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 1287 prodotti
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78/2025 - 12/12/2025
Botti, M.; Mascotto, L.
Trace inequalities for piecewise W^1,p functions over general polytopic meshes | Abstract | | Trace inequalities are crucial tools to derive the stability of partial differential equations with inhomogeneous, natural boundary conditions. In the analysis of corresponding Galerkin methods, they are also essential to show convergence of sequences of discrete solutions to the exact one for data with minimal regularity under mesh refinements and/or degree of accuracy increase. In nonconforming discretizations, such as Crouzeix-Raviart and discontinuous Galerkin, the trial and test spaces consists of functions that are only piecewise continuous: standard trace inequalities cannot be used in this case. In this work, we prove several trace inequalities for piecewise W^{1,p} functions. Compared to analogous results already available in the literature, our inequalities are established:(i) on fairly general polytopic meshes (with arbitrary number of facets and arbitrarily small facets); (ii) without the need of finite dimensional arguments (e.g., inverse estimates, approximation properties of averaging operators); (iii) for different ranges of maximal and nonmaximal Lebesgue indices. |
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77/2025 - 11/12/2025
Bonetti, S.; Botti, M.; Vega, P.
A robust fully-mixed finite element method with skew-symmetry penalization for low-frequency poroelasticity | Abstract | | In this work, we present and analyze a fully-mixed finite element scheme for the dynamic poroelasticity problem in the low-frequency regime. We write the problem as a four-field, first-order, hyperbolic system of equations where the symmetry constraint on the stress field is imposed via penalization. This strategy is equivalent to adding a perturbation to the saddle point system arising when the stress symmetry is weakly imposed. The coupling of solid and fluid phases is discretized by means of stable mixed elements in space and implicit time advancing schemes. The presented stability analysis is fully robust with respect to meaningful cases of degenerate model parameters. Numerical tests validate the convergence and robustness and assess the performances of the method for the simulation of wave propagation phenomena in porous materials. |
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75/2025 - 05/12/2025
Crippa, B.; Scotti, A.; Villa, A.
A one-dimensional reduced plasma model for the electrical treeing | Abstract | | Plasma models, consisting of advection-diffusion Partial Differential Equations coupled with chemical reactions, are widely adopted to describe corona, streamers and dielectric barrier discharges. However, the complex geometry of the electrical treeing represents an obstacle for numerical simulations.
We develop a reduced one-dimensional formulation of a plasma model for the electrical treeing, describing the evolution of charge concentrations under the effect of an electric field. The reduced system consists of weakly coupled advection-diffusion-reaction equations for charge concentrations inside the treeing and on the dielectric surface, coupled with production-destruction Ordinary Differential Equations for the dipole moment.
A numerical scheme based on Finite Volumes and Patankar-type methods allows efficient simulations, while preserving key physical properties. The model is tested on increasingly complex geometries, from a straight line to a realistic electrical treeing. |
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74/2025 - 04/12/2025
Colombo, S.; Gimenez Zapiola, A.; Ieva, F.; Vantini, S.
Multi-state Modeling of Delay Evolution in Suburban Rail Transports | Abstract | | Train delays are a persistent issue in railway systems, particularly in suburban networks where operational complexity is heightened by frequent services and high passenger volumes. Traditional delay models often overlook the temporal and structural dynamics of real delay propagation.
This work applies continuous-time multi-state models to analyze the temporal evolution of delay on the S5 suburban line in Lombardy, Italy. Using detailed operational, meteorological, and contextual data, the study models delay transitions while accounting for observable heterogeneity.
The findings reveal how delay dynamics vary by travel direction, time slot, and route segment. Covariates such as station saturation and passenger load are shown to significantly affect the risk of delay escalation or recovery. The study offers both methodological advancements and practical results for improving the reliability of rail services. |
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72/2025 - 01/12/2025
Antonietti, P. F.; Cancrini, A.; Ciaramella, G.
Numerical verification of PolyDG algebraic solvers for the pseudo-stress Stokes problem | Abstract | | This work focuses on the development of efficient solvers for the pseudo-stress formulation of the unsteady Stokes problem, discretised by means of a discontinuous Galerkin method on polytopal grids (PolyDG). The introduction of the pseudo-stress variable is motivated by the growing interest in non-Newtonian flow models and coupled interface problems, where the stress field plays a fundamental role in the physical description. The space-time discretisation of the problem is obtained by combining the PolyDG approach in space with the implicit Euler method for time integration. The resulting linear system, characterised by a symmetric, positive, definite matrix, exhibits deteriorating convergence with standard solvers as the time step decreases. To address this issue, we investigate two tailored strategies: deflated Conjugate Gradient, which mitigates the effect of the most problematic eigenmodes, and collective Block-Jacobi, which exploits the block structure of the system matrix. Numerical experiments show that both approaches yield iteration counts effectively independent of Delta t, ensuring robust performance with respect to the time step. Future work will focus on extending this robustness to the spatial discretisation parameter h by integrating multigrid strategies with the time-robust solvers developed in this study. |
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73/2025 - 01/12/2025
Antonietti, P.F.; Bertoluzza, S.; Credali, F.
