Plenary
Lecture
Advanced Algorithms for Numerical Simulation of Coupled
Engineering Problems
Associate Professor Ion Carstea
University Of Craiova
Romania
Email:
ion_crst@yahoo.com
Abstract:
In our lecture we intend to review the stateoftheart
of advanced iterative algorithms for solving large
sparse systems such as arising in coupled engineering
problems. The solution of practical problems of
mathematical physics ultimately relies on solving a
system of nonlinear partial derivative equations and
this is only achieved by iterative numerical methods
using parallel computers. Iterative solution methods
proceed by adding successive corrections to some
arbitrary initial approximation, but unfortunately these
methods are very sensitive to specific features of the
system to be solved. A procedure call preconditioning is
possible but is not always used.
Any electromagnetic device is the house of two or more
physical fields that interact by a number of parameters
as the material properties, the field sources etc. In
other words we have not separate problems for engineers
from different science branches although for economic
reasons in terms of computer resources, each physical
field is considered as though it was separate field and
generates a problem which is solved independently. The
subsystems and numerical solutions are finally coupled
together in such way that interactions are satisfied
with an “acceptable” degree of accuracy. This is a
simplified natural approach for the analysis of large or
complex structures but the accuracy of the analysis is
not good. Naturally the systems interact in any time
moment so that an independent analysis can not be
considered.
In our lecture a special attention is for the domain
decomposition method in the context of the finite
element method. Domain decomposition is an efficient
method for large distributedparameter systems. This is
an iterative method at the level of the subdomains. The
technique of dividing a large physical system into a
system of components is very old but is used extensively
nowadays. The motivation of this approach is that we
have an increased computing power with advanced computer
architectures so that it is an antisocial fact to ignore
this real computing power for complex systems.
We limit our presentation to a large class of systems
defined by ellipticparabolic mathematical models that
represents the basis of the electromagneticthermal
problems. The numerical models are obtained by the
finite differences and finite element methods. The
motivation is simple: for parabolic problems we use an
explicit scheme for temporal discretization, and for
elliptic problem we use the finite element method. As
target example we use an electromagneticthermal coupled
problem from electrical engineering. In the algorithmic
skeletons for this class of problems we are guided by
the implementation of the algorithms on the parallel
computers with emphasis on parallel computers (MIMD
architectures).
Brief Biography of the Speaker:
Ion Carstea is a Lecturer at the Computer Engineering
and Communications Department, Faculty of Automatics,
Computers and Electronics, University of Craiova,
Romania.
He has a BSc and MSc in Automatics from the University
of Craiova, Romania. He has a Ph.D. in Automatics from
the University of Ploiesti, Romania. Also, he has a BSc
and MSc in Mathematics from the Natural Sciences
Faculty, University of Craiova, Romania.
He is an active reviewer of WSEAS activities and is an
author of tens of papers included in volumes of the
WSEAS conferences. He attended as plenary lecturer (7)
and chair (7) of WSEAS conferences in Arcachon (France),
Venice (Italy), and Bucharest (Romania).
Ion Carstea was director of the research projects
supported by international grants at University of
Houston (USA) 6 months (Fulbright Fellowship), at the
University of Coimbra, Portugal – 9 months (NATO grant),
at the Polytechnics of Milano, Italy 4 months (a CNRNATO
grant). In 2004 he was member in a research team at the
Mathematics Department, University of Trento, Italy, for
2 months.
Ion Carstea has published 11 books in the area of
programming languages, advanced computers and CAD of the
electromagnetic devices. He is the author of more than
150 papers in revues, scientific journals and
international conference proceedings. He is a reviewer
for several WSEAS International Conferences and was a
member in many international scientific committees. He
was included in editorial board of 5 volumes of the
WSEAS Proceedings edited in 20072008, and is one of the
authors of WSEAS book “The finite element method”.
His research interests include parallel algorithms for
numerical simulation of the distributedparameter
systems of elliptic and parabolic types, development of
software products for coupled and inverse problems in
engineering, CAD of the electromagnetic device based on
the finite element method, and domain decomposition
method for engineering applications.
