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The paper presents a new variant of the H-Φ field formulation for solving 3-D magnetostatic and frequency domain eddy current problems. The suggested formulation uses the vector and scalar tetrahedral elements within conducting and non-conducting domains, respectively. The presented numerical method is capable of solving multiply connected regions and eliminates the need for computing the source current density and the source magnetic field before the actual magnetostatic and eddy current simulations. The obtained magnetostatic results are verified by comparison against the corresponding results of the standard stationary current distribution analysis combined with the Biot-Savart integration. The accuracy of the eddy current results is demonstrated by comparison against the classical A-A-f approach in frequency domain.

The theory and implementation of the new H-Φ magnetostatic and eddy current solver is presented in detail. The method delivers reliable results without the need to compute the source current density and source magnetic field before the actual simulation.

The proposed H-Φ produce radically smaller and considerably better conditioned equation systems than the alternative A-A approach, which usually requires the unphysical regularization in terms of a low electric conductivity value within the nonconductive domain.

The presented numerical method is capable of solving multiply connected regions and eliminates the need for computing the source current density and the source magnetic field before the actual magnetostatic and eddy current simulations.

The purpose of this paper is to extend a (μ/ρ, λ) evolution strategy to perform remarkably more globally and to detect as many solutions as possible close to the Pareto optimal front.

A C‐link cluster algorithm is used to group the parameter configurations of the current population into more or less independent clusters. Following this procedure, recombination (a classical operator of evolutionary strategies) is modified. Recombination within a cluster is performed with a higher probability than recombination of individuals coming from detached clusters.

It is shown that this new method ends up virtually always in the global solution of a multi‐modal test function. When applied to a real‐world application, several solutions very close to the front of Pareto optimal solutions are detected.

Stochastic optimization strategies need a very large number of function calls to exhibit their ability to reach very good local if not the global solution. Therefore, the application of such methods is still limited to problems where the forward solutions can be obtained with a reasonable computational effort.

The main improvement is the usage of approximate number of isolated clusters to dynamically update the size of the population in order to save computation time, to find the global solution with a higher probability and to use more than one objective function to cover a larger part of the Pareto optimal front.