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 1349 prodotti
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24/2019 - 05/07/2019
Masci, C.; Ieva, F.; Agasisti, T.; Paganoni A.M.
Evaluating class and school effects on the joint achievements in different subjects: a bivariate semi-parametric mixed-effects model | Abstract | | This paper proposes an innovative statistical method to measure the impact of the class/school on its student achievements in multiple subjects. We propose a semi-parametric mixed-effects model with a bivariate response variable, where the random effects are assumed to follow a discrete distribution with an unknown number of support points, together with an Expectation-Maximization algorithm to estimate its parameters. The bivariate setting allows to estimate the distributions of the model coefficients related to each response variable as well as their joint distribution. In the case study, we apply the BSPEM algorithm to data about Italian middle schools, considering students nested within classes, and we identify subpopulations of classes, standing on their effects on student achievements in two different subjects (reading and mathematics). The proposed model is extremely informative in exploring the correlation between multiple class effects, which are typical of the educational production function. The estimated class effects on reading and mathematics student achievements are then explained in terms of various class and school level characteristics selected by means of a LASSO regression. |
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23/2019 - 05/07/2019
Laurino, F; Zunino, P.
Derivation and analysis of coupled PDEs on manifolds with high dimensionality gap arising from topological model reduction | Abstract | | Multiscale methods based on coupled partial differential equations defined on bulk and embedded manifolds are still poorly explored from the theoretical standpoint, although they are successfully used in applications, such as microcirculation and flow in perforated subsurface reservoirs. This work aims at shedding light on some theoretical aspects of a multiscale method consisting of coupled partial differential equations defined on one-dimensional domains embedded into three-dimensional ones. Mathematical issues arise because the dimensionality gap between the bulk and the inclusions is larger than one, that is the high dimensionality gap case. First, we show that such model derives from a system of fully three-dimensional equations, by the application of a topological model reduction approach. Secondly, we rigorously analyze the problem, showing that the averaging operators applied for the model reduction introduce a regularization effect that resolves the issues due to the singularity of solutions and to the ill-posedness of restriction operators. Then, we exploit the structure of the model reduction technique to analyze the modeling error. This study confirms that for infinitesimally small inclusions, the modeling error vanishes. Finally, we discretize the problem by means of the finite element method and we analyze the approximation and the model error by means of numerical experiments. |
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22/2019 - 05/07/2019
Gigante, G.; Sambataro, G.; Vergara, C.
Optimized Schwarz methods for spherical interfaces with application to fluid-structure interaction | Abstract | | In this work we consider the Optimized Schwarz method designed for computational domains that feature spherical or almost spherical interfaces. In the first part, we consider the diffusion-reaction problem. We provide a convergence analysis of the generalized Schwarz method, we discuss an optimization procedure for constant interface parameters leading to a Robin-Robin scheme, and we present some numerical results both in spherical and in ellipsoidal domains. In the second part of the
work, we address the fluid-structure interaction problem. Again, we provide a convergence analysis and discuss optimal choices of constant interface parameters. Finally, we present 3D numerical results inspired by hemodynamic applications, to validate the proposed optimal choices in presence of large added mass effect. In particular, we consider numerical experiments both in an ideal spherical domain and in a realistic abdominal aortic aneurysm. |
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21/2019 - 05/07/2019
Martino, A.; Guatteri, G.; Paganoni, A.M.
Hidden Markov Models for multivariate functional data | Abstract | | Hidden Markov Models (HMMs) are a very popular tool used in many fields to model time series data. In this paper we want to extend the usual HMM framework, where the observed objects are univariate or multivariate data, to the case of functional data. In particular, since we have a sequence of multivariate curves that evolves in time, we want to model the temporal structure of the system using HMMs. The functional observations, which rely on the statistical tools related to Functional Data Analysis (FDA), are linked to the state of the HMM according to a similarity function, which depends on some metric in Hilbert spaces. We first assess our results in a simulation setting and then we apply our model to a case study regarding the climate. |
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19/2019 - 17/06/2019
Torti, A.; Pini, A.; Vantini, S.
Modelling time-varying mobility flows using function-on-function regression: analysis of a bike sharing system in the city of Milan. | Abstract | | In today’s world bike sharing systems are becoming increasingly common in all main cities around the world. To understand the spatio-temporal patterns of how people move by bike through the city of Milan, we apply functional data analysis to study the flows of a bike sharing mobility network. We introduce a complete pipeline to properly analyse and model functional data through a concurrent functional-on-functional model taking into account the effects of weather conditions and calendar on the bike flows. |
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18/2019 - 17/06/2019
Delpopolo Carciopolo, L.; Cusini, M.; Formaggia, L.; Hajibeygi, H.
Algebraic dynamic multilevel method with local time-stepping (ADM-LTS) for sequentially coupled porous media flow simulation | Abstract | | This paper presents an algebraic dynamic multilevel method with local time-stepping (ADM-LTS) for transport equations of sequentially coupled flow in heterogeneous porous media. The method employs an adaptive multilevel space-time grid determined on the basis of two error estimators, one in time and one in space.
More precisely, at each time step, first a coarse time step on a coarsest space-grid resolution is taken. Then, based on the error estimators, the transport equation is solved by taking different time step sizes at different spatial resolutions within the computational domain.
In this way, the method is able to use a fine grid resolution, both in space and in time, only at the moving saturation fronts.
In order to ensure local mass conservation, two procedures are developed. First, finite-volume restriction operators and constant prolongation (interpolation) operators are developed to map the system across different space-grid resolutions. Second, the fluxes at the interfaces across two different time resolutions are approximated with an averaging scheme in time.
Several numerical experiments have been performed to analyze the efficiency and accuracy of the proposed ADM-LTS method for both homogeneous and heterogeneous permeability field. The results show that the method provides accurate solutions, at the same time it reduces the number of fine grid-cells both in space and in time. |
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17/2019 - 02/06/2019
Antonietti,P.F.; De Ponti, J.; Formaggia, L.; Scotti, A.
Preconditioning techniques for the numerical solution of flow in fractured porous media | Abstract | | This work deals with the efficient iterative solution of the system of equations stemming from mimetic finite difference discretization of a hybrid-dimensional mixed Darcy problem modeling flow in fractured porous media.
We investigate the spectral properties of a mixed discrete formulation based on mimetic finite differences for flow in the bulk matrix and finite volumes for the fractures, and propose of a class of preconditioning techniques to accelerate convergence of iterative solvers applied to the resulting discrete system.
Numerical tests on significant three dimensional cases have assessed the properties of the proposed procedures. |
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16/2019 - 31/05/2019
Antonietti, P.F.; Houston, P.; Pennesi, G.; Suli, E.
An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids | Abstract | | In this article we design and analyze a class of two-level non-overlapping additive Schwarz preconditioners for the solution of the linear system of equations stemming from discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polytopic meshes. The preconditioner is based on a coarse space and a non-overlapping partition of the computational domain where local solvers are applied in parallel. In particular, the coarse space can potentially be chosen to be non-embedded with respect to the finer space; indeed it can be obtained from the fine grid by employing agglomeration and edge coarsening techniques. We investigate the dependence of the condition number of the preconditioned system with respect to the diffusion coefficient and the discretization parameters, i.e., the mesh size and the polynomial degree of the fine and coarse spaces. Numerical examples are presented which confirm the theoretical bounds.
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