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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29/2014 - 22/07/2014
Arioli, G.; Koch, H.
Some symmetric boundary value problems and non-symmetric solutions | Abstract | | We consider the equation −∆u = wf′(u) on a symmetric bounded domain in Rn with Dirichlet boundary conditions. Here w is a positive function or measure that is invariant under the (Euclidean) symmetries of the domain. We focus on solutions u that are positive and/or have a low Morse index. Our results are concerned with the existence of non-symmetric solutions and the non-existence of symmetric solutions. In particular, we construct a solution u for the disk in R2 that has index 2 and whose modulus |u| has only one reflection symmetry. |
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28/2014 - 13/07/2014
Antonietti, P; Panfili, P.; Scotti, A.; Turconi, L. ; Verani, M.; Cominelli,A.; Formaggia,L.
Optimal techniques to simulate flow in fractured reservoirs | Abstract | | Simulation of multiphase flow in fractured reservoir is a computational challenge. A key issue is the effective coupling between flow in the porous matrix and in the fracture network. It requires computational grids honouring as much as possible the fracture geometry without degenerated/distorted elements. Standard techniques may degrade efficiency and are not a foolproof solution. Moreover, two point flux approximation (TPFA) demands a good quality of the mesh to mitigate discretization error. In this work compare two different approaches. The first one has been proposed by B.T Mallison et al. in 2010. The second method we consider is the one originally proposed by H. Mustapha, in 2009. We evaluate the two techniques by means of 2D synthetic problems based on realistic discrete fracture networks. Steady state and unsteady state simulations are performed using TPFA. We also present results obtained with computational methods based on coupling the fracture network with mimetic finite differences or extended mixed finite elements. The latter two approaches, even though more complex, are more robust with respect to mesh geometry and can be beneficial for the problem at hand. |
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27/2014 - 12/07/2014
Vergara, C; Domanin, M; Guerciotti, B; Lancellotti, R.M.; Azzimonti, L; Forzenigo, L; Pozzoli, M.
Computational comparison of fluid-dynamics in carotids before and after endarterectomy | Abstract | | In this work we provide a computational comparison between the fluid-dynamics before and after carotid endarterectomy (CEA) to assess to influence of this surgical operation on some hemodynamic indices related to the plaque rupture. We perform the numerical simulations in real geometries of the same patients before and after CEA, and with patient-specific boundary data obtained by Echo-color Doppler measurements. The results show a reduction at the systole of the maximum wall shear stress by at least 83%, of the peak velocity by at least 56%, of the vorticity at the internal carotid by at least 57%, and of the pressure gradient across the plaque by at least 83%. Finally, we performed a comparison among measures acquired in internal points and related computed values, highlighting a satisfactory agreement (in any case less than 10%). |
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26/2014 - 03/07/2014
Discacciati, M.; Gervasio, P.; Quarteroni, A.
Interface Control Domain Decomposition (ICDD) Methods for Heterogeneous Problems | Abstract | | This paper is concerned with the solution of heterogeneous problems by the ICDD (Interface Control Domain Decomposition) method, a strategy introduced for the solution of partial differential equations (PDEs) in computational domains partitioned into subdomains that overlap. After reformulating the original boundary value problem by introducing new additional control variables, the unknown traces of the solution at internal subdomain interfaces, the latter are determined by requiring that the (a-priori) independent solutions in each subdomain undergo the minimization of a suitable cost functional. We provide an abstract formulation for coupled heterogeneous problems and a general theorem of wellposedness for the associated ICDD problem. Then, we illustrate and validate an efficient algorithm based on the solution of the Schur-complement system restricted solely to the interface control variables by considering two kinds of heterogeneous boundary value problems: the coupling between pure advection and advection-diffusion equations, and the coupling between Stokes and Darcy equations. In the latter case we also compare the ICDD method with a classical approach based on the Beavers-Joseph-Saffman conditions. |
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25/2014 - 02/07/2014
Hron, K.; Menafoglio, A.; Templ, M.; Hruzova K.; Filzmoser, P.
