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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33/2022 - 05/11/2022
Africa, P.C.; Salvador, M.; Gervasio, P.; Dede', L.; Quarteroni, A.
A matrix-free high-order solver for the numerical solution of cardiac electrophysiology | Abstract | | We propose a matrix-free solver for the numerical solution of the cardiac electrophysiology model consisting of the monodomain nonlinear reaction-diffusion equation coupled with a system of ordinary differential equations for the ionic species. Our numerical approximation is based on the high-order Spectral Element Method (SEM) to achieve accurate numerical discretization while employing a much smaller number of Degrees of Freedom than first-order Finite Elements. We combine sum-factorization with vectorization, thus allowing for a very efficient use of high-order polynomials in a high performance computing framework. We validate the effectiveness of our matrix-free solver in a variety of applications and perform different electrophysiological simulations ranging from a simple slab of cardiac tissue to a realistic four-chamber heart geometry. We compare SEM to SEM with Numerical Integration (SEM-NI), showing that they provide comparable results in terms of accuracy and efficiency. In both cases, increasing the local polynomial degree p leads to better numerical results and smaller computational times than reducing the mesh size h. We also implement a matrix-free Geometric Multigrid preconditioner that entails better performance in terms of linear solver iterations than state-of-the-art matrix-based Algebraic Multigrid preconditioners. As a matter of fact, the matrix-free solver here proposed yields up to 50× speed-up with respect to a conventional matrix-based solver. |
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32/2022 - 05/09/2022
Barbi, C.; Menafoglio, A; Secchi, P.
An object-oriented approach to the analysis of spatial complex data over stream-network domains | Abstract | | We address the problem of spatial prediction for Hilbert data, when their spatial domain of observation is a river network. The reticular nature of the domain requires to use geostatistical methods based on the concept of Stream Distance, which captures the spatial connectivity of the points in the river induced by the network branching. Within the framework of Object Oriented Spatial Statistics (O2S2), where the data are considered as points of an appropriate (functional) embedding space, we develop a class of functional moving average models based on the Stream Distance. Both the geometry of the data and that of the spatial domain are thus taken into account. A consistent definition of covariance structure is developed, and associated estimators are studied. Through the analysis of the summer water temperature profiles in the Middle Fork River (Idaho, USA), our methodology proved to be effective, both in terms of covariance structure characterization and forecasting performance. |
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31/2022 - 05/09/2022
Bortolotti, T; Peli, R.; Lanzano, G; Sgobba, S.; Menafoglio, A
Weighted functional data analysis for the calibration of ground motion models in Italy | Abstract | | Motivated by the crucial implications of Ground Motion Models (GMM) in terms of seismic hazard analysis and civil protection planning, this work extends a scalar ground motion model for Italy to the framework of Functional Data Analysis. The inherent characteristic of seismic data to be incomplete over the observation domain entails embedding the analysis in the context of partially observed functional data. This work proposes a novel methodology that combines pre-existing techniques of data reconstruction with the definition of observation-specific functional weights, which enter the estimation process to reduce the impact that the reconstructed parts of the curves have on the final estimates. The classical methods of smoothing and concurrent functional regression are extended to include weights. The advantages of the proposed methodology are assessed on synthetic data. Eventually, the weighted functional analysis performed on seismological data is shown to provide a natural smoothing and stabilization of the spectral estimates of the GMM. |
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30/2022 - 05/09/2022
Bonetti S.; Botti M.; Antonietti P.F.
Discontinuous Galerkin approximation of the fully-coupled thermo-poroelastic problem | Abstract | | We present and analyze a discontinuous Galerkin method for the numerical modelling of the fully-coupled quasi-static thermo-poroelastic problem. In particular, for the space discretization we introduce a discontinuous Galerkin method over polygonal and polyhedral grids and we present the stability analysis via two different approaches: first exploiting the Poincarè's inequality and second using the generalized inf-sup condition. Error estimates are derived for the resulting semi-discrete formulation in a suitable mesh dependent energy norm. Numerical simulations are presented in order to validate the theoretical analysis and to show the application of the model to a realistic case test. |
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29/2022 - 05/03/2022
Fumagalli, I.; Polidori, R.; Renzi, F.; Fusini, L.; Quarteroni, A.; Pontone, G.; Vergara, C.
