Summary Transient magnetic fields are generated by the gradient coils in an magnetic resonance imaging (MRI) scanner and induce eddy currents in their conducting components, which lead to vibrations, imaging artefacts, noise, and the dissipation of heat. Heat dissipation can boil off the helium used to cool the super conducting magnets and, if left unchecked, will lead to a magnet quench. Understanding the mechanisms involved in the generation of these vibrations, and the heat being deposited in the cryostat, are key for a successful MRI scanner design. This requires the solution of a coupled physics magneto‐mechanical problem, which will be addressed in this work. A novel computational methodology is proposed for the accurate simulation of the magneto‐mechanical problem using a Lagrangian approach, which, with a particular choice of linearisation, leads to a staggered scheme. This is discretised by high‐order finite elements leading to accurate solutions. We demonstrate the success of our scheme by applying it to realistic MRI scanner configurations.

The design of a new MRI scanner requires multiple numerical simulations of the same magneto-mechanical problem for varying model parameters, such as frequency and electric conductivity, in order to ensure that the vibrations, noise and heat dissipation are minimized. The high computational cost required for these repeated simulations leads to a bottleneck in the design process due to an increased design time and, thus, a higher cost. To alleviate these issues, the application of reduced order modelling techniques, which are able to find a general solution to high dimensional parametric problems in a very efficient manner, is considered. Building on the established Proper Orthogonal Decomposition (POD) technique available in the literature, the main novelty of this work is an efficient implementation for the solution of 3D magnetomechanical problems in the context of challenging MRI configurations. This methodology provides a general solution for varying parameters of interest. The accuracy and efficiency of the method is proven by applying it to challenging MRI configurations and comparing with the full order solution.