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 1249 products
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44/2018 - 08/13/2018
Bernardi, M.S.; Sangalli, L.M.
Modelling spatially dependent functional data by spatial regression with differential regularization | Abstract | | In this chapter we describe the modelling of spatially dependent functional data by
regression with differential regularization. |
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43/2018 - 07/29/2018
Fontana, L.; Masci, C.; Ieva, F.; Paganoni, A.M.
Performing Learning Analytics via Generalized Mixed-Effects Trees | Abstract | | Nowadays, the importance of Educational Data Mining and Learning Analytics in higher education institutions is increasingly recognized. The analysis of university careers and of student dropout prediction is one of the most studied topics in the area of Learning Analytics. In the perspective of modeling the student dropout, we propose an innovative statistical method, that is a generalization of mixed-effects trees for a response variable in the exponential family: Generalized Mixed-Effects Trees (GMET). We perform a simulation study in order to validate the performance of our proposed method and to compare GMET to classical models. In the case study, we apply GMET to model Bachelor student dropout in different degree programmes of Politecnico di Milano. The model is able to identify discriminating student characteristics and estimate the degree programme effect on the probability of student dropout. |
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42/2018 - 07/29/2018
Antonietti, P.F.; Melas, L.
Algebraic multigrid schemes for high-order discontinuous Galerkin methods | Abstract | | We present algebraic multigrid (AMG) methods for the efficient solution of the linear system of equations stemming from high-order discontinuous Galerkin discretizations of second-order elliptic problems.
For discontinuous Galerkin methods standard multigrid approaches cannot be employed because of redundancy of the degrees of freedom associated to the same grid point. We present new aggregation procedures and test them on extensive two-dimensional numerical experiments that demonstrate that the proposed AMG method is uniformly convergent with respect to all the discretization parameters, namely the mesh-size and the polynomial approximation degree. |
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41/2018 - 07/24/2018
Mazzieri, I.; Melas, L.; Smerzini, C.; Stupazzini, M.
The role of near-field ground motion on seismic risk assessment in large urban areas | Abstract | | During the last ten years a long series of events like Wenchuan (2008, China), l’Aquila (Italy, 2009), Christchurch (New Zealand, 2010-2011), Emilia-Romagna (Italy, 2012), Meinong (Taiwan, 2016), Kumamoto (Japan, 2016) and Norcia (Italy, 2016) once more proved that the near-field of an earthquake poses a serious threat and even buildings considered earthquake-resistant might be severely affected. As a matter of fact, during the so-called “Christchurch sequence” around 70% of the central business district's (CBD) buildings turned out to be severely damaged and required to be demolished, in spite of the state-of-the-art New Zealand seismic building code and the stringent adoption and enforcement of this latter.
In this study we examine a large and representative set of numerical scenarios generated by means of physics-based simulations (PBS), in order to constrain the ground motion at short distances (within few kilometers range) by taking into account the rupture process, the seismic wave propagation and three-dimensional (3D) complex configurations. The experience gathered in the past years regarding 3D modelling of seismic wave propagation in complex alluvial basin (Guidotti et al., 2011; Smerzini and Villani, 2012) allowed us to enhance the choice of simulated scenarios in order to exhaustively explore the variability of ground motion and overcoming certain deficiency of the GMPEs and especially the insufficient number of records located close to the causative faults. All PBS presented in this study are carried out through the spectral element code SPEED (http://speed.mox.polimi.it).
The large metropolitan area of Beijing (China) is considered because of the (i) proximity with a well-known mapped fault system capable to trigger a severe earthquake, a (ii) relatively good description of the geotechnical characterization of the soil and a (iii) reliable reconstruction of the deep alluvial structure.
Focusing on the class of high-rise buildings and taking into account on one hand suitable fragility curves and on the other hand the aforementioned PBSs, seismic damage scenarios in the Beijing area will be produced and the variability of different damage states, as induced by a wide set of fault rupture scenarios with magnitude in the range 6.5-7.3, will be explored. |
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39/2018 - 07/12/2018
Ferro, N.; Micheletti, S.; Perotto, S.
Density-based inverse homogenization with anisotropically adapted elements | Abstract | | The optimization of manufacturable extremal elastic materials can be carried out via topology optimization using the homogenization method. We combine here a standard density-based inverse homogenization technique with an anisotropic mesh adaptation procedure in the context of a finite element discretization. In this way, the optimized layouts are intrinsically smooth and ready to be manufactured. |
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40/2018 - 07/12/2018
Chiappa, A.S.; Micheletti, S.; Peli, R.; Perotto, S.
