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 1152 prodotti
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15/2023 - 22/02/2023
Ragni, A.; Masci, C.; Ieva, F.; Paganoni, A. M.
Clustering Hierarchies via a Semi-Parametric Generalized Linear Mixed Model: a statistical significance-based approach | Abstract | | We introduce a novel statistical significance-based approach for clustering hierarchical data using semi-parametric linear mixed-effects models designed for responses with laws in the exponential family (e.g., Poisson and Bernoulli). Within the family of semi-parametric mixed-effects models, a latent clustering structure of the highest-level units can be identified by assuming the random effects to follow a discrete distribution with an unknown number of support points. We achieve this by computing alpha-level confidence regions of the estimated support point and identifying statistically different clusters. At each iteration of a tailored Expectation Maximization algorithm, the two closest estimated support points for which the confidence regions overlap collapse. Unlike the related state-of-the-art methods that rely on arbitrary thresholds to determine the merging of close discrete masses, the proposed approach relies on conventional statistical confidence levels, thereby avoiding the use of discretionary tuning parameters. To demonstrate the effectiveness of our approach, we apply it to data from the Programme for International Student Assessment (PISA - OECD) to cluster countries based on the rate of innumeracy levels in schools. Additionally, a simulation study and comparison with classical parametric and state-of-the-art models are provided and discussed. |
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13/2023 - 22/02/2023
Masci, C.; Cannistrà, M.; Mussida, P.
Modelling time-to-dropout via Shared Frailty Cox Models. A trade-off between accurate and early predictions | Abstract | | This paper investigates the student dropout phenomenon in a technical Italian university in a time-to-event perspective. Shared frailty Cox time-dependent models are applied to analyse the careers of students enrolled in different engineering programs with the aim of identifying the determinants of student dropout through time, to predict the time to dropout as soon as possible and to observe how the dropout phenomenon varies across time and degree programs. The innovative contributions of this work are methodological and managerial. First, the adoption of shared frailty Cox models with time-varying covariates is relatively new to the student dropout literature and it allows to take account of the student career evolution and of the heterogeneity across degree programs. Second, understanding the dropout pattern over time and identifying the earliest moment for obtaining its accurate prediction allow policy makers to set timely interventions for students at risk of dropout. |
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11/2023 - 17/02/2023
Gatti, F.; de Falco, C.; Perotto, S.; Formaggia, L.
A parallel well-balanced numerical scheme for the simulation of fast landslides with efficient time stepping | Abstract | | We consider a single phase depth–averaged model for the numerical simulation of
fast–moving landslides with the goal of constructing a well-balanced positivitypreserving,
yet scalable and efficient, second–order time–stepping algorithm. We
apply a Strang splitting approach to distinguish between parabolic and hyperbolic
problems. For the parabolic case, we adopt a second–order Implicit–Explicit Runge–
Kutta–Chebyshev scheme, while we use a two–stage Taylor discretization combined
with a path-conservative strategy, to deal with the purely hyperbolic contribution.
The proposed strategy allows to combine these schemes in such a way that
the corresponding absolute stability regions remain unbiased, while guaranteeing
positivity-preserving and well-balancing property to the overall implementation.
The spatial discretization we adopt is based on a standard finite element method,
associated with a hierarchically refined Cartesian grid. After providing numerical
evidence of the well-balancing property, we demonstrate the capability of the proposed
approach in selecting time steps larger with respect to the ones adopted by
a classical Taylor-Galerkin scheme. Finally, we provide some meaningful scaling
results, both on ideal and realistic scenarios. |
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10/2023 - 14/02/2023
Corti, M.; Antonietti, P.F.; Bonizzoni, F.; Dede', L., Quarteroni, A.
Discontinuous Galerkin Methods for Fisher-Kolmogorov Equation with Application to Alpha-Synuclein Spreading in Parkinson’s Disease | Abstract | | The spreading of prion proteins is at the basis of brain neurodegeneration. The paper deals with the numerical modelling of the misfolding process of alpha-synuclein in Parkinson’s disease. We introduce and analyze a discontinuous Galerkin method for the semi-discrete approximation of the Fisher-Kolmogorov (FK) equation that can be employed to model the process. We employ a discontinuous Galerkin method on polygonal and polyhedral grids (PolyDG) for space discretization, which allows us to accurately simulate the wavefronts typically observed in the prionic spreading. We prove stability and a priori error estimates for the semi-discrete formulation. Next, we use a Crank-Nicolson scheme to advance in time. For the numerical verification of our numerical model, we first consider a manufactured solution, and then we consider a case with wavefront propagation in two-dimensional polygonal grids. Next, we carry out a simulation of alpha-synuclein spreading in a two-dimensional brain slice in the sagittal plane with a polygonal agglomerated grid that takes full advantage of the flexibility of PolyDG approximation. Finally, we present a simulation in a three-dimensional patient-specific brain geometry reconstructed from magnetic resonance images. |
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09/2023 - 10/02/2023
Buchwald, S.; Ciaramella, G.; Salomon, J.
