Antonio Huerta’s research while affiliated with Polytechnic University of Catalonia and other places

Manufacturing new Magnetic Resonance Imaging (MRI) scanners 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 paper presents a novel Proper Generalised Decomposition (PGD) based metamodel for the analysis of electro-magneto-mechanical interactions in the context of MRI scanner design, with three distinct novelties. First, the paper derives, from scratch, a five-dimensional parametrised offline solution process, expressed in terms of (axisymmetric) cylindrical coordinates, external excitation frequency, electrical conductivity of the embedded shields and strength of the static magnetic field. Second, by exploiting the staggered nature of the coupled problem at hand, an efficient sequential PGD algorithm is derived and compared against a previously published monolithic PGD algorithm. As a third novelty, the paper draws some interesting comparisons against an alternative tailor-made ROM technique, where the electromagnetic equations are solved using a Proper Orthogonal Decomposition model. A series of numerical examples are presented in order to illustrate, motivate and demonstrate the validity and potential of the considered approach, especially in terms of cost reduction.

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 fast vibrations, noise, imaging artefacts and, ultimately, heat dissipation, boiling off 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. During production cycles, this is known to be extremely expensive due to the large number of configurations that need to be tested. There is an urgent need for the development of new cost-effective methods whereby previously performed computations can be assimilated as training solutions of a surrogate digital twin model to allow for real-time simulations. In this paper, a Reduced Order Modelling technique based on the Proper Generalised Decomposition method is presented for the first time in the context of MRI scanning design, with two distinct novelties. First, the paper derives from scratch the offline higher dimensional parametrised solution process of the coupled electro-magneto-mechanical problem at hand and, second, a regularised adaptive methodology is proposed for the circumvention of numerical singularities associated with the ill-conditioning of the discrete system in the vicinity of resonant modes. A series of numerical examples are presented in order to illustrate, motivate and demonstrate the validity and flexibility of the considered approach.

The audio recording of the talk can be found here: https://youtu.be/nKSlHcTnMIg

The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different geometrical parameter values and also allowing to compute readily the sensitivities. Instead of problem dependent approaches, a general framework is presented for standard engineering environments where the geometry is defined by means of NURBS. The parameters controlling the geometry are now the control points characterising the NURBS curves or surfaces. The approach proposed here, valid for 2D and 3D scenarios, allows a seamless integration with CAD preprocessors. The proper generalised decomposition (PGD), which is applied here to compute explicit geometrically parametrised solutions, circumvents the curse of dimensionality. Moreover, optimal convergence rates are shown for PGD approximations of incompressible flows.

The NURBS-enhanced finite element method (NEFEM) combined with a hybridisable discontinuous Galerkin (HDG) approach is presented for the first time. The proposed technique completely eliminates the uncertainty induced by a polynomial approximation of curved boundaries that is common within an isoparametric approach and, compared to other DG methods, provides a significant reduction in number of degrees of freedom. In addition, by exploiting the ability of HDG to compute a postprocessed solution and by using a local a priori error estimate valid for elliptic problems, an inexpensive, reliable and computable error estimator is devised. The proposed methodology is used to solve Stokes flow problems using automatic degree adaptation. Particular attention is paid to the importance of an accurate boundary representation when changing the degree of approximation in curved elements. Several strategies are compared and the superiority and reliability of HDG-NEFEM with degree adaptation is illustrated.

An industry-driven computational framework for the numerical simulation of large strain explicit solid dynamics is presented. This work focuses on the spatial discretisation of a system of first order hyperbolic conservation laws using the cell centred Finite Volume Method [1, 2, 3]. The proposed methodology has been implemented as a parallelised explicit solid dynamics tool-kit within the CFD-based open-source platform OpenFOAM. Crucially, the proposed framework bridges the gap between Computational Fluid Dynamics and large strain solid dynamics. A wide spectrum of challenging numerical examples are examined in order to assess the robustness and parallel performance of the proposed solver.

The paper presents a new computational framework for the numerical simulation of fast large strain solid dynamics, with particular emphasis on the treatment of near incompressibility. A complete set of first order hyperbolic conservation equations expressed in terms of the linear momentum and the minors of the deformation (namely the deformation gradient, its co-factor and its Jacobian), in conjunction with a polyconvex nearly incompressible constitutive law, is presented. Taking advantage of this elegant formalism , alternative implementations in terms of entropy-conjugate variables are also possible, through suitable symmetrisation of the original system of conservation variables. From the spatial discretisation standpoint, modern Computational Fluid Dynamics code "OpenFOAM" [http://www.openfoam.com/] is here adapted to the field of solid mechanics, with the aim to bridge the gap between computational fluid and solid dynamics. A cell centred finite volume algorithm is employed and suitably adapted. Naturally, discontinuity of the conservation variables across control volume interfaces leads to a Riemann problem, whose resolution requires special attention when attempting to model materials with predominant nearly incompressible behaviour (κ/µ ≥ 500). For this reason, an acoustic Riemann solver combined with a preconditioning procedure is introduced. In addition, a global a posteriori angular momentum projection procedure proposed in [1] is also presented and adapted to a Total Lagrangian version of the nodal scheme of Kluth and Després [2] used in this paper for comparison purposes. Finally, a series of challenging numerical examples is examined in order to assess the robustness and applicability of the proposed methodology with an eye on large scale simulation in future works.