Towards MRI scanner design: the Proper Generalised Decomposition in the context of coupled magneto-mechanical problems

Latest developments in high-strength Magnetic Resonance Imaging (MRI) scanners, with in-built high resolution, have dramatically enhanced the ability of clinicians to diagnose tumours and rare illnesses. However, their high-strength transient magnetic fields induce unwanted eddy currents in shielding components, which result in high-frequency vibrations, noise, imaging artefacts and, ultimately, heat dissipation and boiling off of the helium used to super-cool the magnets. Optimum MRI scanner design requires the capturing of complex electro-magneto-mechanical interactions with high fidelity computational tools. Moreover, manufacturing new MRI scanners still represents a computational challenge to industry due to the large variability in material parameters and geometrical configurations that need to be tested during the early design phase. This process can be highly optimised through the employment of user-friendly computational metamodels constructed on the basis of Reduced Order Modelling (ROM) techniques, where high-dimensional parametric offline solutions are obtained, stored and assimilated in order to be efficiently queried in real time.This thesis presents a novel a priori Proper Generalised Decomposition (PGD) computational framework for the analysis of the electro-magneto-mechanical inter-actions in the context of MRI scanner design to address the urgent need for the development of new cost-effective methods, whereby previously performed compu-tations can be assimilated as training solutions of a surrogate digital twin model to allow for real-time simulations. The PGD methodology is derived for coupled electro-magneto-mechanical problems in an axisymmetric Lagrangian setting, in-cluding the possibility to vary several material and geometrical parameters (as part of the high-dimensional offline solution), that are relevant for the industrial part-ner of the project, Siemens Healthineers. A regularised-adaptive strategy and a staggered PGD approach are proposed in order to enhance the accuracy and robust-ness of the PGD algorithm while preserving its a priori nature. The Lagrangian adaptation of the governing equations will allow for a comparison between staggered and monolithic solvers, where the staggered approach will be shown to enhance the robustness and accuracy of the PGD technique. Moreover, geometric changes in the computational domain will be accounted for in the PGD solution by using a PGD-projection technique that will enable the computation of a separable expression even for geometrical variations, preserving thus the efficiency of the online PGD stage. A set of numerical problems will be presented in order to validate the PGD formula-tion, which will be benchmarked against the full order (reference) model. Moreover, a comparison between two families of ROM methods, the a priori PGD and the a posteriori Proper Orthogonal Decomposition (POD), will also be performed in order to assess and compare different ROM strategies.