| Abstract: | In this work, we simulate the coupled physics describing a magnetic resonance imaging (MRI) scanner by using a higher‐order finite element discretisation and a Newton‐Raphson algorithm. To apply the latter, a linearisation of the nonlinear system of equations is necessary, and we consider two alternative approaches. In the first approach, ie, the nonlinear approach, there is no approximation from a physical standpoint, and the linearisation is performed about the current solution. In the second approach, ie, the linearised approach, we realise that the MRI problem can be described by small dynamic fluctuations about a dominant static solution and linearise about the latter. The linearised approach permits solutions in the frequency domain and provides a computationally efficient way to solve this challenging problem, as it allows the tangent stiffness matrix to be inverted independently of time or frequency. We focus on transient solutions to the coupled system of equations and address the following two important questions: (i) how good is the agreement between the computationally efficient linearised approach compared with the intensive nonlinear approach and (ii) over what range of MRI operating conditions can the linearised approach be expected to provide acceptable results for outputs of interest in an industrial context for MRI scanner design? We include a set of academic and industrially relevant examples to benchmark and illustrate our approach. |
