MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1242 products
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06/2020 - 01/22/2020
Domanin, M.; Piazzoli, G.; Trimarchi, S.; Vergara, C.
Image-based displacements analysis and computational blood dynamics after endovascular aneurysm repair | Abstract | | Purpose. To examine intra heartbeat displacements (IHD) and geometrical changes over years, defined as follow-up displacements (FUD), of the endograft for abdominal aortic aneurysm repair, and to correlate them with computational fluid dynamics (CFD). Despite the widespread diffusion of endovascular aneurysm repair (EVAR) we still do not know very much about endograft behavior after deployment.
Methods. Two cases, treated with expanded polytetrafluoroethylene (PTFE) on nitinol stent frame (PI) and with woven polyester fabric sutured to stainless steel Z-stent skeleton (PII), respectively, were submitted to dynamic computed tomography angiography (CTA) at 1, 12 and 60 months. After segmentation, IHD were computed as displacements of the reconstructed surface with respect to the diastolic instant. Similarly, FUD were studied using imaging techniques that align temporal successive segmentations. At last, numerical simulations for blood dynamics were performed to compute viscous forces i.e. Wall Shear Stress (WSS) and Time Average WSS (TAWSS).
Results. IHD analysis showed slight translations without deformation for PI endograft with respect to the stiffer stainless steel endograft behaviour of PII. FUD showed in PI motion of the metallic struts mainly focused in the distal main body and in overlapping zone with iliac branches while in PII we observed a huge FUD in the middle and inferior-anterior regions of the main body. CFD analysis revealed changes of velocity patterns associated to remodelling of the iliac zone for PI and of the main body region for PII, where flow impinges the lumen wall and progressively provokes deformation of the endograft wires. TAWSS exhibits flow disturbances in the enlarged region coherently with displacements analysis.
Conclusion. Image-based displacements analysis associated to CFD allow to perform very subtle evaluations of endograft behaviour on different temporal scales. This kind of study could be helpful both for physicians, forecasting evolution during the life span of the endograft, and for manufacturers, giving them useful indication about endograft implant and design.
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05/2020 - 01/22/2020
Artioli, E.; Beiraoda Veiga, L.; Verani, M.
An adaptive curved virtual element method for the statistical homogenization of random fibre-reinforced composites | Abstract | | In the framework of statistical asymptotic homogenization of random fibre-reinforced composites, we propose a curved virtual element procedure that allows an exact geometric representation.
We develop an approach that is able to represent exactly the involved geometry and exploits an adaptive tuning of the optimal mesh resolution through a robust and efficient residual-based a-posteriori error estimator.
Furthermore, by combining such scheme and Monte Carlo simulations, a methodology is developed to determine homogenized material moduli and representative unit cell size. A gallery of numerical tests supports the proposed approach. |
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04/2020 - 01/21/2020
Didkovskyi, O.; Azzone, G.; Menafoglio A.; Secchi P.
Social and material vulnerability in the face of seismic hazard: an analysis of the Italian case | Abstract | | The assessment of the vulnerability of a community endangerd by seismic hazard is of paramount importance for planning a precision policy aimed at the prevention and reduction of its seismic risk. We aim at measuring the vulnerability of the Italian municipalities exposed to seismic hazard, by analyzing the open data offered by the Mappa dei Rischi dei Comuni Italiani provided by ISTAT, the Italian National Institute of Statistics. Encompassing the Index of Social and Material Vulnerability already computed by ISTAT, we also consider as referents of the latent social and material vulnerability of a community, its demographic dynamics and the age of the building stock where the community resides. Fusing the analyses of different indicators, within the context of seismic risk we offer a tentative ranking of the Italian municipalities in terms of their social and material vulnerability, together with differential profiles of their dominant fragilities which constitute the basis for planning precision policies aimed at seismic risk prevention and reduction.
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03/2020 - 01/10/2020
Ferro, N.; Micheletti, S.; Perotto, S.
