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 1322 prodotti
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01/2013 - 04/01/2013
Arnold, D.N.; Boffi, D.; Bonizzoni,F.
Tensor product finite element differential forms and their approximation properties | Abstract | | We discuss the tensor product construction for complexes of differential forms and show how it can be applied to define shape functions and degrees of freedom for finite element differential forms on cubes in n dimensions. These may be extended to curvilinear cubic elements, obtained as images of a reference cube under diffeomorphisms, by using the pullback transformation for differential forms to map the shape functions and degrees of freedom from the reference cube to the image finite element. This construction recovers and unifies several known finite element approximations in two and three dimensions. In this context, we study the approximation properties of the resulting finite element spaces in two particular cases: when the maps from the reference cube are affine, and when they are multilinear. In the former case the rate of convergence depends only on the degree of polynomials contained in the reference space of shape functions. In the latter case, the rate of approximation is degraded, with the loss more severe for differential forms of higher form degree. |
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56/2012 - 22/12/2012
Ieva, F.; Paganoni, A.M.
Risk Prediction for Myocardial Infarction via Generalized Functional Regression Models | Abstract | | In this paper, we propose a generalized functional linear regression model for a binary outcome indicating the presence/absence of a cardiac disease with a multivariate functional data among the relevant predictors. In particular
the motivating problem is an analysis of Electrocardiographic (ECG)traces of patients whose prehospital ECG has been sent to 118 Dispatch Center of Milan (the Italian free-toll number for emergencies) by life support personnel of the basic rescue units. The statistical analysis starts with a preprocessing step of ECGs, treated as multivariate functional data. They are reconstructed from noisy observations, then the biological variability is removed by a nonlinear registration procedure based on landmarks. Thus, a Multivariate Functional Principal Component Analysis (MFPCA) is carried
out on the variance-covariace matrix of the reconstructed and registered ECGs as well as of their first derivatives, in order to perform a data-driven dimensional reduction. The scores of the principal components that result to be significant are then used within a generalized functional regression model, together with other standard covariates of interest. Hence, a new
semi-automatic diagnostic procedure is proposed to model the probability of disease (in the case of interest, the probability of being affected by Left Bundle Brunch Block) and to classify patients. Finally, the performance of this classification method is evaluated through cross validation and compared with other methods proposed in literature. |
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55/2012 - 14/12/2012
Peng Chen, Alfio Quarteroni, Gianluigi Rozza
Uncertainty quantification of the human arterial network | Abstract | | This work aims at identifying and quantifying uncertainties from various sources in human cardiovascular system based on a one dimensional arterial network. A general analysis of different uncertainties and probability characterization with log-normal distribution of these uncertainties is introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish the stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe the blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation method with sparse grid technique, we study systematically the statistics and sensitivity of the solution with respect to many different uncertainties in a relatively complete arterial network validated against clinical measurements for the first time. |
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54/2012 - 13/12/2012
Ettinger, B., Perotto, S.; Sangalli, L.M.
Spatial regression models over two-dimensional manifolds | Abstract | | We propose a regression model for data spatially distributed over nonplanar two-dimensional Riemannian manifolds. The model is a generalized
additive model with a roughness penalty term involving a suitable differential operator computed over the non-planar domain. Thanks to a
semi-parametric framework, the model allows for inclusion of space-varying covariate information. We show that the estimation problem can be solved
first by conformally mapping the non-planar domain to a planar domain and then by applying existing models for penalized spatial regression over planar domains, appropriately modified to account for the domain deformation. The flattening map and the estimation problem are both computed by resorting to a finite element approach. The estimators are linear in the observed data values and classical inferential tools are derived. The application driving this research is the study of hemodynamic forces on the wall of an internal carotid artery affected by an aneurysm. |
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53/2012 - 10/12/2012
Fumagalli, A.; Scotti, A.
An efficient XFEM approximation of Darcy flows in fractured porous media | Abstract | | Subsurface flows are strongly influenced by the presence of faults and large fractures that alter the permeability of the medium acting as barriers or conduits for the flow. An accurate description of the hydraulic properties of the fractures is thus essential for the modelling of oil migration or the exploitation of unconventional sources. However, the width of fractures is often small compared to the typical mesh size. To approximate the problem without refining the mesh to resolve the fracture we replace them with surfaces immersed in the porous matrix. Moreover we allow the surfaces to be non matching with the edges of the grid handling the discontinuities within elements with the XFEM approach. The method, originally developed for the single-phase Darcy problem is extended to the case of passive transport and multiphase flow. |
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52/2012 - 06/12/2012
Perotto, S.
Hierarchical model (Hi-Mod) reduction in non-rectilinear domains | Abstract | | For the numerical solution of second-order elliptic problems featuring dynamics with a dominant direction
(e.g., drug dynamics in the circulatory system), we proposed a Hierarchical Model (HiMod) reduction procedure.
We actually perform a finite element discretization along the mainstream direction and a spectral modal approximation for the transverse dynamics.
The number of modes can locally vary along the centerline to properly fit the relevant transverse dynamics. In previous works we have considered the cases of rectilinear domains. Here we address the more general case of curved domains, where the direction of the dominant component of the solution is non-rectilinear. |
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51/2012 - 29/11/2012
Beck, J.; Nobile, F.; Tamellini, L.; Tempone, R.
A quasi-optimal sparse grids procedure for groundwater flows | Abstract | | In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work “On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods” to a Darcy problem where the permeability is modeled as a lognormal random field. We propose an explicit a-priori/a-posteriori procedure for the construction of such quasi-optimal grid and show its effectiveness on a numerical example. In this approach, the two main ingredients are an estimate of the decay of the Hermite coefficients of the solution and an efficient nested quadrature rule with respect to the Gaussian weight. |
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50/2012 - 28/11/2012
Carcano, S.; Bonaventura, L.; Neri, A.; Esposti Ongaro, T.
A second order accurate numerical model for multiphase underexpanded volcanic jets | Abstract | | An improved version of the PDAC (Pyroclastic Dispersal Analysis Code) numerical model for the simulation of multiphase volcanic flows is presented and validated for the simulation
of multiphase volcanic jets in supersonic regimes.
The present version of PDAC includes second-order time and space discretizations and fully multidimensional advection discretizations, in order to reduce numerical diffusion and
enhance the accuracy of the original model.
The resulting numerical model is tested against the problem of jet decompression in
both two and three dimensions. For homogeneous jets, numerical results show a good quantitative agreement
with experimental results on the laboratory scale in terms of Mach disk location. For multiphase jets, we consider monodisperse and polydisperse mixtures of particles
with different diameter. For fine particles, for which the pseudogas limit is valid,
the multiphase model correctly reproduces
predictions of the pseudogas model. For both fine and coarse particles, we
measure the importance of multiphase
effects with relation to the characteristic time scales of multiphase jets and we quantify how
particles affect the average jet dynamics in terms of pressure, mixture density, vertical velocity and temperature.
Furthermore, time
dependent vent conditions are introduced, in order to achieve numerical
simulation of eruption regimes characterized by transient jet behaviour. We show how in case of rapid change in vent conditions, volcanic jet structures do not evolve through a succession of steady state configurations and the transition between different flow
conditions can result in the collapse of the volcanic column. |
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