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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54/2026 - 23/06/2026
Antonietti, P. F.; Corti, M.; Leimer Saglio, C. B.; Pagani, S.
The lymph 2.0 library: p-adaptive algorithms and parallel assembly strategies for polytopal DG methods | Abstract | | This work presents a new release of the lymph 2.0 library cite{antonietti_lymph_2025}, an open-source MATLAB framework for high-order discontinuous Galerkin discretizations on general polytopal meshes. The lymph 2.0 version is extended to support discretizations with element-wise polynomial approximation degrees, which allows the design of p-adaptive strategies based on a posteriori error indicators. In addition, the library introduces a unified assembly framework that abstracts the construction of discrete operators from the underlying physical model, improving code modularity, parallelism, maintainability, and extensibility. Moreover, the proposed approach enables shared-memory parallelism through dedicated parallel tools. Several numerical examples demonstrate the effectiveness of the proposed developments in reducing the computational cost while preserving approximation accuracy. |
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53/2026 - 23/06/2026
Dong Z., Jiang Y., Ng M., Ciaramella G., Yin J.
Chebyshev-Filtered Randomized Low-rank Preconditioners for Symmetric Positive Definite Linear Systems | Abstract | | Preconditioning is essential for accelerating Krylov methods for large symmet- ric positive definite (SPD) linear systems, especially when a small number of extremal eigenvalues deteriorate the convergence of preconditioned conjugate gradient (PCG) method. In this work, we propose a Chebyshev-filtered randomized low-rank preconditioning framework for SPD systems that targets spectral outliers at both ends of the spectrum of the coefficient matrices. The main idea is to use Chebyshev polynomial filtering to make the near-null eigenspace accessible to randomized subspace extraction. The filter amplifies the lower-tail eigencomponents that often govern PCG convergence, while randomized sketching recovers the amplified subspace using only a small number of matrix-matrix products. The resulting low-rank correction therefore targets small-eigenvalue components that are usually missed by standard randomized subspace extraction methods. The resulting preconditioner is algebraic and admits an efficient low-rank representation. We provide subspace error bounds for the filtered randomized extraction and derive condition-number estimates for the proposed preconditioning tech- niques. Numerical experiments demonstrate that the proposed method improves PCG convergence, especially when small eigenvalues are the main obstruction.
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52/2026 - 23/06/2026
Bonazzoli M.; Ciaramella G.; Mazzieri I.
On the Unmapped Tent Pitching for the Heterogeneous Wave Equation | Abstract | | The Unmapped Tent Pitching (UTP) algorithm is a space–time domain decomposition method for the parallel solution of hyperbolic problems. It was originally introduced for the homogeneous one-dimensional wave equation in [Ciaramella, Gander, Mazzieri, 2024]. UTP is inspired by the Mapped Tent Pitching (MTP) algorithm [Gopalakrishnan, Schöberl, Wintersteiger, 2017], which constructs the solution by iteratively building polytopal space–time subdomains, referred to as tents. In MTP, each physical tent is mapped onto a space–time rectangle, where local problems are solved before being mapped back to the original domain.
In contrast, UTP avoids the nonlinear and potentially singular mapping step by computing the solution directly on a physical space–time rectangle that contains the tent, at the expense of redundant computations in the region outside the tent. In this work, we investigate several strategies to extend UTP to heterogeneous media, where the wave propagation speed is piecewise constant over two subregions of the domain. Among the considered approaches, the most efficient in terms of computational time is the one employing space–time subdomains with identical spatial and temporal dimensions in both regions, determined by the maximum propagation speed. |
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51/2026 - 23/06/2026
Bellezza P.; Ciaramella G.; Macchini C.; Mazzieri I.; Verani M.
ParaFlow: Parareal Acceleration of Gradient-Flow Minimization | Abstract | | This work presents the ParaFlow class of optimization algorithms and its specific realization, the ParaFlowS algorithm. The ParaFlow framework employs the Parareal algorithm to enhance the convergence rate of gradient flows towards a minimum. The ParaFlowS method integrates the Parareal approach with (potentially stochastic) gradient descent (GD) method, resulting in a purely sequential optimization strategy. The proposed acceleration framework is assessed through extensive numerical experiments on unconstrained optimization problems associated with the training of fully connected neural networks. |
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50/2026 - 19/06/2026
Donnarumma, A.; Guagliardi, O.; Di Stazio F.; Mazza E.; Tanelli M.; Paganoni A.M.
Modelling Well-Being and Psychological Risk in Doctoral Education: An Integrated Latent Trait Approach | Abstract | | Doctoral education is increasingly recognized as a context in which psychological distress may emerge, shaped by
academic demands, institutional environments and interpersonal dynamics. However, evidence on how these latent
dimensions jointly configure doctoral well-being remains limited. This study investigates psychophysical well-being,
psychological risk indicators and perceived discrimination among PhD candidates at a large public Italian university,
using data from an anonymous voluntary questionnaire administered to doctoral researchers on well-being, academic
stress, institutional conditions, social support and doctoral experience.
