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Transient solutions to nonlinear acousto-magneto-mechanical coupling for axisymmetric MRI scanner design
International Journal for Numerical Methods in Engineering, Volume: 115, Issue: 2, Pages: 209 - 237
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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 non‐linear system of equations is necessary and we consider two altern...
|Published in:||International Journal for Numerical Methods in Engineering|
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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 non‐linear system of equations is necessary and we consider two alternative approaches. In the first, the non‐linear approach, there is no approximation from a physical standpoint and the linearisation is performed about the current solution. In the second, 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; 1) How good is the agreement between the computationally efficient linearised approach compared with the intensive non‐linear approach? and 2) 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.
Multified systems, Finite element methods, Newton methods, Time integration implicit, Linearisation, Acousto‐magneto‐mechanical coupling, MRI Scanner