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 1346 products
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44/2026 - 06/10/2026
Bonetti, S; Botti, M.; Antonietti, P.F.
Splitting strategies for the fully-coupled nonlinear thermo-hydro-mechanical problem | Abstract | | We propose novel semi-decoupled and fully-decoupled iterative algorithms for efficiently solving the fully-coupled nonlinear four-field thermo-poroelastic model discretized in space by discontinuous Galerkin method on polytopal grids. We present the model problem, its four-field formulation, and the arbitrary-order weighted symmetric interior penalty scheme exploited for its spatial discretization. Such a scheme is robust with respect to strong heterogeneities in the model coefficients. Then, we present the two solution strategies and prove that under suitable conditions both schemes are convergent. A wide set of numerical simulations is presented to assess the convergence and robustness properties of the proposed method. Moreover, we test the scheme with literature and physically sound test cases for proof-of-concept applications in the geophysical context. |
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45/2026 - 06/10/2026
Antonietti, P.F.; Botti, M.; Parolini, N.; Pederzoli, V.; Verani, M.
Polytopal Discontinuous Galerkin Discretizations of Coupled Non-Newtonian Stokes-Darcy Systems | Abstract | | We propose and analyze a polytopal discontinuous Galerkin method for the numerical approximation of a coupled non-Newtonian Stokes-Darcy system modeling the interaction between a non-Newtonian free-flow fluid and a non-Newtonian flow through a porous medium. Due to its geometric flexibility and arbitrary-order accuracy, the proposed discretization scheme is well-suited to configurations with complex geometries. We provide a complete a-priori analysis that considers shear-dependent and velocity-dependent non-Newtonian viscosity models for the free-flow and porous media regions, respectively. The well-posedness, stability, and error bounds of the method are established in the framework of generalized inf-sup theory. Error estimates are confirmed by numerical results. |
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43/2026 - 06/06/2026
Micheletti, S.
A validated MATLAB framework for sparse vectorized finite element assembly | Abstract | | We present a compact MATLAB framework for finite element prototyping based on sparse vectorized assembly. The purpose of the code is not to compete with large-scale production finite element libraries, but to expose, in a transparent and reproducible way, the algebraic structure that connects a variational formulation with an efficient implementation in a high-level language. The codebase reorganizes earlier MATLAB prototypes into functions with explicit inputs and outputs, examples, regression tests and validation scripts. The framework covers piecewise linear and quadratic finite elements on triangular meshes, variable-coefficient diffusion–reaction problems with quadrature, a vectorized tetrahedral implementation for the three-dimensional Poisson equation, and a Mini-element discretization of the incompressible Navier–Stokes equations. Numerical experiments illustrate both performance and reproducibility. In particular, the DFG flow-around-a-cylinder benchmark is used to validate the incompressible-flow module and to discuss the different mesh sensitivities of drag, lift and pressure-difference outputs. |
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42/2026 - 06/05/2026
Fumagalli, I.; Campioni, M.; Sirtori, A.; Pagani, S.; Levi, R.; Politi, L. S.; Capo, G.; Antonietti, P. F.
Patient-specific computational mechanics of functional lumbar spine units | Abstract | | In the current clinical practice, the diagnosis of spinal disorders and their surgical planning are critically based on imaging data. To complement this data, patient-specific finite element models have been developed and showed to be powerful tools for evaluating spine mechanics. Most of them rely on Computational Tomography (CT) scans - which have a high resolution but are seldom available in routine clinical practice - while only a recent few models are on less invasive Magnetic Resonance Imaging (MRI). Yet, despite the proliferation of these computational models, encompassing detailed anatomical and functional information, the rheological assumptions they are built upon are based on tissue-sample mechanical response data, which leaves a gap in the quantitative analysis on how such assumptions influence the macroscopic response of a functional spinal unit.
Aiming at addressing these shortcomings, the main purpose of this work is to introduce a quantitative computational assessment of the macroscopic impact of commonly adopted rheological models - from linear elasticity to fiber-reinforced nonlinear hyperelasticity - in several loading conditions, focusing on a lumbar unit which is considered as a typical benchmark system. We also propose a reconstruction procedure to accurately describe subject-specific anatomy from MRI data, including the intervertebral disc and its nucleus pulposus. Bones are modeled as linear elastic media, whereas for the AF, we consider three different mechanical models - namely, isotropic linear elasticity and the Holzapfel-Gasser-Ogden model with and without fiber reinforcement. Model verification on an idealized geometry demonstrates numerical consistency, while parametric orthostatic simulations highlight the need for nonlinear formulations to capture anisotropy and strain-stiffening behavior of the intervertebral disc. Then, we carry out flexion, lateral bending, and torsion tests on a subject-specific reconstructed functional unit, for which we provide parametric analysis in terms of momentum magnitude and resulting range of motion. These tests further confirm the need for a nonlinear rheology of the annulus fibrosus and provide a quantitative assessment of the differences between the constitutive laws considered.
Moreover, successful comparisons with the literature, in terms of macroscopic deformation under several loading conditions, serve as partial validation for our computational model. |
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40/2026 - 05/28/2026
Marchesin, L.; Menafoglio, A.; Secchi, P.
