Numerical Algorithms for Analysis and Synthesis of Distributed
Parametersystems in Engineering
Professor Ion Carstea
University of Craiova,
ROMANIA
E-mail: incrst@yahoo.com
Abstract: In practical engineering analysis and synthesising the best
engineering solution to a given design problem are of great interest. This
lecture presents numerical algorithms for analysis and synthesis of
distributed-parameter systems with direct applications in electrical
engineering. The algorithms are developed in the context of the finite
element method both for conventional and advanced computers. Many works in
the professional literature present the algorithms for analysis and
synthesis of the systems described by the partial derivative equations. In
our work we present a general class of distributed-parameter systems with
emphasis on continuos parabolic – elliptic problems in a two-dimensional
space. Optimisation methods have been efficiently developed and applied to
electromagnetics and mechanics. Unfortunately, the methods developed always
deal with single systems. The reality is the coupled problems exist and are
complex because of the critical design parameters are in both systems.
Our paper is structured in two parts:
• Analysis of distributed parameter systems
• Synthesis of distributed parameter systems using both boundary and
distributed (internal) commands
The most popular approach for the solution of an optimal control problem
utilises the variational calculus for the development of necessary
conditions for optimality. We consider constrained problems and Lagrange’s
multipliers method. Since the necessary optimality conditions are
distributed, their use in the development of numerical algorithms requires
that they be discretized both in space and time. The finite element method
is an attractive alternative to the well-known finite difference method for
numerical analysis and synthesis of many problems that arise in engineering
and science. The lecture demonstrates the applicability of the finite
element method to numerical simulation of the distributed parameter systems
with emphasis on the engineering problems. The optimal command is found by
gradient techniques for constrained problems. We use sensitivity analysis
that proved to give a proper design in terms of computational efficiency.
For large-scale systems we apply the domain decomposition techniques. The
decomposition is guided by physical considerations in the context of the
finite element method.
Finally, we consider some practical examples from engineering, with emphasis
on coupled models for magneto-thermal and electro-heating applications. We
present some numerical experiments where we try to compute the solution of a
problem with a desired level of accuracy and at the same time minimising the
computational resources.
Brief
Biography of the Speaker:
The
speaker is an Assoc. Professor 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 was
director of the research projects supported by international grants at
University of Houston (USA)- 6 months (Fulbright Grant), at the University
of Coimbra, Portugal – 9 months (NATO grant), at the Polytechnics of Milano,
Italy- 4 months (a CNR-NATO grant). In 2004 he was invited at the
Mathematics Department, University of Trento, Italy, for 2 months.
Ion
Cârstea published 10 books in the area of programming languages, advanced
computers and CAD of the electromagnetic devices. He is the co-author of
the book FINITE ELEMENTS in WSEAS Press, 2007.
He is the
author of more than 130 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. In the year 2007, he was Plenary speaker and chair at the WSEAS
Conferences from Arcachon (France) and Venice (Italy).
His research interests include
parallel algorithms for numerical simulation of the distributed-parameter
systems, software products for coupled and inverse problems in engineering,
domain decomposition method in the context of the finite element method.
