G. Molinari

Stochastic algorithms in electromagnetic optimization

This paper gives an overview of some stochastic optimization strategies, namely, evolution strategies, genetic algorithms, and simulated annealing, and how these methods can be applied to problems in electrical engineering. Since these methods usually require a careful tuning of the parameters which control the behavior of the strategies (strategy parameters), significant features of the algorithms implemented by the authors are presented. An analytical comparison among them is performed. Finally, results are discussed on three optimization problems.

A comparison of adaptive strategies for mesh refinement based on 'a posteriori' local error estimation procedures

A comparative evaluation of the performance of adaptive meshing algorithms with different error estimators is presented. The algorithms are oriented toward electric and magnetic analysis applications. The performance of a selected set of algorithms that are based on an element-by-element h-refinement technique is assessed in some test cases in comparison with analytical results, in a uniform environment. Finally, the features of the various possible error estimation parameters are presented and discussed. >

A parallel simulated annealing algorithm for the design of magnetic structures

A new parallel global optimization algorithm is presented and evaluated. It is based on simulated annealing and on speculative computation. It is particularly suited for parallel architectures from some units to some tens of processors and for problems characterized by a cost function whose evaluation takes a long time, features that fit well with the design of magnetic structures. Comparative tests with respect to traditional sequential SA is presented on the design of a magnet for Magnetic Resonance Imaging. >

A combined approach for the stochastic optimisation of multiminima problems using adaptive fuzzy sets and radial basis functions

The present paper discusses a technique, based on the combined use of Radial Basis Functions (RBF), which provide an analytical approximation of the true cost function, and self adaptive fuzzy sets, which allow a flexible combination of conflicting objectives, for the stochastic optimisation of multiminima problems. The proposed technique is fully described, its features of interest for industrial level design optimisation are outlined and some initial positive results are presented.

Global optimization for discrete magnetostatic problems

The problem of global optimization of magnetic structures composed of solenoids is examined, using a modified simulated annealing algorithm able to deal with the functions of continuous and/or discrete variables. The algorithm is tested using a discrete problem which allows determination of the cost function for every possible configuration of the system, providing information about the pattern of the cost function with respect to design variables. Despite the difficulty of minimizing the function, the proposed algorithm was able to locate the global minimum, or a point where the cost function has a value very close to it, seven times out of a total of ten runs. The algorithm is described, and results are discussed. >

Local error estimation procedures as refinement indicators in adaptive meshing

A comparative evaluation of the quality of three different error estimation procedures used as refinement indicators and final error estimators is presented. The performance of each method, based on an element-by-element h-refinement technique, is assessed in a test case provided with an analytical solution, in a uniform environment. >

Analysis of thermo-electromagnetic stresses in high field tokamak resistive coils

The problem of the accurate computation of thermo-electromagnetic stresses in a toroidal field coil for Tokamak machines will be an important task in the design of future high field Tokamak machines. The high value of flux density, and the pulsed current operation of these machines, imply critical working conditions and require a correct modelling of the thermal and electrical diffusion phenomena. In this paper are presented the thermo-electromagnetic model developed for this aim and the results obtained by implementing this model in the code COMPELL. These results are then used to derive input data for the structural analysis code, ANSYS, thus providing the means for a rather detailed analysis of the structure.

An evaluation of speedup in conjugate gradient routines with a mathematical vector library

The experience in vectorizing finite element and finite difference electromagnetic analysis codes is reported. Techniques to efficiently use vector machines in problems involving sparse, unstructured matrices are discussed. In this context a sparse matrix storage scheme particularly suited to vector architectures is introduced. The results of experience in the use of a library of conjugate-gradient-type solvers suited to vector architectures implemented according to this matrix structure are reported and discussed. >

A flexible environment for an efficient exploitation of vector features in electric and magnetic analysis

The authors present a vector environment, built around a reconfigurable data structure and a library of solver routines, devised for an efficient exploitation of vector features of computers to speed up magnetic analysis codes. The tests performed for the definition of the environment are reported and commented on, and the final results showing significant speedups in real magnetic analysis cases on a selected vector machine are presented and discussed. It is concluded that the use of the vector environment defined by the ITPLUS storage and the APPEAL library of solver routines has proven practical and successful as a way to allow users to efficiently exploit vector architectures, while protecting them from the need of large recoding efforts and of deep knowledge in computer architecture features and performances. >

An approach to the solution of coupled transient non-linear problems solving the set of equations as a single system (electromagnetic fields)

A procedure designed to solve as a single system the set of differential equations describing a coupled problem, including transient nonlinear cases, is presented. The procedure is based on the discretization of the equations to produce a single algebraic system. The implementation of the method is explained, and applications to a nonlinear thermomagnetic problem and a sinusoidal steady-state eddy current problem are described. The potential advantages and drawbacks, as compared to those of other procedures, are discussed. >