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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30/2017 - 20/06/2017
Bacchelli, V.; Micheletti, S.; Perotto, S.; Pierotti, D.
Parameter identification for the linear wave equation with Robin boundary condition | Abstract | | We consider an initial-boundary value problem for the classical linear wave
equation, where mixed boundary conditions of Dirichlet and Neumann/Robin type are enforced at the endpoints of a bounded interval. First, by a careful application of the method of characteristics, we derive a closed-form representation of the solution for an impulsive Dirichlet data at the left endpoint, and valid for either a Neumann or a Robin data at the right endpoint. Then we devise a reconstruction procedure for identifying both
the interval length and the Robin parameter. We provide a corresponding stability result and verify numerically its performance moving from a finite element discretization. |
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29/2017 - 20/06/2017
Antonietti, P.F.; Mascotto, L.; Verani, M.
A multigrid algorithm for the $p$--version of the Virtual Element Method | Abstract | | We present a multigrid algorithm for the solution of the linear systems of equations stemming from the p?version of the Virtual Element discretization of a two-dimensional Poisson problem. The sequence of coarse spaces are constructed decreasing progressively the polynomial approximation degree of the Virtual Element space, as in standard p-multigrid schemes. The construction of the interspace operators relies on auxiliary Virtual Element spaces, where it is possible to compute higher order polynomial projectors. We prove that the multigrid scheme is uniformly convergent, provided the number of smoothing steps is chosen sufficiently large. We also demonstrate that the resulting scheme provides a uniform preconditioner with respect to the number of degrees of freedom that can be employed to accelerate the convergence of classical Krylov-based iterative schemes. Numerical experiments validate the theoretical results. |
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28/2017 - 10/06/2017
Pini, A.; Spreafico, L.; Vantini, S.; Vietti, A.
Multi-aspect local inference for functional data: analysis of ultrasound tongue profiles | Abstract | | Motivated by the functional data analysis of a data set of ultrasound tongue profiles, we present the multi-aspect interval-wise testing (multi-aspect IWT), i.e., a local non-parametric inferential technique for functional data embedded in Sobolev spaces. Multi-aspect IWT is a non-parametric procedure that tests differences between groups of functional data jointly taking into account the curves and their derivatives. The multi-aspect IWT provides adjusted multi-aspect p-value functions that can be used to select intervals of the domain imputable for the rejection of a null hypothesis. As a result, it can impute the rejection of a functional null hypothesis to specific intervals of the domain and to specific orders of differentiation. We show that the multi-aspect p-value functions are provided with a control of the family-wise error rate, and are consistent. We apply the multi-aspect IWT to the functional data analysis of a data set of tongue profiles recorded for a study on Tyrolean, a German dialect spoken in South Tyrol. We test differences between five different manners of articulation of uvular rhotics: trill, tap, fricative, approximant, and vocalized /r/. Multi-aspect IWT-based comparisons result in an informative and detailed representation of the regions of the tongue where a significant difference is located. |
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27/2017 - 10/06/2017
Bonaventura, L.; Ferretti, R.; Rocchi L.;
A fully semi-Lagrangian discretization for the 2D Navier--Stokes equations in the vorticity--streamfunction formulation | Abstract | | A numerical method for the two-dimensional, incompressible Navier--Stokes
equations in vorticity--streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and diffusion terms, thus achieving unconditional stability without the need to solve linear systems beyond that required by the Poisson solver for the reconstruction of the streamfunction. A description of the discretization of Dirichlet boundary conditions for the semi-Lagrangian approach to diffusion terms is also presented. Numerical experiments on classical benchmarks for incompressible flow in simple geometries validate the proposed method. |
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26/2017 - 05/06/2017
Masci, C.; Johnes, G.; Agasisti, T.
Student and School Performance in the OECD: a Machine Learning Approach. | Abstract | | In this paper, we develop and apply novel machine learning and statistical methods to analyse the determinants of students' PISA 2015 test scores in nine countries: Australia, Canada, France, Germany, Italy, Japan, Spain, UK and USA. The aim is to find out which student characteristics are associated with test scores and which school characteristics are associated to school value-added (measured at school level). A specific aim of our approach is to explore non-linearities in the associations between covariates and test scores, as well as to model interactions between school-level factors in affecting results. In order to address these issues, we apply a two-stage methodology using flexible tree-based methods. We first run multilevel regression trees in the first stage, to estimate school value-added. In the second stage, we relate the estimated school value-added to school level variables by means of regression trees and boosting. Results show that while several student and school level characteristics are significantly associated to students' achievements, there are marked differences across countries. The proposed approach allows an improved description of the structurally different educational production functions across countries. |
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25/2017 - 30/05/2017
Paulon, G.; De Iorio, M.; Guglielmi, A.; Ieva, F.
