New technique to enhance the accuracy of 2-D/3-D field quantities and forces obtained by standard finite-element solutions

Useful energy conversion in electromagnetic energy transducers takes place only in the air gap. Numerical field computation techniques which have a range of general applications are used for the design and optimisation of these electromagnetic devices. To predict their operational behaviour, particular attention has to be paid to the computation of the air gap values of the flux densities and the magnetic field strength. Ongoing research on force computations in electromagnetic devices using different approaches indicates the importance of this field. A new method for the accurate computation of the field quantities and, thus, the generated forces in two- and three-dimensional finite-element models, is presented. Solving a local Dirichlet problem analytically enhances the accuracy of the derived field quantities using a numerically computed potential solution. Derivatives required for the values of the flux density are calculated analytically, in order to improve their order of convergence towards the exact solution. A Fourier series is used to represent the local field solution of two- and three-dimensional problems. The paper is focused on the practical application of the static electromagnetic field solution of the Laplace equation in a local post-process. Finite-element test models using standard first-order elements are applied to demonstrate the proposed method. Advantages and drawbacks are discussed