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 1314 prodotti
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33/2013 - 22/08/2013
Menafoglio, A; Guadagnini, A; Secchi, P
A Kriging Approach based on Aitchison Geometry for the Characterization of Particle-Size Curves in Heterogeneous Aquifers | Abstract | | We consider the problem of predicting the spatial field of particle-size curves (PSCs) from a sample observed at a finite set of locations within an alluvial aquifer near the city of T {u}bingen, Germany.
We interpret particle-size curves as cumulative distribution functions and their derivatives as probability density functions. We thus (a) embed the available data into an infinite-dimensional Hilbert Space of compositional functions endowed with the Aitchison geometry and (b) develop new geo-statistical methods for the analysis of spatially dependent functional compositional data. This approach enables one to provide predictions at unsampled locations for these types of data, which are commonly available in hydrogeological applications, together with a quantification of the associated uncertainty.
The proposed functional compositional kriging (FCK) predictor is tested on a one-dimensional application relying on a set of 60
particle-size curves collected along a 5-m deep borehole at the test site.
The quality of FCK predictions of PSCs is evaluated through leave-one-out cross-validation on the available data, smoothed by means of Bernstein Polynomials. A comparison of estimates of hydraulic conductivity obtained via our FCK approach against those rendered by classical kriging of effective particle diameters (i.e., quantiles of the PSCs) is provided. Unlike traditional approaches, our method fully exploits the functional form of particle-size curves and enables one to project the complete information content embedded in the PSC to unsampled locations in the system. |
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32/2013 - 16/08/2013
Taddei, T.; Perotto, S.; Quarteroni, A.
Reduced basis techniques for nonlinear conservation laws | Abstract | | In this paper we present a new reduced basis technique for parametrized nonlinear scalar conservation laws in presence of shocks. The essential ingredients are an efficient algorithm to approximate the shock curve, a procedure to detect the smooth components of the solution at the two sides of the shock, and a suitable interpolation strategy to reconstruct such
smooth components during the online stage. The approach we propose is based on some theoretical properties of the solution to the problem. Some
numerical examples prove the effectiveness of the proposed strategy. |
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31/2013 - 06/08/2013
Dassi, F.; Ettinger, B.; Perotto, S.; Sangalli, L.M.
A mesh simplification strategy for a spatial regression analysis over the cortical surface of the brain | Abstract | | We present a new mesh simplification technique developed for a statistical analysis of cortical surface data. The aim of this approach is to produce a simplified mesh which does not distort the original data distribution and such that the
statistical estimates computed over the new mesh exhibit good inferential properties. To do this, we propose an iterative technique that, for each iteration, contracts the edge of the mesh with the lowest value of a cost function. This cost function takes into account both the geometry of the surface and the distribution of the data
on it. After the data are associated with the simplified mesh, they are analyzed via a spatial regression model for non-planar domains. In particular, we resort to a penalized regression method that first conformally maps the simplified cortical surface mesh into a region in R2. Then, existing planar spatial smoothing techniques
are extended to non-planar domains by suitably including the flattening phase. The effectiveness of the entire process is numerically demonstrated via a simulation study and an application to cortical surface thickness data. |
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30/2013 - 04/07/2013
Cagnoni, D.; Agostini, F.; Christen, T.; de Falco, C.; Parolini, N.; Stefanovic, I.
Multiphysics simulation of corona discharge induced ionic wind | Abstract | | Ionic wind devices or electrostatic fluid accelerators are becoming of increasing interest as tools for thermal management, in particular for semiconductor devices. In this work, we present a numerical model for predicting the performance of such devices, whose main bene t is the ability to accurately predict the amount of charge injected at the corona electrode. Our multiphysics numerical model consists of a highly nonlinear strongly coupled set of PDEs including the Navier-Stokes equations for fluid flow, Poisson s equation for electrostatic potential, charge continuity and heat transfer equations. To solve this system we employ a staggered solution algorithm that generalizes Gummel s algorithm for charge transport in semiconductors. Predictions
of our simulations are validated by comparison with experimental measurements and are shown to closely match. Finally, our simulation tool is used to estimate the eff ectiveness of the design of an electrohydrodynamic cooling apparatus for power electronics applications. |
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29/2013 - 03/07/2013
Lassila, T.; Manzoni, A.; Quarteroni, A.; Rozza, G.
Model order reduction in fluid dynamics: challenges and perspectives | Abstract | | This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlinear convection terms and/or some geometric variability - that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration.
We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of
inf-sup stability, certification through error estimation, computational issues and - in the unsteady case - long-time stability of the reduced model. Moreover, we provide an extensive list of literature references. |
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28/2013 - 24/06/2013
Ekin, T.; Ieva, F.; Ruggeri, F.; Soyer, R.
Statistical Issues in Medical Fraud Assessment | Abstract | | In this paper we provide a survey of the statistical issues in medical fraud assessment. We discuss different types of medical fraud and the type of fraud data that arise in different situations and give a review of the statistical
methods that use such data to assess fraud. We also discuss ”conspiracy fraud” and the associated dyadic data and introduce Co-clustering methods which have not been previously considered in the medical fraud literature.
In so doing, we present some recent work on Bayesian co-clustering for fraud assessment and its extensions. Furthermore, we discuss potential use of decision theoretic methods in fraud detection and demonstrate an example for evaluating fraud detection tools. |
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27/2013 - 19/06/2013
Tagliabue, A.; Dede', L.; Quarteroni, A.
Isogeometric Analysis and Error Estimates for High Order Partial Differential Equations in Fluid Dynamics | Abstract | | In this paper, we consider the numerical approximation of high order Partial Differential Equations (PDEs) by means of NURBS-based Isogeometric Analysis (IGA) in the framework of the Galerkin method, for which global smooth basis functions with degree of continuity higher than C0 can be used. We derive a priori error estimates for high order elliptic PDEs under h-refinement, by extending existing results for second order PDEs approximated with IGA and specifically addressing the case of errors in lower order norms. We present some numerical results which both validate the proposed error estimates and highlight the accuracy of IGA. Then, we apply NURBS-based IGA to solve the fourth order stream function formulation of the Navier-Stokes equations; in particular, we solve the benchmark lid-driven cavity problem for Reynolds numbers up to 5,000. |
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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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