Joint modelling of recurrent events and survival: a Bayesian nonparametric approach | Abstract | | Heart failure (HF) is one of the main causes of morbidity, hospitalization
and death in the western world and the economic burden associated with HF
management is relevant and expected to increase in the future. We consider
hospitalization data for heart failure in the most populated Italian Region, Lombardia. Data were extracted from the administrative data warehouse of the regional healthcare system. The main clinical outcome of interest is time to death and research focus is on investigating how recurrent hospitalizations affect the time to event. The main contribution of the paper is to develop a joint model for gap times between two consecutive hospitalizations and survival time. The probability models for the gap times and for the survival outcome share a common patient specific frailty term. Using a Bayesian nonparametric prior as the random effects distribution accounts for patient heterogeneity in recurrent event trajectories. Moreover, the joint model allows for dependent censoring of gap times by death or administrative reasons and for the correlations between different gap times for the same individual. It is straightforward to include covariates in the survival and/or recurrence process through the specification of appropriate regression terms. Posterior inference is performed through Markov chain Monte Carlo methods. |
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24/2017 - 30/05/2017
Domanin, M.; Bissacco, D.; Le Van, D.; Vergara, C.
Computational fluid-dynamic comparison between patch-based and direct suture closure techniques after carotid endarterectomy | Abstract | | Objective: To describe and analyze hemodynamic modifications in patients submitted to carotid endarterectomy (CEA) with different carotid closure techniques, using a computational fluid-dynamic (CFD) strategy, in order to identify disturbed flow conditions potentially involved in the development of restenosis.
Methods: Data from 8 carotid geometries in 7 asymptomatic patients who underwent CEA were analyzed. In six cases (A-F), CEA was performed using patch graft (PG) closure, while in two cases (G and H) direct suture (DS) closure was performed. Three-dimensional carotid geometries, derived from postoperative Magnetic Resonance Angiography, were reconstructed using a level-set segmentation technique. Where PG was originally used it was virtually removed, creating a virtual DS scenario (PG vs virtual-DS) while, on the contrary, in cases submitted to DS closure, a virtual PG was inserted (DS vs virtual-PG). Modified geometries were designed using visualization-dedicated software. CFD analysis was performed using the finite elements library LifeV and velocity data obtained from Doppler Ultrasound waveforms.
To compare hemodynamic effects, wall shear stress-based quantities were considered indicators of disturbed flow and thus favorable conditions for the development of restenosis. In particular, oscillatory shear index (OSI) and relative residence time (RRT) were calculated both for original and virtual scenarios.
Results: For the six original PG cases, we measured the following: Mean of averaged-in-space OSI of 0.07 ± 0.01 for PG and 0.03 ± 0.02 for virtual-DS (difference 0.04 ± 0.01; P=.0016). Mean of the percentage of area with OSI > 0.2 (%A-OSI > 0.2) 10.08% ± 3.38% (PG) and 3.80% ± 3.22% (virtual-DS) (difference 6.28 ± 1.91; P= .008). Mean of the averaged-in-space RRT 5.48 ± 3.40 1/Pa (PG) and 2.62 ± 1.12 1/Pa (virtual-DS) (difference 2.87 ± 1.46; P =.097). Mean %A RRT > 4 1/Pa of 26.53% ± 12.98% (PG) and 9.95% ± 6.53% (virtual-DS) (difference 16.58 ± 5.93; P= .025).
For the two original DS cases we measured the following: Averaged-in-space OSI 0.02 and 0.04 (DS) and 0.03 and 0.02 (virtual-PG), %A-OSI > 0.2, 0.9% and 7.6% (DS) and 3.0% and 2.2% (virtual-PG), averaged-in-space RRT 1.8 and 2.0 1/Pa (DS) and 2.9 and 1.9 1/Pa (virtual-PG), %A-RRT > 4.0 1/Pa: 6.8% and 9.8% (DS) 9.4% and 6.2% (virtual-PG). These results revealed generally higher disturbed flows in the PG configurations with respect to the DS ones.
Conclusions: OSI and RRT values were higher in PG cases with respect to virtual-DS ones, while, in direct contrast, the virtual insertion of PG gave conflicting results that were primarily determined by the original carotid geometries. |
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23/2017 - 30/05/2017
Quarteroni, A.; Vergara, C.
Computational models for hemodynamics | Abstract | | Mathematical foundation and numerical approximation of the cardiocirculatory
system are addressed |
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