A staggered high-dimensional Proper Generalised Decomposition for coupled magneto-mechanical problems with application to MRI scanners

Barroso, Guillem; Seoane, M.; Gil, Antonio J.; Ledger, P.D.; Mallett, M. J. D.; Huerta, Antonio

doi:10.1016/j.cma.2020.113271

Cited by 13 publications

(18 citation statements)

References 44 publications

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“…In the online stage, the solution can be particularized for any set of the parameters in real time. The method has been tested in the most diverse fields, such as flow problems, 20‐24 thermal problems, 25‐27 solid mechanics, 28,29 fracture mechanics, 30,31 elastic metamaterials, and coupled magneto‐mechanical problems 32,33 …”

Section: Introductionmentioning

confidence: 99%

“…The method has been tested in the most diverse fields, such as flow problems, [20][21][22][23][24] thermal problems, [25][26][27] solid mechanics, 28,29 fracture mechanics, 30,31 elastic metamaterials, and coupled magneto-mechanical problems. 32,33 Despite the wide range of problems where the PGD has shown its potential, the application to geometrically parametrized problems remains particularly challenging, due to the difficulty to obtain a separable expression of the discrete problem. Previous works that dealt with parametric shapes are usually limited to simple geometric dependence.…”

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confidence: 99%

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Nonintrusive reduced order model for parametric solutions of inertia relief problems

Cavaliere

Zlotnik

Sevilla

et al. 2021

Numerical Meth Engineering

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The Inertia Relief (IR) technique is widely used by industry and produces equilibrated loads allowing to analyze unconstrained systems without resorting to the more expensive full dynamic analysis. The main goal of this work is to develop a computational framework for the solution of unconstrained parametric structural problems with IR and the Proper Generalized Decomposition (PGD) method. First, the IR method is formulated in a parametric setting for both material and geometric parameters. A reduced order model using the encapsulated PGD suite is then developed to solve the parametric IR problem, circumventing the so-called curse of dimensionality. With just one offline computation, the proposed PGD-IR scheme provides a computational vademecum that contains all the possible solutions for a predefined range of the parameters. The proposed approach is nonintrusive and it is therefore possible to be integrated with commercial finite element (FE) packages. The applicability and potential of the developed technique is shown using a three-dimensional test case and a more complex industrial test case. The first example is used to highlight the numerical properties of the scheme, whereas the second example demonstrates the potential in a more complex setting and it shows the possibility to integrate the proposed framework within a commercial FE package. In addition, the last example shows the possibility to use the generalized solution in a multi-objective optimization setting. K E Y W O R D Sinertia relief, nonintrusive, proper generalized decomposition, reduced order model, shape optimization INTRODUCTIONUnconstrained structures are widespread in the automotive, aerospace and naval industry. As is well known, due to the singularity of the stiffness matrix, conventional static analyses cannot be performed if the system undergoes rigid body motions. At the same time, imposing dummy constraints in order to make a free-body system statically determinate leadsThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Nonintrusive reduced order model for parametric solutions of inertia relief problems

Cavaliere

Zlotnik

Sevilla

et al. 2021

Numerical Meth Engineering

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“…The application of PGD to coupled magneto-mechanical problems with application to MRI scanners but restricted to axisymmetric configurations was also recently considered in [21,22]. Furthermore, the application of POD and PGD for the solution of this problem was compared in [22].…”

Section: Reduced Order Modellingmentioning

confidence: 99%

“…• Alternative ROM techniques: A further area of research would consist in studying the application of different ROM methodologies. First, the application of PGD could be considered, as this has already been applied to the magneto-mechanical problem of interest in axisymmetric configurations [21,22]. However, based on the comparison between POD and PGD performed in [21] for axisymmetric problems and having into account that preconditioned iterative solvers are required to solve the 3D electromagnetic problem, a new ROM where POD is applied to approximate the electromagnetic solution and PGD is applied to approximate the mechanical solution is suggested.…”

Section: Recommendations For Future Workmentioning

confidence: 99%

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3D simulation of magneto-mechanical coupling in MRI scanners using high order FEM and POD

