An hp-adaptive strategy for the solution of the exact kernel curved wire Pocklington equation

In this paper we introduce an adaptive method for the numerical solution of the Pocklington integro-differential equation with exact kernel for the current induced in a smoothly curved thin wire antenna. The hp-adaptive technique is based on the representation of the discrete solution, which is expanded in a piecewise p-hierarchical basis. The key element in the strategy is an element-by-element criterion that controls the h- or p-refinement. Numerical results demonstrate both the simplicity and efficiency of the approach

Space Mapping and Defect Correction

In this chapter we present the principles of the space-mapping iteration techniques for the efficient solution of optimization problems. We also show how space-mapping optimization can be understood in the framework of defect correction. We observe the difference between the solution of the optimization problem and the computed space-mapping solutions. We repair this discrepancy by exploiting the correspondence with defect correction iteration and we construct the manifold-mapping algorithm, which is as efficient as the space-mapping algorithm but converges to the true solution. In the last section we show a simple example from practice, comparing space-mapping and manifold mapping and illustrating the efficiency of the technique

The Eggshell method in a nutshell.

The Eggshell method was introduced by F. Henrotte as a novel magnetic force computation method. It allows computation of the force by integrating the magnetic stress tensor over a shell surrounding the body of interest. We investigate the numerical properties of this method for current carrying wires, and permanent magnets immersed in two-dimensional stationary magnetic fields, discretized by first and second order isoparametric triangular finite elements. We do so by comparing the accuracy of the method, as a function of the mesh size and element order, with the result of three classical force computation methods: the Lorentz, the Virtual Work and the Maxwell Stress Tensor method. Our numerical results clearly show that for current carrying wires the Lorentz method is the method of choice. For permanent magnets (for which the Lorentz method no longer applies) the isoparametric second order Eggshell method is more accurate than the Virtual Work or the Maxwell Stress Tensor method. These results make the Eggshell method attractive for use in more complex problems. The Eggshell method is applied on second order isoparametric elements. Its implementation is presented in detail as a set of new MATLAB post-processing routines in the FEMLAB simulation environmen

Optimization in Electromagnetics with the Space-Mapping Technique

Abstract: Purpose – Optimisation in electromagnetics, based on finite element models, is often very time-consuming. In this paper, we present the space-mapping (SM) technique which aims at speeding up such procedures by exploiting auxiliary models that are less accurate but much cheaper to compute. Design/methodology/approach – The key element in this technique is the SM function. Its purpose is to relate the two models. The SM function, combined with the low accuracy model, makes a surrogate model that can be optimised more efficiently. Findings – By two examples we show that the SM technique is effective. Further we show how the choice of the low accuracy model can influence the acceleration process. On one hand, taking into account more essential features of the problem helps speeding up the whole procedure. On the other hand, extremely simple auxiliary models can already yield a significant acceleration. Research limitations/implications – Obtaining the low accuracy model is not always straightforward. Some research could be done in this direction. The SM technique can also be applied iteratively, i.e. the auxiliary model is optimised aided by a coarser one. Thus, the generation of hierarchies of models seems to be a promising venue for the SM technique. Originality/value – Optimisation in electromagnetics, based on finite element models, is often very time-consuming. The results given show that the SM technique is effective for speeding up such procedures

Space-mapping techniques applied to the optimization of a safety isolating transformer

Space-mapping optimization techniques allow to allign low-fidelity and high-fidelity models in order to reduce the computational time and increase the accuracy of the solution. The main idea is to build an approximate model from the difference of response between both models. Therefore the optimization process is computed on the surrogate model. In this paper, some recent approaches of space-mapping techniques such as agressive-space-mapping, output-mapping and manifold-mapping algorithms are applied to optimize a safety insulating transformer. The electric, magnetic and thermal phenomena of the device are modeled by an analytical model and a 3D finite element model. It is considered as a benchmark for multi-level optimization to test different algorithms

Adaptive manifold-mapping using multiquadric interpolation applied to linear actuator design

In this work a multilevel optimization strategy based on manifold-mapping combined with multiquadric interpolation for the coarse model construction is presented. In the proposed approach the coarse model is obtained by interpolating the fine model using multiquadrics in a small number of points. As the algorithms iterates, the response surface model is improved by enriching the set of interpolation points. This approach allows to accurately solve the TEAM Workshop Problem 25 using as little as 33 finite element simulations. Furthermore is allows a robust sizing optimization of a cylindrical voice-coil actuator with seven design variables. Further analysis is required to gain a better understand of the role that the initial coarse model accuracy plays the convergence of the algorithm. The proposed allows to carry out such analysis by varying the number of points included in the initial response surface model. The effect of the trust-region stabilization in the presence of manifolds of equivalent solutions is also a topic of further investigations