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 1287 prodotti
-
39/2021 - 15/06/2021
Barnafi, N.; Di Gregorio, S.; Dede', L.; Zunino, P.; Vergara, C.; Quarteroni, A.
A multiscale poromechanics model integratingmyocardial perfusion and systemic circulation | Abstract | | The importance of myocardial perfusion at the outset of cardiac disease remains largely understudied. To address this topic we present a mathematical model that considers the systemic circulation, the coronary vessels, the myocardium, and the interactions among these components. The core of the whole model is the description of the myocardium as a multi-compartment poromechanics system. A novel decomposition of the poroelastic Helmholtz potential involved in the poromechanics model allows for a quasi-incompressible model that adequately describes the physical interaction among all components in the porous medium. We further provide a rigorous mathematical analysis that gives guidelines for the choice of the Helmholtz potential.
To reduce the computational cost of our integrated model we propose decoupling the deformation of the tissue and systemic circulation from the porous flow in the myocardium and coronary vessels, which allows us to apply the model also in combination with pre-computed cardiac displacements, obtained form other models or medical imaging data.
We test the methodology through the simulation of a heartbeat in healthy conditions that replicates the systolic impediment phenomenon,
which is particularly challenging to capture as it arises from the interaction of several parts of the model. |
-
40/2021 - 15/06/2021
Martinolli, M.; Cornat, F.; Vergara, C.
Computational Fluid-Structure Interaction Study of a new Wave Membrane Blood Pump | Abstract | | Purpose: Wave Membrane Blood Pumps (WMBP) are novel pump designs in which blood is propelled by means of wave propagation by an undulating membrane. In this paper, we computationally studied the performance of a new WMBP design (J-shaped) for different working conditions, in view of potential applications in human patients.
Methods: Fluid-Structure Interaction (FSI) simulations were conducted in 3D pump geometries and numerically discretized by means of the Extended Finite Element Method (XFEM). A contact model was introduced to capture membrane-wall collisions in the pump head. Mean flow rate and membrane envelope were determined to evaluate hydraulic performance. A preliminary hemocompatibility analysis was performed via calculation of fluid shear stress.
Results: Numerical results, validated against in-vitro experimental data, showed that the hydraulic output increases when either the frequency or the amplitude of membrane oscillations were higher, with limited increase in the fluid stresses, suggesting good hemocompatility properties.
Also, we showed better performance in terms of hydraulic power with respect to a previous design of the pump. We finally studied an operating point which achieves physiologic flow rate target at diastolic head pressure of $80$ mmHg.
Conclusions: A new design of WMBP was computationally studied.
The proposed FSI model with contact was employed to predict the new pump hydraulic performance and it could help to properly select an operating point for the upcoming first-in-human trials. |
-
37/2021 - 11/06/2021
Dassi, F.; Fumagalli, A.; Mazzieri, I.; Scotti, A.; Vacca, G.
A Virtual Element Method for the wave equation on curved edges in two dimensions | Abstract | | In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as well as internal interfaces corresponding to the change of some mechanical parameters. As opposite to the classic and isoparametric Finite Element approaches, where the geometry of the domain is approximated respectively by piecewise straight lines and by higher order polynomial maps, in the proposed method the geometry is exactly represented, thus ensuring a highly accurate numerical solution. Indeed, if in the former approach the geometrical error might deteriorate the quality of the numerical solution, in the latter approach the curved interfaces/boundaries are approximated exactly guaranteeing the expected order of convergence for the numerical scheme. Theoretical results and numerical findings confirm the validity of the proposed approach. |
-
36/2021 - 11/06/2021
Parolini, N.; Dede', L; Antonietti, P. F.; Ardenghi, G.; Manzoni, A.; Miglio, E.; Pugliese, A.; Verani, M.; Quarteroni, A.
SUIHTER: A new mathematical model for COVID-19. Application to the analysis of the second epidemic outbreak in Italy | Abstract | | The COVID-19 epidemic is the last of a long list of pandemics that have affected humankind in the last century. In this paper, we propose a novel mathematical epidemiological model named SUIHTER from the names of the seven compartments that it comprises: susceptible uninfected individuals (S), undetected (both asymptomatic and symptomatic) infected (U), isolated infected (I), hospitalized (H), threatened (T), extinct (E), and recovered (R). A suitable parameter calibration that is based on the combined use of least squares method and Markov Chain Monte Carlo (MCMC) method is proposed with the aim of reproducing the past history of the epidemic in Italy, surfaced in late February and still ongoing to date, and of validating SUIHTER in terms of its predicting capabilities. A distinctive feature of the new model is that it allows a one-to-one calibration strategy between the model compartments and the data that are daily made available from the Italian Civil Protection. The new model is then applied to the analysis of the Italian epidemic with emphasis on the second outbreak emerged in Fall 2020. In particular, we show that the epidemiological model SUIHTER can be suitably used in a predictive manner to perform scenario analysis at national level. |
-
38/2021 - 11/06/2021
Giusteri, G. G.; Miglio, E.; Parolini, N.; Penati, M.; Zambetti, R.
