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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07/2011 - 02/16/2011
Arioli, G.; Gamba, M.
Automatic computation of Chebyshev polynomials for the study of parameter dependence for hyperbolic systems | Abstract | | We introduce a new intrusive method for studying the parameter dependence of solutions of hyperbolic systems having sharp discontinuities.
Two applications to the study of solutions of Euler s system are presented. |
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06/2011 - 01/20/2011
Secchi, P.; Stamm, A.; Vantini, S.
Large p Small n Data: Inference for the Mean | Abstract | | We provide a generalization of Hotelling’s Theorem that enables inference (i)for the mean vector of a multivariate normal population and (ii) for the comparison of the mean vectors of two multivariate normal populations, when the number p of components is larger than the number n of sample units and the (common) covariance matrix is unknown. We find suitable test statistics and their p-asymptotic
distributions that allow the inferential analysis of large p small n data. |
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05/2011 - 01/18/2011
Arioli, G.; Gamba, M.
An algorithm for the study of parameter dependence for hyperbolic systems | Abstract | | We introduce a new technique for computing the explicit dependence of the result of the numerical integration of a conservation law with respect to one or more parameters. The method is intrusive, but it relies on an automatic differentiation algorithm, therefore it requires minimal modi cations of the code used for the plain numerical integration. We present
an example of application to the study of the shock tube, that is Euler s system of equations with discontinuous initial conditions. |
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04/2011 - 01/14/2011
Ieva, F.; Paganoni, A.M.; Pigoli, D.; Vitelli, V.
Multivariate functional clustering for the analysis of ECG curves morphology | Abstract | | Cardiovascular diseases are one of the main causes of death all over the world.
In this kind of pathologies, it is fundamental to be well-timed in order to obtain good prognosis in reperfusive treatment. In particular, an automatic classification procedure based on statistical analyses of tele-transmitted ECG traces would be very helpful for an early diagnosis. This work is a pilot analysis on electrocardiographic ECG) traces (both normal and pathological ones) of patients whose 12-leads pre-hospital ECG has been sent by life supports to 118 Dispatch Center of Milan. The statistical analysis consists of preliminary steps like reconstructing signals, wavelets denoising and removing the biological variability in the signals
through data registration.
Then, a multivariate functional k-means clustering of reconstructed and registered ECGs is performed, and performances of classification
method are validated. So a semi-automatic diagnostic procedure, based on the sole ECG’s morphology, is proposed to classify patients and predict pathologies. |
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03/2011 - 01/13/2011
Garegnani, G.; Rosatti, G.; Bonaventura, L.
Mathematical and Numerical Modelling of Fully Coupled Mobile Bed Free Surface Flows | Abstract | | We analyze the most widely used formulations of sediment transport modelling in the framework of one dimensional channel flow, thereby assessing the impact of typical simplifying assumptions, such as low sediment concentration and decoupling of hydrodynamics and bed evolution. As a result, the importance of using a quasi two-phase formulation is highlighted. Starting from the
a quasi two-phase model equations, under the hypothesis of quasi-steady free surface and mixture flows, we derive a simplified equation for the bed evolution, that is also valid in the large sediment concentration regime. The solution of such a simplified equation provides a useful benchmark for numerical methods aimed at computing approximate solutions of the quasi two-phase system.
Finally,we propose and evaluate a highly efficient and accurate semi-implicit and
semi-Lagrangian numerical method for quasi two-phase mobile bed system. |
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02/2011 - 01/10/2011
Lassila, T.; Quarteroni, A.; Rozza, G.
A reduced basis model with parametric coupling for fluid-structure interaction problems | Abstract | | We present a new model reduction technique for steady fluid-structure interaction problems. When the fluid domain deformation is suitably
parametrized, the coupling conditions between the
fluid and structure can be formulated in the low-dimensional space of geometric parameters.
Moreover, we apply the reduced basis method to reduce the cost of repeated fluid solutions necessary to achieve convergence of fluid-structure iterations. In this way a reduced order model with reliable a posteriori error bounds is obtained. The proposed method is validated with an example of steady Stokes flow in an axisymmetric channel, where the structure is described by a simple 1-d generalized string model. We demonstrate rapid convergence of the reduced solution of the parametrically coupled problem as the number of geometric parameters is increased. |
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01/2011 - 01/05/2011
Dalla Rosa, M.; Sangalli, L. M.; Vantini, S.
Dimensional Reduction of Functional Data by means of Principal Differential Analysis | Abstract | | We explore the use of principal differential analysis (PDA) as a tool for performing dimensional reduction of functional data sets. In particular, we compare the results provided by PDA and by functional principal component
analysis (FPCA) in the dimensional reduction of three synthetic data sets, and of a real data set concerning 65 vascular geometries (i.e., the AneuRisk data set).
The analyses of the synthetic data sets show that PDA can provide an alternative and effective representation of functional data that is always
easily interpretable in terms of constant, exponential, sinusoidal, or dampedsinusoidal
functions and not affected by the presence of clusters or strong correlations among the original components. Moreover, in the analysis of
the AneuRisk data set, PDA is able to detect important features of the data that FPCA is not able to detect. |
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43/2010 - 12/10/2010
Pennati, G.; Dubini, G.; Migliavacca, F.; Corsini, C.; Formaggia, L.; Quarteroni,A.; Veneziani, A.
Multiscale Modelling with Application to Paediatric Cardiac Surgery | Abstract | | The study of the haemodynamics of 3D models
of vascular districts with complex anatomy with the aid of numerical models requires to prescribe correct conditions at the boundary of the district of interest. The cardiovascular system is a highly integrated circuit and global systemic
effects cannot be neglected even when the interest lays on a specific local area.
To this aim, a novel approach, called geometrical multiscale, has been devised where models of
different level of detail (and computational cost) are coupled together. In particular, we focus in this work on an application where the 3D Navier–Stokes equations are coupled with a non-linear system of ordinary differential
equations governing the systemic circulation. The application is the simulation of different procedures for paediatric cardiac surgery. |
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