, B.C., Canada. Candidates on the
short list will receive invitations to the meeting.

Previous Householder Award winners were F. Robert (Grenoble) in 1971,
Ole Hald (New York University) in 1974, Daniel D. Warner (University
of California, San Diego) in 1977, E. Marques de S{\'a} (Coimbra) and
Paul Van Dooren (K. U. Leuven) in 1981 (shared), Ralph Byers (Cornell
University) and James M. Demmel (University of California, Berkeley)
in 1984 (shared), Nicholas J. Higham (University of Manchester) in
1987, Alan Edelman (Massachusetts Institute of Technology) and Maria
Beth Ong (University of Washington) in 1990 (shared), Hong-Guo Xu
(Fudan University) and Barry Smith (New York University) in 1993
(shared), and Ming Gu (Yale University) in 1996.


From: D. M. Sloan <>
Date: Tue, 7 Jul 1998 10:16:34 +0100
Subject: Scottish Computational Mathematics Symposium

First Announcement
10am-5pm Monday 21st September 1998
University of Strathclyde, Glasgow, Scotland

SYMPOSIUM. The meeting is partly supported by the London Mathematical


Malcolm Bloor Applied Mathematical Studies, University of Leeds
Tim Goodman Mathematics, University of Dundee
Philip Knight Mathematics, University of Strathclyde
Martin Stynes Mathematics, University College, Cork
Yves Tourigny Mathematics, University of Bristol


Fees: 20 pounds ( 15 pounds for graduate students)
To register, send a cheque payable to University of Strathclyde by
11th September to the address below. Fee includes tea, coffee & lunch.

Department of Mathematics
University of Strathclyde
Glasgow G1 1XH

The meeting is organised by D B Duncan (Heriot-Watt University)
and D M Sloan (Strathclyde University). A timetable will be circulated


From: Rick Caron <>
Date: Tue, 7 Jul 1998 10:19:49 EDT
Subject: Canadian Operational Research Society Conference

CORS-SCRO '99, Windsor
The 41st National Conference of the Canadian Operational
Research Society (CORS) will be held June 7-9, 1999 in
Windsor, Ontario. The theme of the conference is
"Operational Research In Motion" and the confirmed plenary
speakers are Harvey Greenberg, Carl Harris, and Gilbert Laporte.
The deadline for abstract submission is March 1, '99.
Early registrations fees are applicable until May 1, 99.
For more information visit <>
or email Richard Caron <>.


From: Trini Flores <>
Date: Thu, 09 Jul 98 10:15:46 -0500
Subject: SIAM Conference on Geometric Design

Sixth SIAM Conference on Geometric Design
November 2-5, 1999
Sheraton Old Town Hotel
Albuquerque, New Mexico

SIAM and the Organizing Committee for the Sixth SIAM Conference
on Geometric Design are pleased to announce that the conference
Call for Papers is now available on the Web. To know more about
the conference themes, invited plenary speakers, minisymposia,
and deadlines for submission of minisymposium proposals or
contributed abstracts, please visit

Trini Flores


From: Timothy Barth <>
Date: Sat, 11 Jul 1998 16:58:30 -0700 (PDT)
Subject: Lecture Series on High Order Discretization Methods in CFD

RTO/VKI/NASA Lecture Series on
"High Order Discretization Methods in CFD"

Two Presentation Locations and Dates:

von Karman Institute for Fluid Dynamics
Rhode-Saint-Genese, Belgium
14-18 September 1998


NASA Ames Research Center
Moffett Field, California, USA
21-25 September 1998


Prof. R. Abgrall
Applied Mathematics
Universite de Bordeaux I, France

Prof. B. Cockburn
School of Mathematics
University of Minnesota, USA

Dr. R. Henderson
Aeronautics & Applied Mathematics

Prof. Y. Maday and C. Bernardi
Laboratoire d'Analyse Numerique
Universite Pierre et Marie Curie, France

