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

Abstract

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.

Citation

Di Barba, P., Dughiero, F. and Sieni, E. (2012), "Non‐parametric optimal shape design of a magnetic device for biomedical applications", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 31 No. 5, pp. 1358-1367. https://doi.org/10.1108/03321641211246419