Seoane¹

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Magnetic Resonance Imaging (MRI) scanners have become an essential tool in the medi-cal industry due to their ability to produce high resolution images of the human body. To generate an image of the body, MRI scanners combine strong static magnetic fields with transient gradient magnetic fields. The interaction of these magnetic fields with the con-ducting components present in superconducting MRI scanners gives rise to an important problem in the design of new MRI scanners. The transient magnetic fields give rise to the appearance of eddy currents in conducting components. These eddy currents, in turn, result in electromagnetic stresses, which cause the conducting components to deform and vibrate. The vibrations are undesirable as they lead to a deterioration in image quality (with image artefacts) and to the generation of noise, which can cause patient discomfort. The eddy currents, in addition, lead to heat being dissipated and deposited into the cryo-stat, which is filled with helium in order to maintain the coils in a superconducting state. This deposition of heat can cause helium boil off and potentially result in a costly magnet quench. Understanding the mechanisms involved in the generation of these vibrations and the heat being deposited into the cryostat are, therefore, key for a successful MRI scanner design. This involves the solution of a coupled magneto-mechanical problem, which is the focus of this work.In this thesis, a new computational methodology for the solution of three-dimensional (3D) magneto-mechanical coupled problems with application to MRI scanner design is presented. To achieve this, first an accurate mathematical description of the magneto-mechanical coupling is presented, which is based on a Lagrangian formulation and the assumption of small displacements. Then, the problem is linearised using an AC-DC splitting of the fields, and a variational formulation for the solution of the linearised prob-lem in a time-harmonic setting is presented. The problem is then discretised using high order finite elements, where a combination of hierarchical H1 and H(curl) basis func-tions is used. An efficient staggered algorithm for the solution of the coupled system is proposed, which combines the DC and AC stages and makes use of preconditioned iter-ative solvers when appropriate. This finite element methodology is then applied to a set of challenging academic and industrially relevant problems in order to demonstrate its accuracy and efficiency.This finite element methodology results in the accurate and efficient solution of the magneto-mechanical problem of interest. However, in the design stage of a new MRI scanner, this coupled problem must be solved repeatedly for varying model parameters such as frequency or material properties. Thus, even if an efficient finite element solver is available for the solution of the coupled problem, the need for these repeated simulations result in a bottleneck in terms of computational cost, which leads to an increase in design time and its associated financial implications. Therefore, in order to optimise this process, the application of Reduced Order Modelling (ROM) techniques is considered. A ROM based on the Proper Orthogonal Decomposition (POD) method is presented and applied to a series of challenging MRI configurations. The accuracy and efficiency of this ROM is demonstrated by performing comparisons against the full order or high fidelity finite element software, showing great performance in terms of computational speed-up, which has major benefits in the optimisation of the design process of new MRI scanners.

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Reduced order modelling using neural networks for predictive modelling of 3d-magneto-mechanical problems with application to magnetic resonance imaging scanners

Miah,

Sooriyakanthan,

Ledger

et al. 2023

Engineering with Computers

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The design of magnets for magnetic resonance imaging (MRI) scanners requires the numerical simulation of a coupled magneto-mechanical system where the effects that different material parameters and in-service loading conditions have on both imaging and MRI performance are key to aid with the design and the manufacturing process. To correctly capture the complex physics, and to obtain accurate solutions, finite element simulations with dense meshes and high order elements are needed. Reduced order model approaches, based on the established proper orthogonal decomposition (POD) approach, are attractive as they can rapidly predict the numerical simulations needed under changing parameters or conditions. However, the projected (PODP) approach has an invasive computational implementation, whilst the interpolated (PODI) approach presents challenges when the dimension of the space of parameters to be investigated becomes large. As an alternative, we investigate a POD technique based on using a neural network regression, which is not as invasive as PODP, but has superior approximation properties compared to PODI. We apply this to the coupled magneto-mechanical system to understand three pressing industrial problems: firstly, the accurate and rapid computation of the resonant frequencies associated with this coupled magneto-mechanical system, secondly, the effects of magnet motion on the Ohmic power and kinetic energy curves, and, thirdly, the prediction of the uncertainty in Ohmic power and kinetic energy curves as a function of exciting frequency for uncertain material parameters.

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A staggered high-dimensional Proper Generalised Decomposition for coupled magneto-mechanical problems with application to MRI scanners

Cited by 13 publications

References 44 publications

Nonintrusive reduced order model for parametric solutions of inertia relief problems

Nonintrusive reduced order model for parametric solutions of inertia relief problems

3D simulation of magneto-mechanical coupling in MRI scanners using high order FEM and POD

Reduced order modelling using neural networks for predictive modelling of 3d-magneto-mechanical problems with application to magnetic resonance imaging scanners

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