Prof. C. Schwab
Seminar fuer Angewandte Mathematik
ETH Zuerich, Switzerland

Prof. C-W Shu
Division of Applied Mathematics
Brown University, USA

Lecture Series Topics:

- Runge Kutta Discontinuous Galerkin method for nonlinear hyperbolic
systems and extension for convection-dominated problems
- formal high-order accuracy, nonlinear stability and parallelization of
discontinuous Galerkin methods
- applications to inviscid and high Reynolds number viscous compressible
flow, shallow water flow, MHD, and semiconductor device simulation.
- h-p FE variational formulation of stationary problems: convection
diffusion, incompressible fluid flow, non-Newtonian fluids.
- h-p FE subspaces: nonuniform element order, geometric mesh refinements,
irregular nodes, isoparametric hp-FEM, spectral elements.
- algorithmic issues: selection of shape functions and quadrature, mass
lumping, hp-elements as Fortran90 objects, irregular nodes, parallel static
condensation, direct and iterative solution.
- a-posteriori error estimation
- h-p FE application to viscous, incompressible flow: regularity of the
solution, mesh design, selection of hp-subspaces, stable element pairs,
stabilization techniques
- application to convection dominated problems: boundary layers, numerical
resolution and robust spectral approximation of viscous boundary layers and
shock profiles, stabilization of hp-FEM for convection dominated problems
- application to time dependent problems, hp-time stepping schemes for
transient calculations
- construction, analysis, and application of ENO (Essentially
Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes
for hyperbolic conservation laws
- techniques to extend ENO schemes on unstructured meshes
- implementation and theoretical issues
- modified higher order TVD techniques
- applications for flow problems containing both shocks and complicated
smooth solution structures such as compressible turbulence simulations and
- numerical basics of spectral and spectral element methods for elliptic,
parabolic and hyperbolic problems
- mortar element methods
- numerical analysis of the approximation of the Stokes and Navier-Stokes
- strategies for adaptive mesh refinement
- applications to transition studies and direct numerical simulations of
- current developments for expansions on triangles and tetrahedra,
multipole methods, and the use of high-order B-splines


Prof. H. Deconinck
von Karman Institute for Fluid Dynamics
Chaussee de Waterloo, 72
1640 Rhode-Saint-Genese, Belgium
Tel: 32 2 359 9611 Fax 32 2 359 9600

Dr. T. J. Barth
NASA Ames Research Center
Information Sciences Directorate
Mail Stop T27A-1
Moffett Field, CA 94035, USA
Tel: 1 (650)604-6740 FAX: 1 (650)604-3957


Marcia Redmond (Local Coordinator)
NASA Ames Research Center
NAS Systems Division
Mail Stop 258-6
Moffett Field, CA 95035, USA
(650) 604-4373

On-Line Registration Information:

VKI Presentation:
NASA Ames Presentation:

Financial Assistance (NASA Ames Presentation):

No registration fee will be required for the NASA Ames presentation.

A limited number of travel stipends are available to students and
other individuals located within the U.S. who wish to attend the
lecture series. These stipends are awarded on a competitive basis
with the stipend amount depending on the number of applicants. For
further information send Email to T. Barth (
before August 15, 1998.

Tim Barth
NASA Ames Research Center
Information Sciences Directorate
NAS Division
Mail Stop T27A-1
Moffett Field, CA 94035
Tel (650)604-6740
FAX (650)604-3957


From: Steve McCormick <>
Date: Wed, 15 Jul 1998 14:00:34 -0600 (MDT)
Subject: Copper Mountain Conference on Multigrid Methods


Ninth Copper Mountain Conference on Multigrid Methods
April 11-16, 1999
Copper Mountain, Colorado, USA


The University of Colorado
The Society for Industrial and Applied Mathematics
The Center for Advanced Scientific Computation at LLNL
The Institute for Algorithms and Scientific Computing of the GMD
Front Range Scientific Computations, Inc.