Fluid-structure interaction analysis of transcatheter aortic valve implantation | Abstract | | Transcatheter aortic valve implantation (TAVI) is a minimally invasive intervention for the treatment of severe aortic valve stenosis. The main cause of failure is the structural deterioration of the implanted prosthetic leaflets, possibly inducing a valvular re-stenosis 5-10 years after the implantation. Based solely on pre-implantation data, the aim of this work is to identify fluid-dynamics and structural indices that may predict the possible valvular deterioration, in order to assist the clinicians in the decision-making phase and in the intervention design. Patient-specific, preimplantation geometries of the aortic root, the ascending aorta, and the native valvular calcifications were reconstructed from computed tomography images. The
stent of the prosthesis was modeled as a hollow cylinder and virtually implanted in the reconstructed domain. The fluid-structure interaction between the blood flow, the stent, and the residual native tissue surrounding the prosthesis was simulated by a computational solver with suitable boundary conditions. Hemodynamical and structural indicators were analyzed for five different patients that underwent TAVI – three
with prosthetic valve degeneration and two without degeneration – and the comparison of the results showed a correlation between the leaflets' structural degeneration and the wall shear stress distribution on the proximal aortic wall. This investigation represents a first step towards computational predictive analysis of TAVI degeneration, based on pre-implantation data and without requiring additional peri-operative or follow-up information. Indeed, being able to identify patients more likely to experience degeneration after TAVI may help to schedule a patient-specific timing of follow-up. |
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28/2022 - 05/01/2022
Ciarletta, P.; Pozzi, G.; Riccobelli, D.
The Föppl–von Kármán equations of elastic plates with initial stress | Abstract | | Initially stressed plates are widely used in modern fabrication techniques, such as additive manufacturing and UV lithography, for their tunable morphology by application of external stimuli. In this work, we propose a formal asymptotic derivation of the Föppl–von Kármán equations for an elastic plate with initial stresses, using the constitutive theory of nonlinear elastic solids with initial stresses under the assumptions of incompressibility and material isotropy. Compared to existing works, our approach allows to determine the morphological transitions of the elastic plate without prescribing the underlying target metric of the unstressed state of the elastic body.
We explicitly solve the derived FvK equations in some physical problems of engineering interest, discussing how the initial stress distribution drives the emergence of spontaneous curvatures within the deformed plate. The proposed mathematical framework can be used to tailor shape on demand, with applications in several engineering fields ranging from soft robotics to 4D printing. |
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27/2022 - 04/27/2022
Lazzari J., Asnaghi R., Clementi L., Santambrogio M. D.
Math Skills: a New Look from Functional Data Analysis | Abstract | | Mental calculations involve various areas of the brain. The frontal, parietal and temporal lobes of the left hemisphere have a principal role in the completion of this typology of tasks. Their level of activation varies based on the mathematical competence and attentiveness of the subject under examination and the perceived difficulty of the task. Recent literature often investigates patterns of cerebral activity through fMRI, which is an expensive technique. In this scenario, EEGs represent a more straightforward and cheaper way to collect information regarding brain activity. In this work, we propose an EEG based method to detect differences in the cerebral activation level of people characterized by different abilities in carrying out the same arithmetical task. Our approach consists in the extraction of the activation level of a given region starting from the EEG acquired during resting state and during the completion of a subtraction task. We then analyze these data through Functional Data Analysis, a statistical technique that allows operating on biomedical signals as if they were functions. The application of this technique allowed for the detection of distinct cerebral patterns among the two groups and, more specifically, highlighted the presence of higher levels of activation in the parietal lobe in the population characterized by a lower performance. |
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26/2022 - 04/27/2022
Orlando, G.
A filtering monotonization approach for DG discretizations of hyperbolic problems | Abstract | | We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious oscillations that arise in presence of discontinuities when high order spatial discretizations are employed. This goal is achieved using a filter function that keeps the high order scheme when the solution is regular and switches to a monotone low order approximation if it is not. The method has been implemented in the framework of the deal.II numerical library, whose mesh adaptation capabilities are also used to reduce the region in which the low order approximation is used. A number of numerical experiments demonstrate the potential of the proposed filtering technique. |
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