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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63/2017 - 23/11/2017
Masci, C.; Paganoni, A.M.; Ieva, F.
Non-parametric mixed-effects models for unsupervised classification of Italian schools | Abstract | | This paper proposes an EM algorithm for non-parametric mixed-effects models (NPEM algorithm) and applies it to the National Institute for the Educational Evaluation of Instruction and Training (INVALSI) data of 2013/2014 as a tool for unsupervised clustering of Italian schools. The main novelties introduced by NPEM algorithm, when applied to hierarchical data, are twofold: first NPEM allows the covariates to be group specific; second, it assumes the random effects to be distributed according to a discrete distribution P* with an (a priori) unknown number of support points. In doing so, it induces an automatic clustering of the grouping factor at higher level of hierarchy, enabling the identification of latent groups of schools that differ in their effect on student achievements. The clustering may then be exploited through the use of school level features. |
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62/2017 - 23/11/2017
Barbarotta, L.; Rossi, S.; Dede', L.; Quarteroni, A.
A Transmurally Heterogeneous Orthotropic Activation Model for Ventricular Contraction and its Numerical Validation | Abstract | | Models for cardiac mechanics require an activation mechanism properly representing the stress-strain relations in the contracting myocardium. In this paper, we propose a new activation model which accounts for the transmural heterogeneities observed in myocardial strain measurements. In order to take into account the anisotropy of the active mechanics, our model is based on an active strain formulation. Thanks to its multiplicative decomposition of the deformation gradient tensor, in this formulation the active strains orthogonal to the fibers can be naturally described. We compare the results of our novel orthotropic formulation against different anisotropic models of the active contraction of the cardiac muscle and, moreover, against experimental data available in the literature. We show that the currently available models can represent only some global quantities, but the strain distributions are not in agreement
with the reported experimental measurements. Conversely, we show that our new transmurally heterogeneous orthotropic activation model improves the accuracy of shear strains related to in-plane rotations and torsion. |
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61/2017 - 22/11/2017
Vadacca, L.; Colciago, C. M.; Micheletti, S.; Scotti, A.
Three-dimensional fault representation by interface and solid elements: effects of the anisotropy of the fault zone permeability on the timing of triggered earthquakes | Abstract | | In the last years numerous seismological evidences have shown a strict correlation between fluid injection and seismicity. An important topic that is currently under discussion in the scientific community concerns the prediction of the earthquake magnitude that may be triggered by fluid injection activities. Coupled fluid flow and geomechanical deformation models can aim at understand the evolution of pore pressure and rock deformation due to fluid injection in the subsurface. To perform an accurate numerical study of the correlation among fluid injection, seismicity rates and maximum earthquake magnitude, it is necessary to characterize the model with two fundamental features: first, the presence of a system of faults possibly intersecting among each other; second, the variability of the hydro-mechanical properties across the region surrounding each fault plane (fault zone). The novelty of this work is to account for these two aspects combining together two different numerical techniques that have been proposed in literature for the fault's modelling: for the first feature, interface elements are used to describe the frictional contacts occurring on the faults surfaces; for the second feature, solid elements are adopted to describe the heterogeneous hydro-mechanical behavior across the fault zone. Moreover, we account for a spatial variation of the permeability in the fault zone both along the dip and the normal direction with respect to the fault plane. We compute the numerical solution for six models among which we vary the permeability contrasts between protolith rocks and damage zone and between damage zone and fault core. We demonstrate that the anisotropy of permeability of the fault zone has a strong impact both on the timing and on the magnitude of triggered earthquakes. We suggest that a similar approach, which includes the entire architecture of the fault zone, shall be included in fluid-flow-geomechanical simulations to improve fault stability analysis during fluid injection. |
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60/2017 - 07/11/2017
Bonaldi, F.; Di Pietro, D. A.; Geymonat, G.; Krasucki, F.
