A shape optimisation of mutual inductances among coils

TL;DR

This paper presents a shape optimisation framework for coils to achieve specific mutual inductances using wire modelling and gradient-based methods, validated through numerical examples and addressing a novel area in magnetostatic MI optimisation.

Contribution

It introduces a shape derivative derivation for mutual inductance objectives, enabling gradient-based coil design optimisation within a wire modelling framework.

Findings

Effective coil shape optimisation demonstrated through numerical examples.

The framework provides a computationally efficient alternative to finite element methods.

Addresses a largely unexplored area of magnetostatic mutual inductance optimisation.

Abstract

This paper introduces a shape optimisation framework for achieving desired mutual inductances (MIs) among coils in 3D space. Utilising a wire modelling approach, the coils are discretised using B-spline curves, with control points (CPs) serving as design variables. The key contribution is the derivation of the shape derivative of the objective function in terms of MIs, enabling the use of gradient-based quasi-Newton optimisation methods. A coil length constraint is also incorporated. The study demonstrates the effectiveness of the framework through numerical examples, validating the theoretical and numerical developments. This approach addresses the largely unexplored area of magnetostatic MI optimisation within the wire modelling framework, offering a computationally efficient alternative to finite element methods etc.