Simplicial principal component analysis for density functions in Bayes spaces | Abstract | | Probability density functions are frequently used to characterize the distributional properties of large-scale database systems. As functional compositions, densities carry primarily relative information. As such, standard methods of functional data analysis (FDA) are not appropriate for their statistical processing. The specific features of density functions are accounted for in Bayes spaces, which result from the generalization to the infinite dimensional setting of the Aitchison geometry for compositional data. The aim of the paper is to build up a concise methodology for functional principal component analysis of densities. We propose the simplicial functional principal component analysis (SFPCA), which is based on the geometry of the Bayes space B^2 of functional compositions. We perform SFPCA by exploiting the centred log-ratio transform, an isometric isomorphism between B^2 and L^2 which enables one to resort to standard FDA tools. Advances of the proposed approach are demonstrated using a real-world example of population pyramids in Upper Austria. |
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24/2014 - 01/07/2014
Ieva, F., Jackson, C.H., Sharples, L.D.
Multi-State modelling of repeated hospitalisation and death in patients with Heart Failure: the use of large administrative databases in clinical epidemiology | Abstract | | In chronic diseases like Heart Failure (HF), the disease course and associated clinical event histories for the patient population vary widely. To improve understanding of the prognosis of patients and enable health-care providers to assess and manage resources, we wish to jointly model disease progression, mortality and their relation with patient characteristics. We show how episodes of hospitalisation for disease-related events, obtained from administrative data, can be used as a surrogate for disease status. We propose flexible multi-state models for serial hospital admissions and death in HF patients, that are able to accommodate important features of disease progression, such as multiple ordered events and competing risks. Markov and semi-Markov models are implemented using freely available software in R. The models were applied to a dataset from the administrative data bank of the Lombardia region in Northern Italy, which included 15,298 patients who had a first hospitalisation ending in 2006 and 4 years of follow up thereafter. This provided estimates of the associations of of age and gender with rates of hospital admission and length of stay in hospital, and estimates of the expected total time spent in hospital. For example, older patients and men were readmitted more frequently, though the total time in hospital was roughly constant with age. We also discuss the relative merits of parametric and semi-parametric multi-state models, and assessment of the Markov assumption. |
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23/2014 - 13/06/2014
Ieva, F., Paganoni, A.M., Tarabelloni, N.
Covariance Based Unsupervised Classification in Functional Data Analysis | Abstract | | In this paper we propose a new algorithm to perform unsupervised classification of multivariate and functional data when the difference between the two populations lies in their covariances, rather than in their means. The algorithm relies on a proper quantification of distance between the estimated covariance operators of the populations, and identifies as clusters those groups maximising the distance between their induced covariances. The naive implementation of such an algorithm is computationally forbidding, so we propose an heuristic formulation with a much lighter complexity and we study its convergence properties, along with its computational cost. We also propose to use an enhanced estimator for the estimation of discrete covariances of functional data, namely a linear shrinkage estimator, in order to improve the precision of the classification. We establish the effectiveness of our algorithm through applications to both synthetic data and a real dataset coming from a biomedical context, showing also how the use of shrinkage estimation may lead to substantially better results. |
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22/2014 - 10/06/2014
Arioli, G.
Insegnare Matematica con Mathematica | Abstract | | n questo articolo vogliamo discutere le possibilità offerte da soft- ware di calcolo simbolico, in particolare parliamo di Mathematica, nell’insegnamento della Matematica nelle scuole primarie e secondarie. Dopo un breve excursus sulla ricerca recente in didattica della matematica e sull’importanza del problem solving nell’insegnamento della matematica, illustriamo come Mathematica possa essere un ottimo strumento didattico, e introduciamo tre applet create con Mathematica per illustrare le possibilità di questo strumento. |
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