Abstract: In our lecture we intend to review the state-of-the-art 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 non-linear 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 distributed-parameter 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 elliptic-parabolic mathematical models that represents the basis of the electromagnetic-thermal 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 electromagnetic-thermal 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 CNR-NATO 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 2007-2008, and is one of the authors of WSEAS book “The finite element method”.
His research interests include parallel algorithms for numerical simulation of the distributed-parameter 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.