A high order finite element formulation for the simulation of 3D Magneto-Mechanical problems with application to MRI scanners

Transient magnetic fields generated by the gradient coils in MRI scanners 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 the coupled physics magneto-mechanical problem, which will be addressed in this work. For the accurate simulation of this problem, a Lagrangian approach is used, which leads to a staggered scheme. This is discretised by high order finite elements leading to accurate solution. We demonstrate the success of our scheme by applying to realistic MRI scanner configurations and increase the efficiency of our technique by using a reduced order model based on the proper orthogonal decomposition. New symmetry conditions and an approach to map the current source to the space of divergence free functions are added as novel contributions.