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 1251 prodotti
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85/2022 - 28/11/2022
Lurani Cernuschi , A.; Masci, C.; Corso, F.; Muccini, C.; Ceccarelli, D.; San Raffaele Hospital Galli, L.; Ieva, F.; Paganoni, A.M.; Castagna, A.
A neural network approach to survival analysis for modelling time to cardiovascular diseases in HIV patients with longitudinal observations | Abstract | | At the end of 2021, 38.4 million People were Living With HIV (PLWH)
worldwide. The advent of Anti Retroviral Therapy (ART) has significantly reduced the mortality and increased life expectancy of PLWH. Nowadays, the management of people with HIV on virological suppression is partly focused on the onset of comorbidities, such as the occurrence of CardioVascular Diseases (CVDs). In this study, we analyse the 15-year CVD risk in PLWH, following a survival analysis approach based on Neural Networks (NNs). We adopt a NN-based deep learning approach to flexibly model and predict the time to a CVD event, relaxing the linearity
and the proportional-hazard assumptions typical of the COX model and
including time-varying features. Results of this approach are compared
to the ones obtained via more classical survival analysis methods, both
in terms of predictive performance and interpretability, in order to
explore the potential of deep learning approaches in modelling survival
data with time-varying features. |
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84/2022 - 28/11/2022
Ciaramella, G.; Gambarini, M.; Miglio, E.
A preconditioner for free-surface hydrodynamics BEM | Abstract | | A preconditioner for the boundary element method applied to linear hydrodynamics is proposed. In particular, the problem of computing wave loads on large arrays of floating objects using a source-distribution BEM is considered. The preconditioner is based on block-Jacobi iterations combined with a coarse correction. Each vector of the coarse space is constant on the surface of one of the bodies, and zero on the others. An algorithm for the efficient construction of the coarse space using hierarchical matrices is presented. The method is implemented by integration with the hierarchical matrices interface of an existing BEM code. In combination with GMRES, scalability in terms of number of iterations is achieved and demonstrated by extensive numerical experiments. |
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83/2022 - 28/11/2022
Ciaramella, G.; Gander, M.; Mazzieri, I.
Unmapped tent pitching schemes by waveform relaxation | Abstract | | We propose a new unmapped tent pitching (UTP) algorithm that avoids the
mapping in the classical mapped tent pitching (MTP) algorithm using
Schwarz waveform relaxation (SWR) techniques. To derive the UTP, we prove
first an equivalence relation between MTP and the red-black version of SWR. This result suggests
using SWR and redundant computations in space-time cylinders to avoid the mapping process of MTP.
The new UTP computes approximations that are equivalent to the MTP ones,
but its computational cost is lower, since it does not have to compute the tent mappings, and
the volume of the redundant computations is also present in the tents after the mapping to space-time cylinders. |
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82/2022 - 28/11/2022
Ciaramella, G.; Gander, M.; Van Criekingen, S.; Vanzan, T.
A PETSc Parallel Implementation of Substructured One- and Two-level Schwarz Methods | Abstract | | Substructured Schwarz methods are interpretations of volume Schwarz methods as algorithms on interface variables. In this work, we consider the substructured version of the Parallel Schwarz Method (PSM) and a recent extention to a two-level (i.e. coarse-corrected) framework. In particular, we present an implementation of the substructured PSM based on the PETSc (Portable, Extensible Toolkit for Scientific Computation) linear algebra package of one- and two-level methods. |
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81/2022 - 28/11/2022
Bonizzoni, F.; Hauck, M.; Peterseim, D.