Simulation of viscoelastic Cosserat rods based on the geometrically exact dynamics of special Euclidean strands | Abstract | | We propose a method for the description and simulation of the nonlinear dynamics of slender structures modeled as Cosserat rods. It is based on interpreting the strains and the generalized velocities of the cross sections as basic variables and elements of the special Euclidean algebra. This perspective emerges naturally from the evolution equations for strands, that are one-dimensional submanifolds, of the special Euclidean group. The discretization of the corresponding equations for the three-dimensional motion of a Cosserat rod is performed, in space, by using a staggered grid. The time evolution is then approximated with a semi-implicit method. Within this approach we can easily include dissipative effects due to both the action of external forces and the presence of internal mechanical dissipation. The comparison with results obtained with different schemes shows the effectiveness of the proposed method, which is able to provide very good predictions of nonlinear dynamical effects and shows competitive computation times also as an energy-minimizing method to treat static problems. |
-
35/2021 - 04/06/2021
Regazzoni, F.; Quarteroni, A.
Accelerating the convergence to a limit cycle in 3D cardiac electromechanical simulations through a data-driven 0D emulator | Abstract | | The results of numerical simulations of 3D cardiac electromechanical models are typically characterized by a long transient before reaching a periodic solution known as limit cycle. Since the only clinically relevant output is the one associated with such limit cycle, a long transient translates into a serious computational overhead. To accelerate the convergence to the limit cycle, we propose a strategy based on a surrogate model, wherein the computationally demanding 3D components are replaced by a 0D emulator. This emulator is built through an automated data-driven algorithm on the basis of pressure-volume transients of as few as three heartbeats simulated through the 3D model. The 0D emulator, consisting of a time-dependent pressure-volume relationship, allows to accurately detect the location of the limit cycle in less than one minute on a standard laptop. Then, using as an initial guess for the 3D model the solution obtained with its 0D surrogate, it is possible to reach in just two heartbeats a solution that is as close to the limit cycle as the one obtained after more than 20 heartbeats with the full-order 3D model. In this manner, the proposed approach achieves an overall speedup in the simulation of about an order of magnitude.
In practical applications, an electromechanical model needs to be coupled with a model for the external circulation. The latter is typically represented by either a Windkessel-type preload-afterload model, emulating the boundary conditions, or by a closed-loop model of the entire circulatory network. The closed-loop model provides higher quality results in terms of physiological soundness; however, reaching a limit cycle is more challenging in this setting. It is in this context that our 0D emulator turns out to be particularly effective.
The 0D emulator is also recommended in many-query settings (e.g. when performing sensitivity analysis, parameter estimation and uncertainty quantification), that call for the repeated solution of the model for different values of the parameters. As a matter of fact, the emulator does not depend on the circulation model to which it is coupled, hence its construction does not have to be repeated when the parameters of the circulation model vary. Finally, should the parameters of the 3D electromechanical model vary as well, we propose a parametric emulator, obtained by interpolation of emulators constructed for given values of the parameters. In all these cases, our numerical results show that the emulator is able to provide the 3D model with an initial guess such that, after only two heartbeats, the solution is very close to the limit cycle. This paper is accompanied by a Python library implementing the proposed algorithm, open to the integration with existing cardiac solvers. |
-
34/2021 - 04/06/2021
Bonaventura, L.; Gatti F.; Menafoglio A.; Rossi D.; Brambilla D.; Papini M.; Longoni L.
An efficient and robust soil erosion model at the basin scale | Abstract | | We present a numerical model of soil erosion at the basin scale that allows one to describe surface run-off without a priori identifying drainage zones, river beds and other water bodies. The model is based on robust and unconditionally stable numerical techniques and guarantees
mass conservation and positivity of the surface and subsurface water layers. Furthermore, the method is equipped with a geostatistical preprocessor that can perform downscaling of data retrieved from digital databases at coarser resolutions and integrate them with
field measurements. Numerical experiments on both idealized and realistic configurations demonstrate the
effectiveness of the proposed method in reproducing transient high resolution features at a reduced computational cost and to reproduce correctly the main hydrographic features of the considered catchment. Furthermore, probabilistic forecasts can
be carried out, also with limited computational effort, based on soil data automatically generated by the geostatistical preprocessor. Even though the model results are still far from full quantitative agreement with the available data, robust estimates of water levels, discharge and of the order of magnitude of the total sediment yield were achieved in two validation experiments on realistic benchmarks. |
-
33/2021 - 02/06/2021
Lupo Pasini, M.; Gabbi, V.; Yin, J.; Perotto, S.; Laanait, N.
Scalable balanced training of conditional generative adversarial neural networks on image data | Abstract | | We propose a distributed approach to train deep convolutional generative adversarial neural network (DC-CGANs) models. Our method reduces the imbalance between generator and discriminator by partitioning the training data according to data labels, and enhances scalability by performing a parallel training where multiple generators are concurrently trained, each one of them focusing on a single data label. Performance is assessed in terms of inception score and image quality on MNIST, CIFAR10, CIFAR100, and ImageNet1k datasets, showing a significant improvement in comparison to state-of-the-art techniques to training DC-CGANs.
Weak scaling is attained on all the four datasets using up to 1,000 processes and 2,000 NVIDIA V100 GPUs on the OLCF supercomputer Summit. |
|