A Hybrid High-Order method for Kirchhoff-Love plate bending problems | Abstract | | We present a novel Hybrid High-Order (HHO) discretization of fourth-order elliptic problems arising from the mechanical modeling of the bending behavior of Kirchhoff--Love plates, including the biharmonic equation as a particular case. The proposed HHO method supports arbitrary approximation orders on general polygonal meshes, and reproduces the key mechanical equilibrium relations locally inside each element. When polynomials of degree $kge 1$ are used as unknowns, we prove convergence in $h^{k+1}$ (with $h$ denoting, as usual, the meshsize) in an energy-like norm. A key ingredient in the proof are novel approximation results for the oblique biharmonic projector on local polynomial spaces. Under biharmonic regularity assumptions, a sharp estimate in $h^{k+3}$ is also derived for the $L^2$-norm of the error on the deflection. The theoretical results are supported by numerical experiments, which additionally show the robustness of the method with respect to the choice of the stabilization. |
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59/2017 - 03/11/2017
Grujic, O.; Menafoglio, A.; Guang, Y.; Caers, J.
Cokriging for multivariate Hilbert space valued random fields. Application to multifidelity computer code emulation | Abstract | | In this paper we propose Universal trace co-kriging (UTrCoK), a novel methodology for interpolation of multivariate Hilbert space valued functional data. Such data commonly arises in multi-fidelity numerical modeling of the subsurface and it is a part of many modern uncertainty quantification studies. Besides theoretical developments we also present methodological evaluation and comparisons with the recently published projection based approach by Bohorquez et al (2016). Our evaluations and analyses were performed on synthetic (oil reservoir) and real field (Uranium contamination) subsurface uncertainty quantification case studies. Monte Carlo analyses were conducted to draw important conclusions and to provide practical guidelines for all future practitioners. |
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58/2017 - 02/11/2017
Landajuela, M.; Vergara, C.; Gerbi, A.; Dede', L.; Formaggia, L.; Quarteroni, A.
Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network | Abstract | | In this work, we consider the numerical approximation of the electromechanical
coupling in the left ventricle with inclusion of the Purkinje network.
The mathematical model couples the 3D elastodynamics and bidomain
equations for the electrophysiology in the myocardium with the 1D
monodomain equation in the Purkinje network. For the numerical solution
of the coupled problem, we consider a fixed-point iterative algorithm that
enables a partitioned solution of the myocardium and Purkinje network
problems. Different levels of myocardium-network splitting are considered
and analyzed. The results are compared with those obtained using standard
strategies proposed in the literature to trigger the electrical activation. Finally,
we present a physiological cardiac simulation, including the initiation
of the signal in the Purkinje network, the systolic phase and the beginning
of the filling phase. |
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57/2017 - 31/10/2017
Ballarin, F.; D'Amario, A.; Perotto, S.; Rozza, G.
A POD-Selective Inverse Distance Weighting method for fast parametrized shape morphing | Abstract | | Efficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid-structure interaction or shape optimization problems. In this paper, we focus on Inverse Distance Weighting (IDW) interpolation techniques, where a reference domain is morphed into a deformed one via the displacement of a set of control points. We aim at reducing the computational burden characterizing a standard IDW approach without compromising the accuracy. To this aim, first we propose an improvement of IDW based on a geometric criterion which automatically selects a subset of the original set of control points. Then, we combine this new approach with a model reduction technique based on a Proper Orthogonal Decomposition of the set of admissible displacements. This choice further reduces computational costs. We verify the performances of the new IDW techniques on several tests by investigating the trade-off reached in terms of accuracy and efficiency. |
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56/2017 - 31/10/2017
Alberti, G. S.; Santacesaria, M.
Infinite dimensional compressed sensing from anisotropic measurements | Abstract | | In this paper, we consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The main result gives explicit bounds on the number of measurements in order to achieve stable recovery, which depends on the mutual coherence of the two systems. As a simple corollary, we prove the efficiency of non-uniform sampling strategies in cases when the two systems are not incoherent, but only asymptotically incoherent, as with the recovery of wavelet coefficients from Fourier samples. This general framework finds applications to several inverse problems in partial differential equations, in which the standard assumptions of compressed sensing are not satisfied: several examples are discussed. |
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