Mesh adaptation-aided image segmentation | Abstract | | We focus on a variational approach to image segmentation based on the
Ambrosio-Tortorelli functional. To make the procedure more effective with
respect to standard algorithms, we combine the functional minimization
with the the employment of an optimal discretization. More precisely, we
perform a finite element approximation of the Ambrosio-Tortorelli func-
tional on a triangular adapted mesh able to follow exactly the contours
present in the images, in the spirit of a mesh adaptation-aided image seg-
mentation. This challenging goal is reached via a rigorous a posteriori
error analysis enriched with anisotropic information. The benefits due to
the proposed algorithm are evident both in terms of increased resolution
in the edge detection and in a considerable reduction of the computational
costs, as confirmed by an extensive numerical investigation. |
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38/2018 - 07/12/2018
Domanin, M.; Gallo, D.; Vergara, C.; Biondetti, P.; Forzenigo, L.V.; Morbiducci, U.
Prediction of long term restenosis risk after surgery in the carotid bifurcation by hemodynamic and geometric analysis | Abstract | | Objective- Carotid restenosis is a common complication occurring after carotid endarterectomy (CEA). This study aimed to explore the potential of local hemodynamic disturbances and carotid bifurcation geometry to predict long-term restenosis at 60 months after CEA.
Methods- Thirteen carotid bifurcations with a stenosis greater than 70% were submitted to CEA. Arteriotomy repair was performed with patch graft (PG) angioplasty in 9 cases, with primary closure (PC) in 4 cases. MRI acquisitions were performed within a month after surgery for hemodynamic and geometric characterization. Personalized computational fluid dynamic simulations were performed and hemodynamic disturbances were quantified in terms of exposure to low and oscillatory wall shear stress (WSS). Each carotid geometry was characterized automatically in terms of flare (i.e., the expansion at the carotid bulb) and tortuosity proximal to the bifurcation. Based on hemodynamics and geometry, cases were classified into three categories of “geometric” or “hemodynamic” restenosis risk. At 60 months after CEA, eligible participants underwent duplex ultrasound scan and peak systolic velocity measurement for the detection of restenosis, with extraction of intima-media thickness from five selected locations along the carotid bifurcation.
Results- More unfavorable hemodynamic conditions established in PG than PC cases. Carotid flare was found to be significantly associated with the exposure to low WSS and therefore considered to define the geometric restenosis risk. No significant associations were found for tortuosity. The two cases characterized by the highest flare and the largest exposure to low WSS developed restenosis >50% at 60 months. A high correspondence was found between morphological DUS observations of myointimal thickening or new atheroma development and low and oscillatory WSS regions.
Conclusions- The quantitative analysis of hemodynamics and geometry holds potential for the stratification of patients at risk for development of late restenosis after CEA. Moreover, it can help the understanding of the mechanistic processes underlying restenosis development, potentially guiding the clinical decision between PG vs. PC. Our findings suggest that arteriotomy repair should avoid an artificial flare, that is linked with restenosis via the generation of flow disturbances. Geometric characterization from imaging data is a convenient, fast and easy method that can be integrated in the clinical practice.
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37/2018 - 06/06/2018
Bonaventura, L.; Della Rocca A.;
Convergence analysis of a cell centered finite volume diffusion operator on non-orthogonal polyhedral meshes | Abstract | | A simple but successful strategy for building a discrete diffusion operator in finite volume schemes of industrial use is to correct the standard two-point flux approximation with a term accounting for the local mesh non-orthogonality. Practical experience with a variety of different mesh typologies, including non-orthogonal tetrahedral, hexahedral and polyhedral meshes, has shown that this discrete diffusion operator is accurate and robust whenever the mesh is not too distorted and sufficiently regular. In this work, we show that this approach can be interpreted as equivalent to introducing an anisotropic operator that accounts for the preferential directions induced by the local mesh non-orthogonality. This allows to derive a convergence analysis of the corrected method under a quite weak global assumption on mesh distortion. This convergence proof, which is obtained for the first time for this finite volume method widely employed in industrial applications, provides a reference framework on how to interpret some of its variants commonly implemented in commercial finite volume codes. Numerical experiments are presented that confirm the accuracy and robustness of the results. Furthermore, we also show empirically that a least square approach to the gradient computation can
provide second order convergence even when the mild non-orthogonality condition on the mesh is violated. |
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