Every effort will be made to encourage contributions from anyone whose
interest lies in these important and rapidly evolving fields.


STUDENT PAPER COMPETITION. We are hoping to support the participation of
several students, depending on availability of grant funds.

MULTIGRID TUTORIAL. We will offer an updated tutorial on basic multigrid
and advanced multilevel techniques, including algebraic multigrid (AMG).


Student Papers Dec. 15, 1998
Author Abstracts Feb. 1, 1999
Early Registration Feb. 1, 1999
Guaranteed Lodging March 1, 1999


Please access our web site at

or contact

Cathy Lee
1390 Claremont Drive
Boulder, CO 80303
(303) 554-1232


From: Panos Pardalos <>
Date: Sat, 18 Jul 98 13:13:02 EDT
Subject: Conference on Advances in Convex Analysis and Global Optimization


Conference on "Advances in Convex Analysis and Global Optimization"
Honoring the memory of C. Caratheodory (1873-1950)

Date: June 5-9, 2000
Location: Pythagorion - Samos, Greece


Nicolas Hadjisavvas <> and Dimitrios Kandilakis <>
University of the Aegean, Greece

Panos Pardalos <>
University of Florida, USA

The conference on Advances in Convex Analysis and Global Optimization
aims at fostering the cooperation among practitioners and theoreticians
in the fields of convex analysis and global optimization.
Several invited talks will report on original research (both theoretical
and experimental) in all areas of convex analysis and global optimization,
including surveys of important recent results/directions.

The conference will be held in the city of Pythagorion, on the island
of Samos, Greece. Samos, an island of astonishing natural beauty and
very old history is located in the Northeast Aegean sea, and is the
birthplace of Pythagoras, Epikouros and Aristarchos.

Additional information on travel and local accommodations will be
provided at a later date. More information on the conference can be
obtained from the organizers.


From: Sergei Molokov <>
Date: Tue, 14 Jul 1998 15:41:51 +0100 (BST)
Subject: Postdoctoral Positions at Coventry and Oxford


Two Postdoctoral Research Assistants are required to work on a two year
EPSRC project on the fragmentation of wires due to pulsed currents. The
research involves the simulation of the propagation of stress waves in wires
carrying electric currents. The successful candidates will be required to
have considerable experience in numerical modelling; previous experience in
dealing with problems in elasticity would be an advantage. The project is a
joint one between Coventry University and the University of Oxford. One
Research Assistant will be based at each University and a close working
collaboration will be established. The salary will be 17,958 pounds sterling
p.a. rising in the second year to 18,864 (somewhat higher in Coventry).

Further particulars may be found at or obtained from
Mr. C.J.Scotcher, The Senior Administrator, University of Oxford, Department
of Engineering Science, Parks Road, Oxford, OX1 3PJ, UK, to whom written
applications should be made, enclosing a curriculum vitae and the names and
addresses of two referees. Please quote "RA/JEA" in all correspondence. The
closing date for applications is 14th August, 1998. Applicants are asked to
arrange directly with their referees for references to be sent by this date.
For an informal discussion contact Dr. Sergei Molokov at


From: John Maddocks <>
Date: Tue, 07 Jul 1998 11:58:19 +0200
Subject: Positions at Swiss Federal Institute of Technology, Lausanne

There are positions available within the Chair of Applied Analysis at
the EPFL to work in the areas of

i) Visualization techniques applied to steered, parameter-continuation


ii) Mathematical modelling of the mechanical properties of DNA

Appointments in either area may be possible at either the PhD or
Postdoctoral level with a range of possible starting dates. However
there are two focussed postdoctoral appointments available immediately,
with the specific research projects of

a) implementing a port of an existing continuation and visualization
code to Java3D running under NT on an alpha-chip parallel super-computer
that is being developed at the EPFL

b) bridging the gap between numerical simulations of DNA based on
Molecular Dynamics and continuum mechanics models