Gauss-Newton oriented greedy algorithms for the reconstruction of operators in nonlinear dynamics | Abstract | | This paper is devoted to the development and convergence analysis of greedy reconstruction algorithms based on the strategy presented in [Y. Maday and J. Salomon, Joint Proceedings of the 48th IEEE Conference on
Decision and Control and the 28th Chinese Control Conference, 2009, pp. 375--379]. These procedures allow the design of a sequence of control functions that ease the
identification of unknown operators in nonlinear dynamical systems.
The original strategy of greedy reconstruction algorithms is based on an offline/online
decomposition of the reconstruction process and on an ansatz for the unknown operator obtained by an a priori chosen set of linearly independent matrices. In the previous work [S. Buchwald, G. Ciaramella and J. Salomon, SIAM J. Control Optim., 59(6), pp. 4511-4537], convergence results were obtained in the case of linear identification problems. We tackle here the more general case of nonlinear systems. More precisely, we show that the controls obtained with the greedy algorithm on the corresponding linearized system lead to the local convergence of the classical Gauss-Newton method applied to the online nonlinear identification problem. We then extend this result to the controls obtained on nonlinear systems where a local convergence result is also obtained. The main convergence results are obtained for the reconstruction of drift operators in linear and bilinear dynamical systems. |
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08/2023 - 07/02/2023
Bonizzoni, F.; Hu, K.; Kanschat, G.; Sap, D.
Discrete tensor product BGG sequences: splines and finite elements | Abstract | | In this paper, we provide a systematic discretization of the
Bernstein-Gelfand-Gelfand (BGG) diagrams and complexes over cubical
meshes of arbitrary dimension via the use of tensor-product structures of one-dimensional piecewise-polynomial spaces, such as spline and finite element spaces. We demonstrate the construction of the Hessian, the elasticity, and divdiv complexes as examples for our construction. |
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07/2023 - 06/02/2023
Garcia-Contreras, G.; Còrcoles, J.; Ruiz-Cruz, J.A.; Oldoni, M; Gentili, G.G.; Micheletti, S.; Perotto, S.
Advanced Modeling of Rectangular Waveguide Devices with Smooth Profi les by Hierarchical Model Reduction | Abstract | | We present a new method for the analysis of smoothly varying tapers, transitions and fi lters in rectangular waveguides. With this aim, we apply a Hierarchical Model (HiMod) reduction to the vector Helmholtz equation. We exploit a suitable coordinate transformation and, successively, we use the waveguide modes as a basis for the HiMod expansion. We show that accurate results can be obtained with an impressive speed-up factor when compared with standard commercial codes based on a three-dimensional fi nite element discretization. |
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06/2023 - 06/02/2023
Artoni, A.; Antonietti, P. F.; Mazzieri, I.; Parolini, N.; Rocchi, D.
A segregated finite volume - spectral element method for aeroacoustic problems | Abstract | | We propose a segregated Finite Volume (FV) - Spectral Element Method (SEM) for modelling aeroacoustic phenomena based on the Lighthill's acoustic analogy. First the fluid solution is computed employing a FV method. Then, the sound source term is projected onto the acoustic grid and the inhomogeneous Lighthill's wave equation is solved employing the SEM. The novel projection method computes offline the intersections between the acoustic and the fluid grids in order to preserve the accuracy. The proposed intersection algorithm is shown to be robust, scalable and able to efficiently compute the geometric intersection of arbitrary polyhedral elements.
We then analyse the properties of the projection error and we numerically assess the obtained theoretical estimates. Finally, we address two relevant aeroacoustic benchmarks, namely the corotating vortex pair and the noise induced by a laminar flow around a squared cylinder, to demonstrate in practice the effectiveness of the proposed approach. The flow computations are performed with OpenFOAM , an open-source finite volume library, while the inhomogeneous Lighthill's wave equation is solved with SPEED, an open-source spectral element library. |
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