Compliance-stress constrained mass minimization for topology optimization on anisotropic meshes | Abstract | | In this paper, we generalize the SIMPATY algorithm, which combines the SIMP method with anisotropic mesh adaptation to solve the minimum compliance problem with a mass costraint. In particular, the mass of the final layout is now minimized and both a maximum compliance and a maximum stress can be enforced as either mono- or multi-constraints. The new algorithm, named MSC-SIMPATY, is able to sharply detect the material-void interface, thanks to the anisotropic mesh adaptation. The presented test cases deal with three different scenarios, with a focus on the effect of the constraints on the final layouts and on the performance of the algorithm. |
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02/2020 - 01/10/2020
Fresca, S.; Dede', L.; Manzoni, A.
A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs | Abstract | | Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs, because of the fundamental assumption of linear superimposition of modes they are based on. For this reason, in the case of problems featuring coherent structures that propagate over time such as transport, wave, or convection-dominated phenomena, the RB method usually yields inefficient reduced order models (ROMs) if one aims at obtaining reduced order approximations sufficiently accurate compared to the high-fidelity, full order model (FOM) solution. To overcome these limitations, in this work, we propose a new nonlinear approach to set reduced order models by exploiting deep learning (DL) algorithms. In the resulting nonlinear ROM, which we refer to as DL-ROM, both the nonlinear trial manifold (corresponding to the set of basis functions in a linear ROM) as well as the nonlinear reduced dynamics (corresponding to the projection stage in a linear ROM) are learned in a non-intrusive way by relying on DL algorithms; the latter are trained on a set of FOM solutions obtained for different parameter values. In this paper, we show how to construct a DL-ROM for both linear and nonlinear time-dependent parametrized PDEs; moreover, we assess its accuracy on test cases featuring different parametrized PDE problems. Numerical results indicate that DL-ROMs whose dimension is equal to the intrinsic dimensionality of the PDE solutions manifold are able to approximate the solution of parametrized PDEs in situations where a huge number of POD modes would be necessary to achieve the same degree of accuracy. |
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01/2020 - 01/05/2020
Pozzi, S.; Vergara, C.
Mathematical and numerical models of atherosclerotic plaque progression in carotid arteries | Abstract | | We propose a mathematical model for the description of plaque progression in carotid arteries.
This is based on the coupling of a fluid-structure interaction problem, arising between blood and vessel wall,
and differential problems for the cellular evolution. A numerical model is also proposed. This is based on
the splitting of the coupled problem based on a suitable strategy to manage the multiscale-in-time
nature of the problem. We present some preliminary numerical results both in ideal and real scenarios. |
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60/2019 - 12/30/2019
Ieva, F; Paganoni, A.M.; Romo, J.; Tarabelloni, N.
roahd Package: Robust Analysis of High Dimensional Data | Abstract | | The focus of this paper is on the open-source R package roahd (RObust Analysis
of High dimensional Data), see Tarabelloni et al. (2017). roahd has been developed to gather
recently proposed statistical methods that deal with the robust inferential analysis of univariate
and multivariate functional data. In particular, efficient methods for outlier detection and related
graphical tools, methods to represent and simulate functional data, as well as inferential tools for
testing differences and dependency among families of curves will be discussed, and the associated
functions of the package will be described in details. |
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58/2019 - 12/30/2019
Antonietti, P.F; Manzini, G.; Mourad, H.M.; Verani, M.
The virtual element method for linear elastodynamics models. Design, analysis, and implementation | Abstract | | We design the conforming virtual element method for the numerical simulation of two dimensional time-dependent elastodynamics problems. We investigate the performance of the method both theoretically and numerically. We prove the stability and the convergence of the semi-discrete approximation in the energy norm and derive optimal error estimates. We also show the convergence in the $L^2$ norm.
The performance of the virtual element method is assessed on a set
of different computational meshes, including non-convex cells up to order four in the $h$-refinement setting. Exponential convergence is also experimentally seen in the $p$-refinement setting. |
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