Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1249 prodotti
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03/2022 - 09/01/2022
Giacomini, M.; Perotto, S.
Anisotropic mesh adaptation for region-based segmentation accounting for image spatial information | Abstract | | A finite element-based image segmentation strategy enhanced by an anisotropic mesh adaptation procedure is presented. The methodology relies on a split Bregman algorithm for the minimisation of a region-based energy functional and on an anisotropic recovery-based error estimate to drive mesh adaptation. More precisely, a Bayesian energy functional is considered to account for image spatial information, ensuring that the methodology is able to identify inhomogeneous spatial patterns in complex images.
In addition, the anisotropic mesh adaptation guarantees a sharp detection of the interface between background and foreground of the image, with a reduced number of degrees of freedom.
The resulting split-adapt Bregman algorithm is tested on a set of real images showing the accuracy and robustness of the method, even in the presence of Gaussian, salt and pepper and speckle noise. |
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02/2022 - 09/01/2022
Antonietti, P.F.; Scacchi, S.; Vacca, G.; Verani, M.
$C^1$-VEM for some variants of the Cahn-Hilliard equation: a numerical exploration | Abstract | | We consider the $C^1$-Virtual Element Method (VEM) for the conforming numerical approximation of some variants of the Cahn-Hilliard equation on polygonal meshes. In particular, we focus on the discretization of the advective Cahn-Hilliard problem and the Cahn-Hilliard inpainting problem. We present the numerical approximation and several numerical results to assess the efficacy of the proposed methodology.
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01/2022 - 09/01/2022
Gavazzoni, M.; Ferro, N.; Perotto, S.; Foletti, S.
Multi-physics inverse homogenization for the design of innovative cellular materials: application to thermo-mechanical problems | Abstract | | We present a new algorithm to design lightweight cellular materials with required properties in a multi-physics context. In particular, we focus on a thermo-mechanical setting, by promoting the design of unit cells characterized both by an isotropic and an anisotropic behaviour with respect to mechanical and thermal requirements. The proposed procedure generalizes microSIMPATY algorithm to a multi-physics framework, by preserving all the good properties of the reference design methodology. The resulting layouts exhibit non-standard topologies and are characterized by very sharp contours, thus limiting the post-processing before manufacturing. The new cellular materials are compared with the state-of-art in engineering practice in terms of thermo-mechanical properties, thus highlighting the good performance of the new layouts which, in some cases, outperform the consolidated choices. |
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95/2021 - 28/12/2021
Di Gregorio, S.; Vergara, C.; Montino Pelagi, G.; Baggiano, A.; Zunino, P.; Guglielmo, M.; Fusini, L.; Muscogiuri, G.; Rossi, A.; Rabbat, M.G.; Quarteroni, A.; Pontone, G.
Prediction of myocardial blood flow under stress conditions by means of a computational model | Abstract | | Purpose. Quantification of myocardial blood flow (MBF) and functional assessment of coronary artery disease (CAD) can be achieved through stress myocardial computed tomography perfusion (stress-CTP). This requires an additional scan after the resting coronary computed tomography angiography (cCTA) and administration of an intravenous stressor. This complex protocol has limited reproducibility and non-negligible side effects for the patient. We aim to mitigate these drawbacks by proposing a computational model able to reproduce MBF maps.
Methods. A computational perfusion model was used to reproduce MBF maps. The model parameters were estimated by using information from cCTA and MBF measured from stress-CTP (MBFCTP) maps. The relative error between the computational MBF under stress conditions (MBFCOMP) and MBFCTP was evaluated to assess the accuracy of the proposed computational model.
Results. Applying our method to 9 patients (4 control subjects without ischemica vs 5 patients with myocardial ischemia), we found an excellent agreement between the values of MBFCOMP and MBFCTP. In all patients, the relative error was below 8% over all the myocardium, with an average-in-space value below 4%.
Conclusion. The results of this pilot work demonstrate the accuracy and reliability of the proposed computational model in reproducing MBF under stress conditions. This consistency test is a preliminary step in the framework of a more ambitious project which is currently under investigation, i.e. the construction of a computational tool able to predict MBF avoiding the stress protocol and potential side effects while reducing radiation exposure.
