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 1275 prodotti
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24/2013 - 29/05/2013
Mazzieri, I.; Stupazzini, M.; Guidotti, R.; Smerzini, C.
SPEED-SPectral Elements in Elastodynamics with Discontinuous Galerkin: a non-conforming approach for 3D multi-scale problems | Abstract | | This work presents a new high performance open-source numerical code,
namely SPEED (SPectral Elements in Elastodynamics with Discontinuous Galerkin), to approach seismic wave propagation analysis in visco-elastic heterogeneous three-dimensional media on both local and regional scale. Based on non-conforming high-order techniques, like the Discontinuous Galerkin spectral approximation, along with efficient and scalable algorithms, the code allows one to deal with a non-uniform polynomial degree distribution as well as a locally varying mesh size. Validation benchmarks are illustrated to check the accuracy, stability and performance features of the parallel kernel, while illustrative examples are discussed to highlight the engineering applications of the method. The proposed method turns out to be particularly useful for a variety of earthquake engineering problems, such as modeling of dynamic soil structure and site-city interaction effects, where accounting for multi-scale wave propagation phenomena as well as sharp discontinuities in mechanical properties of the media is crucial.
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25/2013 - 29/05/2013
Cattaneo, Laura; Zunino, Paolo
Computational models for coupling tissue perfusion and microcirculation | Abstract | | The aim of this work is to develop a computational model able to capture the interplay between microcurculation and interstitial tissue perfusion. Such phenomena are at the basis of the exchange of nutrients, wastes and pharmacological agents between the cardiovascular system and the organs. They are particularly interesting for the study of effective targeting techniques to treat vascularized tumors with drugs. We develop a model applicable at the microscopic scale, where the capillaries and the interstitial volume can be described as independent structures capable to propagate flow. We facilitate the analysis of complex configurations of the capillary bed, by representing the capillaries as a one-dimensional network, ending up with a heterogeneous system characterized by channels embedded into a porous medium. We use the immersed boundary method to couple the one-dimensional with the three-dimensional flow through the network and the interstitial volume, respectively. The main idea consists in replacing the immersed network with an equivalent concentrated source. After dealing with the issues arising in the implementation of a computational solver, we apply it to compare tissue perfusion between healthy and tumor tissue samples. |
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26/2013 - 29/05/2013
Ieva, F.; Paganoni, A.M.
Detecting and visualizing outliers in provider profiling via funnel plots and mixed effect models | Abstract | | In this work we propose the use of a graphical diagnostic tool (the funnel
plot) to detect outliers among hospitals that treat patients affected by Acute
Myocardial Infarction (AMI). We consider an application to data on AMI hospitalizations
arising from administrative databases. The outcome of interest is the in-hospital mortality, a variable indicating if the patient has been discharged dead or alive. We then compare the results obtained by graphical diagnostic
tools with those arising from fitting parametric mixed effects models to the same data. |
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23/2013 - 22/05/2013
Sørensen, H.; Goldsmith, J.; Sangalli, L.M.
An introduction with medical applications to functional data analysis | Abstract | | Functional data are data that can be represented by suitable functions, such as curves (potentially multi-dimensional) or surfaces. This paper gives an introduction to some basic but important techniques for the analysis of such data, and the techniques are applied to two datasets from biomedicine. One dataset is about white matter structures in the brain in multiple sclerosis patients; the other dataset is about three-dimensional vascular geometries collected for the study of cerebral aneurysms. The techniques described are smoothing, alignment,
principal component analysis, and regression. |
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22/2013 - 03/05/2013
Falcone, M.; Verani, M.
Recent Results in Shape Optimization and Optimal Control for PDEs | Abstract | | In this paper we will present some recent advances in the numerical approximation of two classical problems: shape optimization and optimal control for evolutive partial differential equations. For shape optimization we present two novel techniques which have shown to be rather efficient on some applications. The first technique is based on multigrid methods whereas the second relies on an adaptive sequential quadratic programming. With respect to the optimal control of evolutive problems, the approximation is based on the coupling between a POD representation of the dynamical system and the classical Dynamic Programming approach. We look for an approximation of the value function characterized as the weak solution (in the viscosity sense) of the corresponding Hamilton-Jacobi equation.
Several tests illustrate the main features of the above methods. |
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21/2013 - 02/05/2013
Perotto, S.; Veneziani, A.
Coupled model and grid adaptivity in hierarchical reduction of elliptic problems | Abstract | | In this paper we propose a surrogate model for advection-diffusion-reaction problems characterized by a dominant direction in their dynamics. We resort to a hierarchical-model reduction where we couple a modal representation of the transverse dynamics with a finite element approximation along the mainstream. This different treatment of the dynamics entails a surrogate model enhancing a purely 1D description related to the leading direction. The coefficients of the finite element expansion along this direction introduce a generally non-constant description of the transversal dynamics. Aim of this paper is to provide an automatic adaptive approach to locally determine the dimension of the modal expansion as well as the finite element step in order to satisfy a prescribed tolerance on a goal functional of interest. |
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20/2013 - 01/05/2013
Azzimonti, L.; Nobile, F.; Sangalli, L.M.; Secchi, P.
Mixed Finite Elements for spatial regression with PDE penalization | Abstract | | We study a class of models at the interface between statistics and numerical analysis. Specifically, we consider non-parametric regression models for the estimation of spatial fields from pointwise and noisy observations, that account for problem specific prior information, described in terms of a PDE governing the phenomenon under study. The prior information is incorporated in the model via a roughness term using a penalized regression framework. We prove the well-posedness of the estimation problem and we resort to a mixed equal order Finite Element method for its discretization. We prove the well posedness and the optimal convergence rate of the proposed discretization method. Finally the smoothing technique is extended to the case of areal data, particularly interesting in many applications. Keywords: mixed Finite Element method, fourth order problems, non-parametric regression, smoothing. |
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19/2013 - 30/04/2013
Azzimonti, L.; Sangalli, L.M.; Secchi, P.; Domanin, M.; Nobile, F.
Blood flow velocity field estimation via spatial regression with PDE penalization | Abstract | | We propose an innovative method for the accurate estimation of surfaces and spatial fields when a prior knowledge on the phenomenon under study is available. The prior knowledge included in the model derives from physics, physiology or mechanics of the problem at hand, and is formalized in terms of a partial differential equation governing the phenomenon behavior, as well as conditions that the phenomenon has to satisfy at the boundary of the problem domain. The proposed models exploit advanced scientific computing techniques and specifically make use of the Finite Element method. The estimators have a typical penalized regression form and the usual inferential tools are derived. Both the pointwise and the areal data frameworks are considered. The driving application concerns the estimation of the blood flow velocity field in a section of a carotid artery, using data provided by echo-color doppler; this applied problem arises within a research project that aims at studying atherosclerosis pathogenesis. Keywords: functional data analysis, spatial data analysis, object-oriented data analysis, penalized regression, Finite Elements. |
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