Latent constructs of psychological well-being were extracted using Item Response Theory models: among the tested
specifications, the Four-Parameter Nested Logistic Regression Model (4PLnRM) provided the best empirical fit,
capturing heterogeneity in item response patterns and improving representation of the latent trait structure. Results
show that doctoral well-being is primarily driven by personal resources and perceived institutional quality, whereas
social support has a comparatively limited association, challenging conventional assumptions regarding the protective
role of peer networks in doctoral contexts.
With respect to perceived discrimination, a clear asymmetry emerges between vertical and horizontal dynamics.
Supervisor-related (“hierarchical”) discrimination is strongly associated with higher stress and poorer psychological
outcomes, particularly among women and candidates considering program withdrawal, while peer-related
(“horizontal”) discrimination shows weak associations. Overall, findings indicate that doctoral mental health is more
strongly associated with supervisory and institutional conditions than with informal support networks, suggesting that
improving doctoral well-being may require structural interventions targeting supervisory relationships and
institutional governance rather than relying exclusively on individual coping resources. |
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49/2026 - 17/06/2026
Bortolotti, T.; Troilo, R.; Casu, F.; Vantini, S.; Menafoglio, A.
Regularized covariance estimation from partially observed interferometric data | Abstract | | The Small BAseline Subset technique provides remote measurements of ground displacement with high spatial resolution, making it a key tool for monitoring geophysical processes in hazard-prone areas. An effective analysis of this type of data requires reliable estimation of their second-order structure, which is difficult to achieve because the measurements are systematically missing over relatively large portions of the investigated areas. We tackle the problem from a functional data analysis perspective and treat the observations as partially observed functional data with two-dimensional domain. To properly characterize the data, we introduce the fragmented regime of partial observation, where parts of the curves are systematically missing across replicates. For this regime, we propose a novel method for covariance estimation, formulating the task as a matrix completion problem with Laplacian regularization. The estimator is nonparametric and free of stationarity or isotropy assumptions. Extensive simulations show that our method achieves consistently low estimation error across a range of covariance structures. Application to ground displacement data relative to the Phlegraean Fields demonstrates its ability to recover meaningful spatial dependence patterns, highlighting its potential for environmental risk assessment and monitoring. |
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48/2026 - 14/06/2026
Antonietti, P.F.; Corti, M.; Orlando, G.
Optimized high-order IMEX-RK schemes for degenerate diffusion-reaction problems with application to travelling waves phenomena | Abstract | | We study a class of IMplicit-EXplicit Runge--Kutta (IMEX-RK) schemes for the numerical approximation of reaction and diffusion-reaction problems arising in a variety of biological and physical applications. Such models may admit travelling wave solutions, with the Fisher--Kolmogorov equation representing a prototypical example. Motivated by this feature, the proposed time integration schemes are designed to accurately capture sharp propagating fronts. We also investigate a less standard use of IMEX-RK methods that circumvents a splitting of reaction terms into linear and nonlinear components, while still requiring the solution of linear systems at each stage. This semi-implicit formulation, referred to as SI-IMEX-RK, enables a targeted treatment of stiffness by isolating its relevant contributions. The time discretization is coupled with a high-order polygonal discontinuous Galerkin method for space discretization, resulting in a flexible and robust framework for the treatment of multiscale dynamics in complex geometries. A comprehensive validation strategy is presented to assess the accuracy and stability properties of the proposed schemes across a hierarchy of increasingly challenging test problems. |
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46/2026 - 12/06/2026
Cancrini, A.; Ciaramella, G.; Antonietti, P.F.
A Scalable Deflated Conjugate Gradient Solver for the Time-Dependent Pseudo-Stress Stokes Problem | Abstract | | We propose a novel iterative solution framework for the unsteady Stokes equations in the pseudo-stress formulation. When solving this class of problems by using implicit time-integration schemes, standard solvers suffer from deteriorating convergence properties for small time steps, independently of the chosen space discretisation method. This is due to the singular modes of the dev-dev operator. For this reason, we introduce a computational framework obtained by combining a deflated Conjugate Gradient method with a W-cycle multigrid scheme that employs a Restricted Additive Schwarz smoother. The key point is to choose the deflation subspace so that the inner system to be solved within a deflated Conjugate Gradient scheme corresponds to a Laplace problem defined on the singular modes of the original dev-dev operator. This results to be independent of the spatial discretisation method and allows one to use efficient multigrid iterative solvers. Numerical experiments show that the proposed strategy significantly accelerates the Conjugate Gradient convergence and provides stable performance with respect to the time step, confirming its robustness for solving linear systems in the pseudo-stress framework. |
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