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94/2021 - 27/12/2021
Antonietti, P.F.; Berrone, S.; Busetto, M.; Verani, M.
Agglomeration-based geometric multigrid schemes for the Virtual Element Method | Abstract | | In this paper we analyse the convergence properties of two-level, W-cycle and V-cycle agglomeration-based geometric multigrid schemes for the numerical solution of the linear system of equations stemming from the lowest order C0-conforming Virtual Element discretization of two-dimensional second-order elliptic partial differential equations. The sequence of agglomerated tessellations are nested, but the corresponding multilevel virtual discrete spaces are generally non-nested thus resulting into non-nested multigrid algorithms. We prove the uniform convergence of the two-level method with respect to the mesh size and the uniform convergence of the W-cycle and the V-cycle multigrid algorithms with respect to the mesh size and the number of levels. Numerical experiments confirm the theoretical findings. |
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93/2021 - 27/12/2021
Parolini, N.; Dede', L; Ardenghi, G.; Quarteroni, A.
Modelling the COVID-19 epidemic and the vaccination campaign in Italy by the SUIHTER model | Abstract | | Several epidemiological models have been proposed to study the evolution of COVID-19 pandemic. In this paper, we propose an extension of the SUIHTER model, first introduced in [Parolini et al, Proc R. Soc. A., 2021] to analyse the COVID-19 spreading in Italy, which accounts for the vaccination campaign and the presence of new variants when they become dominant. In particular, the specific features of the variants (e.g. their increased transmission rate) and vaccines (e.g. their efficacy to prevent transmission, hospitalization and death) are modeled, based on clinical evidence. The new model is validated comparing its near-future forecast capabilities with other epidemiological models and exploring different scenario analyses. |
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92/2021 - 27/12/2021
Antonietti, P.F.; Manzini, G.; Scacchi, S.; Verani, M.
On arbitrarily regular conforming virtual element methods for elliptic partial differential equations | Abstract | | The Virtual Element Method (VEM) is a very effective framework to
design numerical approximations with high global regularity to the
solutions of elliptic partial differential equations.
In this paper, we review the construction of such approximations
for an elliptic problem of order $p_1$ using conforming, finite
dimensional subspaces of $H^2{p_2}(Omega)$, where $p_1$ and
$p_2$ are two integer numbers such that $p_2geqp_1geq1$
and $OmegainR^2$ is the computational domain.
An abstract convergence result is presented in a suitably defined
energy norm.
The space formulation and major aspects such as the choice and
unisolvence of the degrees of freedom are discussed, also
providing specific examples corresponding to various practical
cases of high global regularity.
Finally, the construction of the ``enhanced'' formulation of the
virtual element spaces is also discussed in details with a proof
that the dimension of the ``regular'' and ``enhanced'' spaces is
the same and that the virtual element functions in both spaces can
be described by the same choice of the degrees of freedom. |
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91/2021 - 16/12/2021
Arnone, E.; Sangalli, L.M.; Vicini, A.
Smoothing spatio-temporal data with complex missing data patterns | Abstract | | We consider spatio-temporal data and functional data with spatial dependence, characterized by complicated missing data patterns. We propose a new method capable to efficiently handle these data structures, including the case where data are missing over large portions of the spatio-temporal domain. The method is based on regression with partial differential equation regularization. The proposed model can accurately deal with data scattered over domains with irregular shapes and can accurately estimate fields exhibiting complicated local features. We demonstrate the consistency and asymptotic normality of the estimators. Moreover, we illustrate the good performances of the method in simulations studies, considering different missing data scenarios, from sparse data to more challenging scenarios where the data are missing over large portions of the spatial and temporal domains and the missing data are clustered in space and/or in time. The proposed method is
compared to competing techniques, considering predictive accuracy and uncertainty quantification measures. Finally, we show an application to the analysis of lake surface water temperature data, that further illustrates the ability of the method to handle data featuring complicated patterns of missingness and highlights its potentiality for environmental
studies. |
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