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 1249 products
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83/2022 - 11/28/2022
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 - 11/28/2022
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 - 11/28/2022
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 - 11/09/2022
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 - 11/04/2022
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 - 11/04/2022
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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77/2022 - 10/31/2022
Ziarelli, G.; Dede', L.; Parolini, N.; Verani, M.; Quarteroni, A.
Optimized numerical solutions of SIRDVW multiage model controlling SARS-CoV-2 vaccine roll out: an application to the Italian scenario. | Abstract | | In the context of SARS-CoV-2 pandemic, mathematical modelling has played a fundamental role for making forecasts, simulating scenarios and evaluating the impact of preventive political, social and pharmaceutical measures. Optimal control theory can be a useful tool based on solid mathematical bases to plan the vaccination campaign in the direction of eradicating the pandemic as fast as possible. The aim of this work is to explore the optimal prioritisation order for planning vaccination campaigns able to achieve specific goals, as the reduction of the amount of infected, deceased and hospitalized in a fixed time frame, among age classes. For this purpose, we introduce an age stratified SIR-like epidemic compartmental model settled in an abstract framework for modelling two-doses vaccination campaigns and conceived with the description of COVID19 disease. Overall, we formalize an optimal control framework adopting the model as state problem by acting on the administrations of vaccine-doses. An extensive campaign of numerical tests, featured in the Italian scenario and calibrated on available data from Dipartimento di Protezione Civile Italiana, shows that the presented framework can be a valuable tool to support the planning of vaccination campaigns minimizing specific goals. |
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76/2022 - 10/25/2022
Spreafico, M.; Ieva, F.; Fiocco, M.
Longitudinal Latent Overall Toxicity (LOTox) profiles in osteosarcoma: a new taxonomy based on latent Markov models | Abstract | | Due to the presence of multiple types of adverse events with different levels of severity, the analysis of longitudinal toxicity data is a difficult task in cancer studies. In this work, a novel approach based on latent Markov models and compositional data techniques is proposed. The latent status of interest is the Latent Overall Toxicity (LOTox) condition of each patient. The main objectives are to identify different latent states of overall toxicity burden and to investigate the evolution of individual toxicity risk during cancer treatment. This methodology is applied to osteosarcoma treatment data to provide novel techniques that may support medical decisions in childhood cancer therapy. |
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