The Reduced Basis Multigrid scheme for the Virtual Element Method. | Abstract | | We present a non-nested W-cycle multigrid scheme for the lowest order Virtual Element Method on polygonal meshes. To avoid the implicit definition of the Virtual Element space, which poses several issues in the computation of intergrid operators that underpin multigrid methods, the proposed scheme uses a fully-conforming auxiliary space constructed by cheaply computing the virtual basis functions via the reduced basis method. |
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71/2025 - 27/11/2025
Paolo, F.; Tonini, A.; Valenti, G.; Hoxha, S.; Bassareo, P.P.; Dede', L.; Quarteroni, A.; Dimopoulos, K.
Analytical interpretation of hemodynamic data in patients with intracardiac shunts: role of mathematical modeling | Abstract | | Introduction
Shunt lesions are categorized into pre- and post-tricuspid. Although it is well recognized that these two entities have a different pathophysiology, hemodynamic variables involved are still poorly understood. This paper aims to analytically appraise shunt physiology exploiting a lumped parameters mathematical model.
Methods
Circulatory system was split into arterial and venous compartments, each of them being described by resistive, capacitive and inductive components. The model was modified including a communication between atria and ventricles. Predicted changes in the ratio between pulmonary blood flow and systemic blood flow (Qp/Qs), obtained by manipulating pulmonary resistances (PVR) and ventricular stiffness were computed.
Results
A twofold rise of pulmonary vascular resistance resulted in a significant reduction of Qp/Qs in the setting of isolated ventricular septal defect (VSD) and VSD associated with atrial septal defect (ASD) but did not produced a sizable effect in case of isolated ASD. In the model describing an isolated ASD, a similar magnitude of Qp/Qs reduction was predicted by simulating an increase of right ventricular passive elastance and relaxation time. In this type of shunt, the dependance of Qp/Qs from PVR and ventricular elastance appeared analytically linked.
Conclusions
According to this model, shunt through an ASD is minimally affected by PVRs. The marginal change of pulmonary flow produced by large variations of PVR appeared mediated by changes in right ventricular elastance. According to the model the effect of pulmonary vasodilators in patients with ASD can be concealed or enhanced by increased stiffness of the right or left ventricle, respectively.
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70/2025 - 24/11/2025
Greco, M.; Milan, G.; Ieva, F.; Secchi, P.
The Social Growth Index: Measuring Socioeconomic Resilience at the Municipal Level in Italy | Abstract | | This study introduces the Social Growth Index (SGI), an integrated framework for assessing socioeconomic resilience at the municipal level across Italy. The SGI builds on the idea that a territory is resilient if it can sustain long-term growth despite exposure to external shocks—both positive, such as large-scale public investments under the National Recovery and Resilience Plan (PNRR), and negative, such as the COVID-19 pandemic. These events represent structural tests for local systems, revealing their ability to adapt, recover, and convert temporary disturbances into lasting development trajectories.
Using harmonized data for 2010–2022, the SGI integrates three standardized variables—GDP density (GDP per m2), GDP per capita, and population density—that jointly capture productive intensity, individual prosperity, and demographic vitality within a consistent spatial structure.
To obtain the SGI, we design a methodological framework integrating Fixed Rank Kriging (FRK) for the spatial downscaling of Gross Domestic Product (GDP) with Copeland aggregation for multi-criteria ranking. FRK enables spatially coherent GDP estimates at fine resolution, while the Copeland method aggregates municipalities’ relative performance without imposing arbitrary weights.
Results reveal a persistent North–South divide, with higher resilience levels in Northern and Central Italy and lower values in Southern, Sicilian, and inland Sardinian areas. Temporal analysis indicates structural persistence in highly resilient urban and industrial systems alongside localized improvements around regional capitals. Comparison with ISTAT’s Municipal Fragility Index (IFC)exhibits consistency among indicators measuring intersecting economic aspects.
Future extensions include developing a spatio-temporal FRK model and incorporating additional drivers—such as employment, innovation, and environmental sustainability—to enhance temporal coherence and policy relevance. |
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