Further details of the group's research, terms of the appointments, and
the application procedure can be found at

Professor John H. Maddocks
DMA (Department of Mathematics)
EPFL (Swiss Federal Institute of Technology)
CH-1015 Lausanne


From: Bob Mattheij <>
Date: Wed, 8 Jul 1998 17:13:19 +0200 (MET DST)
Subject: Research Position at Eindhoven University of Technology

A PhD-position for research on Contour Dynamics for Chaotic Advection Studies

In the groups Scientific Computing of the Mathematics Department and Vortex
Dynamics of the Physics Department at Eindhoven University of Technology (The
Netherlands) a fundamental research program is focused on the properties of
quasi-2D flows and simulations of such flows with state-of-the-art numerical
techniques. Present project is a continuation of a successful collaboration
between both groups during the last years in the field of the dynamics of coherent
vortices in stratified or rotating fluids, self-organisation and chaotic advection
in 2D turbulence. Applications for a PhD position are invited in the area of
numerical studies of chaotic advection in quasi-2D flows with a Contour
Dynamics algorithm.

For this PhD-project a master's degree in (theoretical) physics or mathematics
and a good background in both fluid dynamics and numerical techniques are
For a PhD position, the conditions are approximately as follows: As a PhD
student you will receive a gross salary that increases during your 4 year contract.
It is Dfl 2843/month in the first year and increases to Dfl 3841/month in the fourth

Further information on these PhD-projects can be obtained from:
Prof.dr. R.M.M. Mattheij (email:,
(Physics) G.J.F. van Heijst (email:
Dr. H.J.H. Clercx (email: H.J.H.Clercx@
For more information about the research activities of both groups see the
WWW-pages at: (scientific computing) and (fluid dynamics laboratory).

Send detailed resume and names/addresses of three professional references to:
Prof.dr. R.M.M. Mattheij
Mathematics Department (Building HG 8.36)
Eindhoven University of Technology
P.O. Box 513
NL-5600 MB Eindhoven
The Netherlands


From: C.-W. Shu <>
Date: Wed, 8 Jul 1998 15:19:59 -0400
Subject: Faculty Position at Brown University

Position for Assistant Professorship in Scientific Computing
Division of Applied Mathematics - Brown University

The Division of Applied Mathematics, Brown University has an opening of a
tenure track position at the Assistant Professor level in the area of
Scientific Computing. Preference will be given to researchers in high order
accuracy methods with applications such as Fluid Mechanics, Electromagnetics,
Optics and/or Materials Science. Postdoctoral experience preferred. Excellent
communication skills are required for teaching at the undergraduate and
graduate levels.

The starting date for the position is February 1999. A Ph.D is required; all
requirement for the degree must be completed by January 31, 1999.

Applicants should have a curriculum vitae, at least three letters of
recommendation and relevant publications sent to: Professor C.-W. Shu, Chair,
Scientific Computing Position, Division of Applied Mathematics, Box F, Brown
University, Providence R.I. 02912.

To receive full consideration, complete applications should be received by
November 1, 1998.

Brown University is an affirmative action/equal opportunity employer. Women
and minorities are encouraged to apply.


From: Henry Greenside <>
Date: Wed, 8 Jul 1998 17:25:54 -0400
Subject: Postdoctoral Position at Duke University

A strong highly-motivated researcher is sought for a
joint Caltech-Duke postdoctoral position in computational
fluid dynamics and nonequilibrium physics. The research
will be done in collaboration with Professor Michael
Cross (Department of Physics, Caltech) and Professor
Henry Greenside (Department of Physics, Duke University)
and will involve the development and application of new
three-dimensional computer codes that will allow
quantitative comparisons of theory with experiment for
convecting fluids in large-aspect-ratio cells. A
particular emphasis will be on studying and understanding
the transitions to weak turbulence and properties of weak
turbulence as functions of Rayleigh, Taylor, and Prandtl
numbers. Applicants should have substantial prior
experience with computational fluid dynamics (especially
algorithms for integrating the time-dependent
incompressible Navier-Stokes equations) and with writing
large scientific codes, as well as a strong interest in
the physics of weakly turbulent systems. This is a
two-year position that will begin in fall of 1998.