A Convolution Process for Sea Surface Temperature Hot-Spot Identification in the Mediterranean Sea | Abstract | | Sea surface temperature (SST) is a fundamental determinant of global climate dynamics and economic activity. Reliable projections of future SST patterns depend critically on a rigorous characterization of the underlying spatial random field. In this study, we introduce a novel convolution-based covariance framework tailored to geostatistical domains constrained by physical barriers and influenced by vector-driven flows. By discretizing the continuous marine domain into a directed linear network that preserves the orientation of ocean currents, we construct a moving-average stochastic process whose dynamic is encoded via a Markovian transitionprobability matrix on the network’s vertices. The induced covariance structure emerges as a weighted combination of a spatial kernel and flow-dependent weights, giving rise to a complex
estimation problem. To stabilize inference, we propose a penalized estimator that regularizes covariance parameters while enforcing consistency with known hydrodynamic properties. We then embed this covariance model into a Monte Carlo simulation framework to refine RCPbased SST projections and to identify thermal “hot spots” of heightened ecological risk. Our approach delivers a statistically principled framework that prevents physical inconsistencies –
such as correlations across land barriers – providing a robust basis for quantifying uncertainty in future SST forecasts and for guiding targeted environmental assessments. |
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41/2026 - 05/28/2026
Sosta, L.; Ciancarelli, C; Marini, L.; Pagani, S.; Regazzoni, F.; Parolini, N.
Physics-constrained identification of graph-based thermal networks for spacecraft digital twins | Abstract | | Reconstructing a thermal model capable of efficiently simulating the behavior of a spacecraft from sparse and localized temperature measurements remains a challenging task. To address this,
we introduce a physically-constrained calibration framework for Lumped Parameter Thermal Models (LPTMs), formulated as a trajectory-based inverse problem for graph dynamical systems. The model reconstructs thermal dynamics directly from temperature measurements and known inputs, without relying on a priori parameter values derived from material properties or geometric assumptions.
Physical admissibility is enforced at the parameterization level: positivity of nodal coefficients and symmetry of conductive interactions are imposed by construction. This guarantees stable dynamics and restricts the identification problem to a physically meaningful parameter space, improving conditioning without the need of additional regularization.
The identification problem is addressed through trajectory matching, ensuring stable rollout over extended time horizons.
The methodology is validated on synthetic datasets generated from high-fidelity finite element simulations under progressively complex forcing conditions. The calibrated LPTMs accurately reproduce long-term temperature evolution and exhibit robustness to measurement noise.
The proposed framework provides a systematic approach to the calibration of reduced-order thermal models by combining physical structure with data-driven identification. The numerical results show a favorable balance between accuracy and computational efficiency, making the models suitable for integration in spacecraft thermal Digital Twin applications. |
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38/2026 - 05/14/2026
Clemente, A.; Arnone, E.; Mateu, J.; Sangalli, L.M.
Nonparametric estimators over metric graphs | Abstract | | This work discusses a theory of functional spaces over metric graphs, that permits the definition of penalized likelihood methods for data observed over spatial supports that are graphs. Within the considered mathematical framework, we recover classical results in functional analysis, such as a Poincaré-type inequality. This, in turn, enables us to uplift, to the considered setting, the theory of some fundamental penalized likelihood methods. Specifically, we present two important classes of statistical models: nonparametric regression and nonparametric density estimation, here defined for data observed over graphs. We derive theoretical results regarding the well-posedness of the associated estimation problems and the consistency of the estimators. We also demonstrate the performances of the defined estimators with respect to state-of-art alternatives. |
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39/2026 - 05/14/2026
Patanè, G.; Menafoglio, A.; Krauth, A.; Fechner, P.; Dede', L.; Colosimo, B.M.; Nicolussi, F.
K-Models: a Flexible and Interpretable Method for Ordinal Clustering with Application to Antigen-Antibody Interaction Profiles | Abstract | | Existing clustering methods for functional data often prioritize partitioning accuracy over interpretability, making it challenging to extract meaningful insights when the data-generating process follows a specific underlying structure and an ordinal relationship among clusters is suspected. This work introduces K-Models, a novel framework that integrates ordinal constraints and estimates key underlying elements of the random process generating the observed functional profiles, improving both interpretability and structure identification. The proposed method is evaluated through simulations and real-world applications. In particular, it is tested on Region of Interest (ROI) curves, which represent reaction profiles from a reflectometric sensor monitoring biomolecular interactions, such as antigen-antibody binding. These curves represent changes in reflected light intensity over time at multiple measurement spots with immobilized antigens during analyte exposure, capturing the binding dynamics of the system. The goal is to identify intrinsic signal patterns solely from the observed dynamics, making this dataset an ideal benchmark for assessing the added interpretability of the proposed approach. By incorporating structural assumptions into the clustering process, K-Models enhances interpretability while maintaining performance comparable to state-of-the-art techniques, providing a valuable tool for analyzing functional data with an underlying ordinal structure. |
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