A reduced basis super-localized orthogonal decomposition for reaction-convection-diffusion problems | Abstract | | This paper presents a method for the numerical treatment of reaction-convection-diffusion problems with parameter-dependent coefficients that are arbitrary rough and possibly varying at a very fine scale. The presented technique combines the reduced basis (RB) framework with the recently proposed super-localized orthogonal decomposition (SLOD). More specifically, the RB is used for accelerating the typically costly SLOD basis computation, while the SLOD is employed for an efficient compression of the problem's solution operator requiring coarse solves only. The combined advantages of both methods allow one to tackle the challenges arising from parametric heterogeneous
coefficients. Given a value of the parameter vector, the method outputs a corresponding compressed solution operator which can be used to efficiently treat multiple, possibly non-affine, right-hand sides at the same time, requiring only one coarse solve per right-hand side. |
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80/2022 - 09/11/2022
Balduzzi, G.; Bonizzoni, F.; Tamellini, L.
Uncertainty quantification in timber-like beams using sparse grids: theory and examples with off-the-shelf software utilization | Abstract | | When dealing with timber structures, the characteristic strength and stiffness of the material are made highly variable and uncertain by the unavoidable, yet hardly predictable, presence of knots and other defects. In this work we apply the sparse grids stochastic collocation method to perform uncertainty quantification for structural engineering in the scenario
described above. Sparse grids have been developed by the mathematical community in the last decades and their theoretical background has been rigorously and extensively studied. The document proposes a brief practice-oriented introduction with minimal theoretical background, provides detailed instructions for the use of the already implemented Sparse Grid Matlab kit (freely available on-line) and discusses two numerical examples inspired from timber engineering problems that highlight how sparse grids exhibit superior performances compared to the plain Monte Carlo method. The Sparse Grid Matlab kit requires only a few lines of code to be interfaced with any numerical solver for mechanical problems (in this work we used an isogeometric collocation method) and provides outputs that can be easily interpreted and used in the engineering practice. |
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79/2022 - 04/11/2022
Antonietti, P. F.; Farenga, N.; Manuzzi, E.; Martinelli, G.; Saverio, L.
Agglomeration of Polygonal Grids using Graph Neural Networks with applications to Multigrid solvers | Abstract | | Agglomeration-based strategies are important both within adaptive refinement algorithms and to construct scalable multilevel algebraic solvers. In order to automatically perform agglomeration of polygonal grids, we propose the use of Graph Neural Networks (GNNs) to partition the connectivity graph of a computational mesh. GNNs have the advantage to process naturally and simultaneously both the graph structure of mesh and the geometrical information, such as the areas of the elements or their barycentric coordinates. This is not the case with other approaches such as METIS, a standard algorithm for graph partitioning which is meant to process only the graph information, or the k-means clustering algorithm, which can process only the geometrical information. Performance in terms of quality metrics is enhanced for Machine Learning (ML) strategies, with GNNs featuring a lower computational cost online. Such models also show a good degree of generalization when applied to more complex geometries, such as brain MRI scans, and the capability of preserving the quality of the grid. The effectiveness of these strategies is demonstrated also when applied to MultiGrid (MG) solvers in a Polygonal Discontinuous Galerkin (PolyDG) framework. |
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78/2022 - 04/11/2022
Bucelli, M.; Gabriel, M. G.; Gigante, G.; Quarteroni, A.; Vergara, C.
A stable loosely-coupled scheme for cardiac electro-fluid-structure interaction | Abstract | | We present a loosely coupled scheme for the numerical simulation of the cardiac electro-fluid-structure interaction problem, whose solution is typically computationally intensive due to the need to suitably treat the coupling of the different submodels. Our scheme relies on a segregated treatment of the subproblems, in particular on an explicit Robin-Neumann algorithm for the fluid-structure interaction, aiming at reducing the computational burden of numerical simulations. The results, both in an ideal and a realistic cardiac setting, show that the proposed scheme is stable at the regimes typical of cardiac simulations. From a comparison with a scheme with implicit fluid-structure interaction, it emerges that, while conservation properties are not fully preserved, computational times significantly benefit from the explicit scheme. Overall, the explicit discretization represents a good trade-off between accuracy and cost, and is a valuable alternative to implicit schemes for fast large-scale simulations. |
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