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 1347 prodotti
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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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69/2025 - 14/11/2025
Marino, F.; Guagliardi, O.; Di Stazio, F.; Mazza, E.; Paganoni, A.M.; Tanelli, M.
Measuring Academic Stress and Well-Being in Higher Education: A Psychometric Study | Abstract | | This study investigates the assessment of perceived academic stress and its impact on students’ mental health by employing advanced psychometric and statistical models. A dataset of 9,000 university students was analyzed using Item Response Theory (IRT), specifically the Four-parameter Nested Logistic Regression Model (4PLnRM), to estimate latent parameters that quantify well-being across nine stress-related domains. Linear and mixed-effects models were applied to identify the most relevant socio-demographic, psychosocial and academic risk factors, highlighting the strong influence of economic conditions, exam backlog, and academic self-perceptions. To further validate these measures, Random Forest classification models were trained to identify students at different levels of psychological vulnerability psychological risk, demonstrating that latent parameters are effective predictors of distress and well-being. Additionally, Exploratory Factor Analysis (EFA) on self-reported mental health symptoms psychological symptoms revealed four interpretable latent factors—anxiety, depression, motivational block, and somatization—used in subsequent clustering to classify students into low, medium, and high-risk groups. Across methods, consistent associations emerged between risk classes and demographic variables such as gender, age, academic performance, and economic satisfaction. The results emphasize the value of latent psychometric modeling for identifying stress mechanisms and developing targeted interventions aimed at improving the academic climate and supporting students’ mental health. |
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68/2025 - 13/11/2025
Leimer Saglio, C. B.; Corti, M.; Pagani, S.; Antonietti, P. F.
A novel mathematical and computational framework of amyloid-beta triggered seizure dynamics in Alzheimer's disease | Abstract | | The association of epileptic activity and Alzheimer's disease (AD) has been increasingly reported in both clinical and experimental studies, suggesting that amyloid-beta accumulation may directly affect neuronal excitability. Capturing these interactions requires a quantitative description that bridges the molecular alterations of AD with the fast electrophysiological dynamics of epilepsy. We introduce a novel mathematical model that extends the Barreto-Cressman ionic formulation by incorporating multiple mechanisms of calcium dysregulation induced by amyloid-beta, including formation of calcium-permeable pores, overactivation of voltage-gated calcium channels, and suppression of calcium-sensitive potassium currents. The resulting ionic model is coupled with the monodomain equation and discretized using a p-adaptive discontinuous Galerkin method on polytopal meshes, providing an effective balance between efficiency and accuracy in capturing the sharp spatiotemporal electrical wavefronts associated with epileptiform discharges. Numerical simulations performed on idealized and realistic brain geometries demonstrate that progressive amyloid-beta accumulation leads to severe alterations in calcium homeostasis, increased neuronal hyperexcitability, and pathological seizure propagation. Specifically, high amyloid-beta concentrations produce secondary epileptogenic sources and spatially heterogeneous wavefronts, indicating that biochemical inhomogeneities play a critical role in shaping seizure dynamics. These results illustrate how multiscale modeling provides new mechanistic insights into the interplay between neurodegeneration and epilepsy in Alzheimer's disease. |
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67/2025 - 10/11/2025
Antonietti, P.F.; Corti, M.; Gómez S.; Perugia, I.
Structure-preserving local discontinuous Galerkin discretization of conformational conversion systems | Abstract | | We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. The model is first reformulated in terms of auxiliary variables involving suitable nonlinear transformations, which allow us to enforce positivity and boundedness at the numerical level. Then, we prove a discrete entropy-stability inequality, which we use to show the existence of discrete solutions, as well as to establish the convergence of the scheme by means of some discrete compactness arguments. As a by-product of the theoretical analysis, we also prove the existence of global weak solutions satisfying the system's physical bounds. Numerical results validate the theoretical results and assess the capabilities of the proposed method in practice. |
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66/2025 - 09/11/2025
Speroni, G.; Mondini, N.; Ferro, N.; Perotto, S.
A topology optimization framework for scaffold design in soilless cultivation | Abstract | | In this work, we customize the microSIMPATY algorithm, combining Solid Isotropic Material with Penalization (SIMP) topology optimization with anisotropic mesh adaptation, within a multi-physics framework to design cellular material scaffolds suitable for soilless cultivation systems.
The design of these novel substrates is driven by optimization criteria that balance mechanical and fluid-dynamic performance, with the aim of effectively supporting plant growth.
The numerical validation results and the in silico root growth simulations carried out in virtual vase-like containers confirm promising potential toward replacing conventional organic and inorganic substrates with an optimized, sustainable, and readily accessible alternative. |
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