Proposal for a Strategic University Program
in Computational Science and Engineering at NTNU
1 Background
1.1 What is Computational Science and Engineering?
Advanced computation and simulation in science and engineering
constitute an important area in rapid growth in many leading
industrial nations. The background for this is the continuing
development of efficient computer hardware that has been seen over the
past few decades which in turn has imposed an exceptional activity in
the progress of vector and parallel computing, numerical algorithms
and visualization. The consequence is that new vistas have been opened
for realistic computer simulations of mathematical models in
engineering and science. We will here use the term Computational
Science and Engineering or CSE for those activities in science and
engineering where computers play a significant role. The importance
of CSE has been realized in many countries like USA, Japan, Australia
and several European countries. A variety of research programs have
been initiated and funded within the fields of high performance
computing and its applications, algorithm design, and scientific
visualization.
1.2 Ingredients of CSE
The use of CSE is ubiquitous in applications, like e.g. solid and
structural mechanics, fluid mechanics, optimization in processing and
production technology, technological design, aerodynamics,
meteorology, electromagnetism, chemistry, physics, medicine and so
on. The field of CSE is vast and relies on methods which are
interdisciplinary. There is a common core of numerical methods,
mathematical analysis and modelling and aspects of computer science.
- Mathematics play a central role, a very large and
important class of mathematical models in engineering are
formulated by means of partial differential equations,
including complex geometries and boundary conditions, phenomena
occurring on different time scales etc. The prior mathematical
analysis of the model is paramount to a successful numerical
simulation.
- The most popular numerical methods for partial
differential equations include finite -difference, -element,
-volume, and spectral methods. In most cases these
discretization techniques lead to a system of algebraic
equations that needs to be solved, and to overcome the vast
computational challenges in solving such equations, it is
necessary to develop and use algorithms that can take advantage
of the potential of parallel machine architectures. Modern
numerical methods also include grid generation techniques,
convergence acceleration, error estimation and adaptivity. It
is important to keep in mind that the fast development of new
computers and machine architectures causes a dynamic change in
optimal numerical methods. Algorithms that were popular ten
years ago may have become obsolete in view of today's
technology.
- Obviously, the modelling and design of software for these
simulations is complicated by the existence of a large variety
of machine architectures and numerical algorithms that are
tailored for particular applications and computer hardware. It
is necessary to make use of modern methods for design and
modelling of such software, in recent years there has been a
significant increase in the activity of developing object
oriented numerical software, the aim being to overcome the
difficulties of writing portable and reusable code. Finally,
when large scale simulations are performed on problems with
complex geometries, there is a need to be able to interpret the
results of the simulations. The recent development of advanced
visualisation equipment is of great importance in CSE, and the
task of utilising this equipment in an optimal way is
considered an inherent part of the field.
CSE is apparently multidisciplinary with dynamic activity of great
complexity. The aim of this activity is to improve the quality of
computer simulations in applications. To exploit the potential for
such improvements in full, it is necessary to use state of the art
techniques from a variety of fields. The time when it was possible for
engineers to acquire sufficient depth knowledge in all aspects of
computation seems to be a bygone era. On the other hand, to succeed in
breaking computational barriers within a particular application area,
detailed knowledge of the nature of the physical problem is required,
knowledge that can only be achieved through experience with
computation and observation of physical phenomena where they occur,
either in the real world or in a laboratory. Ideally there should thus
be a symbiotic relationship between engineers, mathematical and
numerical analysts and computer scientists. We have tried to picture
the ingredients of CSE as traditionally seen by the engineer in
the figure below. The application is in the center of his attention,
but in order to solve the computational problems involved, he needs
elements of mathematical modelling, numerical analysis and computer
science. In the modern setting, sometimes denoted the third
paradigm, the generic aspects of computation are put in focus.
1.3 International trends
Today, we are seeing a trend on the international scene, where
consortia are being formed between the various disciplines involved in
computation. An example of a contemporary university program of high
standing is the Computational and Applied
Matematics (CAM) graduate
program at The University of Texas at Austin. From the
Information for Prospective Applicants we have the found the
following interesting quotes:
``The Computational and Applied Mathematics (CAM) graduate program at
The University of Texas at Austin prepares students for the
ever-growing applications of mathematical modeling. It will also lead
you to a research area of growing significance within the mathematical
sciences.''
``CAM is interdisciplinary in content, scope and structure. You will
complete advanced coursework in mathematics and computer science, and
in a field of science or engineering or both. CAM draws faculty from
the Colleges of Engineering and of Natural Sciences.''
Another example is The Institute for
Mathematics and Its Applications. From the mission statement for
IMA we quote:
``The Institute for Mathematics and Its Applications is located at the
University of Minnesota, Twin Cities Campus, in Vincent Hall. It is
affiliated with the School of Mathematics, the Minnesota Center for
Industrial Mathematics, as well as with our Participating
Organizations.
The IMA was established in 1982 by the National Science Foundation, as
a result of a national competition. A Board of Governors oversees the
activities of the IMA and approves budget and scientific programs. The
mission of the Institute is to close the gap between theory and its
applications. This is a two-fold task:
- To identify problems and areas of mathematical research needed
in other sciences.
- To encourage the participation of mathematicians in these areas
of application by providing settings conducive to the solution
of such problems, and by demonstrating that first-rate
mathematics can make a real impact in the sciences.''
1.4 CSE at NTNU
In the Fall 1994, a committee was established at NTNU, the intention
being to elucidate and plan activities in CSE at NTNU in education as
well as research. The work was concluded with a report Fall 94. An executive
committee was established from 1995 and awarded a grant from NTNU of
NOK 500 000 per year for a period of 3 years. The work of this
committee includes the initiation of three CSE related NTNU courses at
the PhD level, and several short term courses in visualization and
parallel computing. A workshop is planned in association with other
Nordic institutions and will be held in the Fall of 1997. Two
professorships have been allocated at the Faculty of Physics,
Informatics and Mathematics (FIM) one at the Department of
Mathematical Sciences (MS) and one at the Department of Computer and
Information Science (CS). The applicants for the positions are
currently being evaluated and the new professors are expected to be
appointed from January 1998.
NTNU has strong traditions within computational engineering, there are
many examples of research groups in engineering departments who have
taken part in pushing the frontiers of computing throughout the past
decades. An example is the Department of Structural Engineering where
several researchers played an important role in the development of the
finite element method starting in the early 60's. A number of research
groups enjoy a distinguished international reputation, with liasons to
world famous institutions like MIT and Berkeley in USA. Many more
examples of the merits of engineering research at NTNU could be
given. Instead we should look to the future and the many challenges
that are to be met in view of the rapid development of technology
which influence aspects of computation. We believe that a necessity
for the continuing success of computational engineering at NTNU is a
collaboration between research groups in engineering, computer science
and mathematics. It is no longer possible for experts in one field of
engineering to keep up with all the various disciplines involved in
computation. The required knowledge for each discipline exists within
separate research groups at NTNU, the missing ingredient is the
ability and resources to pull the expertise together in joint research
projects. In completing one such project aimed at a particular
application, valuable generic skills and experience will be obtained,
and can thus be applied to other application areas. Naturally, each
new application will consist of new elements and challenges, but the
experience built in a first project will be useful in all the
disciplines involved. For instance, the mathematical models used in
different application areas are often similar, in some cases almost
identical, the same goes for the numerical algorithms that are used
for the simulation. And perhaps most importantly, if a proper design
of the software which implements the models has been conducted, there
is the potential for reuse of software components.
