CST EM STUDIO® (CST EMS) has a myriad of features which facilitates the generation of complex geometries, accurate results and rapid simulation. Most complex geometries are imported into CST EMS via its integrated CAD Interface but, in the case of optimization, it may be better to create the object in EMS itself even for complex components. A combination of the two approaches is also possible i.e. local remodeling of the electrode in an imported CAD model.
An example of an optimization task is the geometry of an electrode as found in switchgear. The model is set up to emulate the conditions found in a Basic Insulation Level (BIL) test. The electrostatic solver was used to calculate the electric field. Even if the final optimized geometry may be difficult to manufacture, some insight can be gained by optimization. The example here demonstrates the principle which can be applied in the optimization of real world applications....
Figure 1 shows the simple arrangement devised to demonstrate the principles involved. Here, only two conductors have been created as opposed to a 3 conductor system typically found in switchgear and similar equipment. Another deviation from a real switchgear is the environment - here the electrode is modelled in free space. Furthermore, the rounding has been applied to the extremities of all conductors which is a further difference which, for the purpose of this demonstration, should not affect the optimization result.
Although there are many approaches that can be applied, such as splines, this example uses the blend and loft features combined with parameterization. It's imperative, however, that the parameterized geometry can be reliably generated for each optimizer pass, especially for models which involve complex interactions between geometrical parameters and features.
Figure 2 summarises a part of the electrode geometry construction. Three curves are created prior to a lofting operation. The profile curves are defined using the edges of a dummy brick with blended edges. The path curve is defined using the polygon curve tool. The coordinates of the polygon are defined as parameters which are used for the subsequent optimization. The position of the polygon points are scaled as shown in the figure. More flexibility can be applied at this point for even more complex geometries.
The potentials can be defined to emulate any particular condition or test set-up such as Basic Insulation Level (BIL) or Basic Impulse Level tests. Typical values are shown in Figure 3 where -100 kV and 650kV have been applied to conductor set 1. The user may determine the default conditions, grounded or floating for any undefined PEC components. In this case, the undefined conductors are grounded.
CST EMS supports curved elements as shown in Figure 4 which ensure excellent approximation of rounded geometries - a critical feature for such problems especially for the optimization of smooth, complex electrode geometries. This alleviates doubts that would normally arise regarding the accuracy of the simulations and the validity of the optimization.
Simply increasing the solver (basis function) order will not improve the result from a standard mesh since the mesh is not a true representation of the real geometry. In fact, the situation becomes worse. On the other hand, a higher order solution may be used in conjunction with curved elements. In this case, 2nd order was used. The maginitude and, equally important, the location of the maximum electric field required for this optimization will vary between the standard and curved mesh results.
The absolute component of the electric field strength in the electrode system is shown logarithmically scaled in Figure 5. The maximum field strength will be extracted automatically from this result via the integrated Template Based Post-Processing system (TBPP) and used as the goal function for the optimization.
The integrated CST EMS Optimizer has many optimization algorithms at its disposal. For this model, the CMA (Covariance Matrix Adaptation) Evolutionary Strategy  was chosen. This is the most sophisticated approach of the implemented global optimizers and uses a statistical model in combination with a step size parameter. CMA-ES also exploits the history of successful optimization steps to improve the algorithm's performance without sacrificing its global optimization properties. As an alternative to CMA-ES, the state-of-the-art Trust Region Framework algorithm could equally be used for this optimization. The results of the optimization are shown in Figure 6, where the goal function, the maximum electric field in the structure, is plotted as a function of optimizer step.
The optimized geometry is shown in Figure 7. The usefulness of optimization depends not just on factors such as the accurate approximation of the geometry and solver accuracy but also the definition of the problem. In this model, a scaling factor is applied to the polygonal points. This degree of freedom may be extended possibly at the expense of creating geometries which may geometrically fail. Although simulation is a powerful tool, it is not intended to replace the judgement and experience of the user who needs to set a model up that may not just be optimized but also manufactured.
The features shown in this article can also be applied to other types of problems e.g. magnet optimization. The integrated approach to model construction, simulation, post-processing and optimization leads to an efficient workflow for the optimization of practical components and devices. The above procedure was applied to a simplified electrode system in free space. In reality, such an electrode system found in switchgear is confined to a closed structure with complex conductor arrangements. The real environment of the electrode system can easily be imported with CST EMS's CAD Interoperability tools  in which remodeling of electrodes and attribution of parameters can be carried out in the same way.