A method of free-form optimisation for shaping an electrode surface is proposed in the context of shape design of high voltage devices. The subsequent comparison of various optimisation approaches in dielectric design is developed. In particular, a mesh-based model, driven by free-form optimisation, is presented and compared with a parameter-based model and a NURBS-based model driven by parametric optimisation algorithms. In each model, the electric field analysis is computed by means of the Boundary Element Method. In order to assess the proposed method in a comparative way, the optimal shape design of a L-shaped tunnel electrode and a ring electrode are considered as the case studies.
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