Non-parametric optimal shape design of a magnetic device for biomedical applications

Purpose - The purpose of the paper is to propose a cost-effective method of non-parametric optimisation in order to explore shapes of a magnetic pole, in the search for the optimal one fulfilling a prescribed objective function. Design/methodology/approach - The boundary of the magnetic field region to synthesize is considered as a moving boundary separating two materials (air and ferrite). An objective-function dependent velocity field is defined, in order to update the position of nodes located along the unknown boundary. Specifically, a uniform magnetic field within the controlled region is aimed at. Findings - The application of the proposed method to the design of a magnet for magnetic-fluid hyperthermia made it possible to reduce the field deviation with a little computational effort. Practical implications - Instead of using a standard algorithm of numerical minimisation to find the optimal search direction, a field-dependent velocity proportional to the objective function value is exploited. This way, the motion of the boundary towards the optimal shape is automatically driven: in principle, in fact, the velocity reaches the zero value at the optimum. Originality/value - Thanks to the kinematic law governing the movement of the boundary to synthesize, the overall computational cost is low. Moreover, the non-parametric approach to the shape synthesis preserves the advantage of a broad search space.