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: