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 1239 products
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04/2023 - 01/10/2023
Quarteroni, A.; Dede’, L.; Regazzoni, F.; Vergara, C.
A mathematical model of the human heart suitable to address clinical problems | Abstract | | In this paper, we present a mathematical model capable of simulating
the human cardiac function. We review the basic equations of the
model, their coupling, the numerical approach for the computer solution of this mathematical model, and a few examples of application to specific problems of clinical interest. |
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03/2023 - 01/05/2023
Africa, P.C.; Perotto, S.; de Falco, C.
Scalable Recovery-based Adaptation on Quadtree Meshes for Advection-Diffusion-Reaction Problems | Abstract | | We propose a mesh adaptation procedure for Cartesian quadtree meshes, to discretize scalar advection-diffusion-reaction problems.
The adaptation process is
driven by a recovery-based a posteriori estimator for the L^2-norm of the discretization error, based on suitable higher order approximations of both the solution and the associated gradient. In particular, a metric-based approach exploits the information furnished by the estimator to iteratively predict the new adapted mesh.
The new mesh adaptation algorithm is successfully assessed on different configurations, and turns out to perform well also when dealing with discontinuities in the data as well as in the presence of internal layers not
aligned with the Cartesian directions.
A cross-comparison with a standard
estimate--mark--refine approach and with other adaptive strategies available in the literature shows the remarkable accuracy and parallel scalability
of the proposed approach. |
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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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