Interested candidates should send a resume with three
references to:

Professor Henry Greenside
Department of Physics
P. O. Box 90305
Duke University
Durham, NC 27708-0305

This information can also be sent via e-mail to the
address Further information about this
position can be obtained by contacting Professor Henry
Greenside at 919-660-2548 or at


From: Mike Pettipher <>
Date: Thu, 9 Jul 1998 09:19:02 +0100 (BST)
Subject: Positions at the University of Manchester

Manchester Computing
The University of Manchester
United Kingdom

High Performance Computing Staff

Manchester Computing, the computing service of the University of
Manchester, in conjunction with Silicon Graphics Cray Research
Division and Computer Sciences Corporation Supercomputing Division has
just secured the prestigious contract to provide, on
behalf of the Research Councils, the new flagship high performance
computing service to UK Academia. We wish to recruit a number
of staff to help provide this and other high performance computing
services. The new service will be based around a 576 processor
Cray T3E system, (the fourth most powerful computer in the world), and a
Silicon Graphics Origin2000 system. In addition, the
University runs a number of other Origin2000 servers.

We are seeking to fill the following posts;

Project Manager (#23,000 - #33,000) (ref: 439/98)

Senior Application Specialists (circa #25,000)

Application Specialists (#18,000-#20,000)

Trainee Application Specialists(#15,000-#17,000) (ref: 440/98)

Front-line Support Staff (#15,000 - #22,000) (ref: 441/98)

The University is also establishing an Institute of Computational
Science and is seeking applications for

Research Assistants/Software Engineers: (#15,000-#22,000) (ref: 441b/98)

All the above posts are fixed term appointments for two years, with the
possibility of further extensions dependent upon the success
of this six-year contract with the Research Councils. All salaries are
in UK pounds sterling.

As an Equal Opportunities Employer, the University welcomes applications
from suitably qualified people from all sections of the
community, regardless of race, religion, gender or disability.

For informal discussion about the positions contact Terry Hewitt on 0161
275 6095 (44 161 275 6095 from outside the UK).

Further information and application forms can be obtained from Ms Sue
Wan, Office of the Director of Personnel, University of
Manchester, Manchester M13 9PL, telephone: 0161 275 2442; email: quoting one of the above reference
numbers. The closing date for applications is 24th July 1998.

For further details of HPC at Manchester please see

For further details of the posts themselves please see

For preliminary details of the new HPC service see


From: T. N. Phillips <>
Date: Thu, 09 Jul 1998 10:15:21 +0100
Subject: Postdoctoral Positions at University of Wales, Aberystwyth


The Department of Mathematics has been awarded funding for
two postdoctoral positions. The first is funded by the
EPSRC Chemical Engineering Programme for a project concerned with
the computation of non-Newtonian flows on heterogeneous
networks of processors.
This project will start on 1 December 1998
or possibly at a later date to be mutually agreed.
Familiarity with the spectral element method and/or
parallel computing hardware and message passing
software would be an advantage.
The second is funded by the EU for a project
concerned with the dynamics of polymeric liquids.
This project can begin with immediate effect and
is part of a European Network involving ten universities.

Applicants for both positions should hold, or expect to obtain in the near
future, a PhD in applied mathematics or engineering.
Applications should be made by sending a curriculum vitae and names
of two academic referees to Dr. T.N. Phillips, Department
of Mathematics, University of Wales, Aberystwyth SY23 3BZ.
Informal enquiries are welcomed either by phone
(01970 622769) or by email (


From: Chris Petrie <>
Date: Thu, 9 Jul 1998 17:14:16 +0100 (BST)
Subject: Position at University of Newcastle upon Tyne




This post is available from 1st August 1998. The person appointed
should have a PhD and research interests in applied mathematics or the
fundamentals of engineering science. He or she will be required to
contribute to teaching mathematics in the Faculty of Engineering and to
research in the Department, which was awarded a Grade 4 in the 1996 RAE.

