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 1253 products
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02/2023 - 01/05/2023
Boon, W. M.; Fumagalli, A.; Scotti, A.
Mixed and multipoint finite element methods for rotation-based poroelasticity | Abstract | | This work proposes a mixed finite element method for the Biot poroelasticity equations that employs the lowest-order Raviart-Thomas finite element space for the solid displacement and piecewise constants for the fluid pressure. The method is based on the formulation of linearized elasticity as a weighted vector Laplace problem. By introducing the solid rotation and fluid flux as auxiliary variables, we form a four-field formulation of the Biot system, which is discretized using conforming mixed finite element spaces. The auxiliary variables are subsequently removed from the system in a local hybridization technique to obtain a multipoint rotation-flux mixed finite element method. Stability and convergence of the four-field and multipoint mixed finite element methods are shown in terms of weighted norms, which additionally leads to parameter-robust preconditioners. Numerical experiments confirm the theoretical results. |
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01/2023 - 01/05/2023
Zingaro, A.; Bucelli, M.; Piersanti, R.; Regazzoni, F.; Dede', L.; Quarteroni, A.
An electromechanics-driven fluid dynamics model for the simulation of the whole human heart | Abstract | | We introduce a multiphysics and geometric multiscale computational model, suitable to describe the hemodynamics of the whole human heart, driven by a four-chamber electromechanical model. We first present a study on the calibration of the biophysically detailed RDQ20 activation model (Regazzoni et al., 2020) that is able to reproduce the physiological range of hemodynamic biomarkers. Then, we demonstrate that the ability of the force generation model to reproduce certain microscale mechanisms, such as the dependence of force on fiber shortening velocity, is crucial to capture the overall physiological mechanical and fluid dynamics macroscale behavior. This motivates the need for using multiscale models with high biophysical fidelity, even when the outputs of interest are relative to the macroscale. We show that the use of a high-fidelity electromechanical model, combined with a detailed calibration process, allows us to achieve a remarkable biophysical fidelity in terms of both mechanical and hemodynamic quantities. Indeed, our electromechanical-driven CFD simulations -- carried out on an anatomically accurate geometry of the whole heart -- provide results that match the cardiac physiology both qualitatively (in terms of flow patterns) and quantitatively (when comparing in silico results with biomarkers acquired in vivo). Moreover, we consider the pathological case of left bundle branch block, and we investigate the consequences that an electrical abnormality has on cardiac hemodynamics thanks to our multiphysics integrated model. The computational model that we propose can faithfully predict a delay and an increasing wall shear stress in the left ventricle in the pathological condition. The interaction of different physical processes in an integrated framework allows us to faithfully describe and model this pathology, by capturing and reproducing the intrinsic multiphysics nature of the human heart. |
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85/2022 - 11/28/2022
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 - 11/28/2022
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 - 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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