The Department has strong research interests in application of
mathematics to engineering and physical problems, in particular
multiphase flow, non-Newtonian fluids, wave propagation and
mathematical modelling of engineering systems.

Salary will be at an appropriate point on either the Lecturer Grade A
scale: 16,366 - 21,436 pounds per annum or Lecturer Grade B scale:
22,332 - 28,545 pounds per annum, according to qualifications and

For further information, including how to apply, please telephone
(0191) 222 5429 (24 hour answerphone) quoting reference A6312 or
write to: Personnel Section, University of Newcastle, 1 Park Terrace,
Newcastle upon Tyne NE1 7RU.

Closing date for applications: 7th August 1998.

See (soon)

Informal enquiries to "".

Information supplied by
Chris Petrie, Professor of Non-Newtonian Fluid Mechanics
Department of Engineering Mathematics, University of Newcastle upon Tyne.


From: Christof Eck <>
Date: Fri, 10 Jul 1998 15:56:44 -0600
Subject: Research Position at University Erlangen-Nuremberg


The Institute for Applied Mathematics of the University Erlangen-Nuremberg,
Germany, is searching candidates for a position connected with a research
project in applied mathematics.

Funding for the project is applied for at the Bavarian Research Foundation.
Its aims are the modeling and simulation of solidification, fluid flow and
solute transport in casting processes. The task of the project researcher
is the simulation of fluid flow and solute transport in the porous
intermediate zone between liquid and solid material. The models are
nonlinear partial differential equations. The algorithm shall be implemented
into an existing code for the simulation of casting processes which is
written in C++. The position depends on the confirmation of the Bavarian
Research Foundation and is expected to have a term of two years.

The ideal candidate has a degree in mathematics or a similar subject.
He/She should be familiar with applied mathematics/scientific computing
and/or partial differential equations. Knowledge of the German language is
not expected and only advantageous as far as everyday life is concerned. The
candidate is expected to write a PhD thesis during the work on the project.

Salary is according to the German BAT IIa/2 tariff for both positions.
It depends on age and family status. (A 25 year old unmarried person
receives about DEM 33,000 / US$ 20,000 gross payment per annum.)

Candidates which are interested in this position should contact
me as soon as possible, and provide their CV and a description of their
scientific background and interests.

Prof. Dr. Peter Knabner
Institute for Applied Mathematics Tel. +49(0)9131 857015 or 857016
Martensstr. 3 Fax. +49(0)9131 857670
D 91058 Erlangen e-mail:


From: Iain Duff <>
Date: Fri, 10 Jul 1998 09:45:36 +0100 (BST)
Subject: Contents, IMA Journal of Numerical Analysis


Goodman, T. N. T., Micchelli, C. A., Rodriguez, G., and Seatzu, S.
On the limiting profile arising from orthonormalizing shifts of exponentially
decaying functions.
pp 331-354

Dussault J-P
Augmented penalty algorithms.
pp 355-372

Hegland, M. and Osborne, M. R.
Wrap-around partitioning for block bidiagonal linear systems.
pp 373-383

Vasconcelos P B and d'Almeida F D
Preconditioned iterative methods for coupled discretizations of fluid flow
pp 385-397

Guglielmi N
Delay dependent stability regions of $\THETA$-methods for delay differential
pp 399-418

Bj{\/o}rhus M
Operator splitting for abstract Cauchy problems.
pp 419-443

Jeltsch, R, Renaut, R A, and Smit, J H
An accuracy barrier for stable three-time-level difference schemes for
hyperbolic equations.
pp 445-484


End of NA Digest