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 1242 products
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11/2021 - 03/02/2021
Antonietti,P.F.; Manzini, G.; Mazzieri, I.; Scacchi, S.; Verani, M.
The conforming virtual element method for polyharmonic and elastodynamics problems: a review | Abstract | | In this paper we review recent results on the conforming virtual element approximation of polyharmonic and elastodynamics problems. The structure and the content of this review is motivated by three paradigmatic examples of applications: classical and anisotropic Cahn-Hilliard equation and phase field models for brittle fracture, that are briefly discussed in the first part of the paper. We present and discuss the mathematical details of the conforming virtual element approximation of linear polyharmonic problems, the classical Cahn-Hilliard equation and linear elastodynamics problems. |
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10/2021 - 03/02/2021
Di Michele, F.; May, J.; Pera, D.; Kastelic, V.; Carafa, M.; Smerzini, C.; Mazzieri, I.; Rubino, B.; Antonietti, P.F.; Quarteroni, A.; Aloisio, R.; Marcati, P.
Spectral elements numerical simulation of the 2009 L’Aquila earthquake on a detailed reconstructed domain | Abstract | | In this paper we simulate the earthquake that hit the city of L’Aquila on the 6th of April 2009 using the SPEED code (SPectral Elements in Elastodynamics with Discontinuous Galerkin), an open source library able to simulate the propagation of seismic waves in complex three dimensional (3D) domains. Our model includes an accurate 3D reconstruction of the Quaternary deposits, according to the most up-to-date data obtained from the Microzonation studies in Central Italy and a detailed reconstruction of the topography reported using a newly developed tool [61].
The sensitivity of our results with respect to different kinematic seis- mic sources is investigated. The results obtained are in good agreement with the recordings at all available seismic stations at epicentral dis- tances within 20 km range. Finally, a blind source prediction scenario shows that an acceptable agreement between simulations and recordings can be obtained by simulating stochastic rupture realizations with basic input data. A similar approach can be used to model future and past earthquakes for which little information is generally available, thus allowing an enhancement of the associated risk assessment. |
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09/2021 - 02/13/2021
Riccobelli, D.; Noselli, G.; DeSimone, A.
Rods coiling about a rigid constraint: Helices and perversions | Abstract | | Mechanical instabilities can be exploited to design innovative structures, able to change their shape in the presence of external stimuli. In this work, we derive a mathematical model of an elastic beam subjected to an axial force and constrained to smoothly slide along a rigid support, where the distance between the rod midline and the constraint is fixed and finite.
Using both theoretical and computational techniques, we characterize the bifurcations of such a mechanical system, in which the axial force and the natural curvature of the beam are used as control parameters. We show that, in the presence of a straight support, the rod can deform into shapes exhibiting helices and perversions, namely transition zones connecting together two helices with opposite chirality. The mathematical predictions of the proposed model are also compared with some experiments, showing a good quantitative agreement. In particular, we find that the buckled configurations may exhibit multiple perversions and we propose a possible explanation for this phenomenon based on the energy landscape of the mechanical system. |
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08/2021 - 02/13/2021
Antonietti, P. F.; Manuzzi, E.
Refinement of polygonal grids using Convolutional Neural Networks with applications to polygonal Discontinous Galerkin and Virtual Element methods | Abstract | | We propose new strategies to handle polygonal grids refinement based on Convolutional Neural Networks (CNNs). We show that CNNs can be successfully employed to identify correctly the "shape" of a polygonal element so as to design suitable refinement criteria to be possibly employed within adaptive refinement strategies. We propose two refinement strategies that exploit the use of CNNs to classify elements' shape, at a low computational cost. We test the proposed idea considering two families of finite element methods that support arbitrarily shaped polygonal elements, namely Polygonal Discontinuous Galerkin (PolyDG) methods and Virtual Element Methods (VEMs). We demonstrate that the proposed algorithms can greatly improve the performance of the discretization schemes both in terms of accuracy and quality of the underlying grids. Moreover, since the training phase is performed off-line and is problem independent the overall computational costs are kept low. |
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07/2021 - 02/13/2021
Diquigiovanni, J.; Fontana, M.; Vantini, S.
The Importance of Being a Band: Finite-Sample Exact Distribution-Free Prediction Sets for Functional Data | Abstract | | Functional Data Analysis represents a field of growing interest in statistics. Despite
several studies have been proposed leading to fundamental results, the problem of
obtaining valid and efficient prediction sets has not been thoroughly covered. Indeed,
the great majority of methods currently in the literature rely on strong distributional
assumptions (e.g, Gaussianity), dimension reduction techniques and/or asymptotic
arguments. In this work, we propose a new nonparametric approach in the field of
Conformal Prediction based on a new family of nonconformity measures inducing
conformal predictors able to create closed-form finite-sample valid or exact prediction
sets under very minimal distributional assumptions. In addition, our proposal ensures
that the prediction sets obtained are bands, an essential feature in the functional
setting that allows the visualization and interpretation of such sets. The procedure is also fast, scalable, does not rely on functional dimension reduction techniques and allows the user to select different nonconformity measures depending on the problem at hand always obtaining valid bands. Within this family of measures, we propose also a specific measure leading to prediction bands asymptotically no less efficient than those obtained by not modulating. |
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06/2021 - 01/27/2021
Negrini, G.; Parolini, N.; Verani, M.
A diffuse interface box method for elliptic problems | Abstract | | We introduce a diffuse interface box method (DIBM) for the numerical approximation on complex geometries of elliptic problems with Dirichlet boundary conditions. We derive a priori H1 and L2 error estimates highlighting the role of the mesh discretization parameter and of the diffuse interface width. Finally, we present a numerical result assessing the theoretical findings. |
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05/2021 - 01/25/2021
Antonietti, P.F.; Mazzieri, I.; Migliorini, F.
A discontinuous Galerkin time integration scheme for second order differential equations with applications to seismic wave propagation problems | Abstract | | In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation.
By rewriting the original equation as a system of first order differential equations we introduce the method and show that the resulting discrete formulation is well-posed, stable and retains super-optimal rate of convergence with respect to the discretization parameters, namely the time step and the polynomial approximation degree. A set of two- and three-dimensional numerical experiments confirm the theoretical bounds. Finally, the method is applied to real geophysical applications. |
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04/2021 - 01/25/2021
Orlando, V.; Rea, F.; Savaré, L.; Guarino, I; Mucherino, S.; Perrella, A.; Trama, U.; Coscioni, E.; Menditto, E.; Corrao, G.
Development and validation of a clinical risk score to predict the risk of SARS-CoV-2 infection from administrative data: A population-based cohort study from Italy | Abstract | | Background
The novel coronavirus (SARS-CoV-2) pandemic spread rapidly worldwide increasing exponentially in Italy. To date, there is lack of studies describing clinical characteristics of the people at high risk of infection. Hence, we aimed (i) to identify clinical predictors of SARSCoV-2 infection risk, (ii) to develop and validate a score predicting SARS-CoV-2 infection risk, and (iii) to compare it with unspecific scores.
Methods
Retrospective case-control study using administrative health-related database was carried
out in Southern Italy (Campania region) among beneficiaries of Regional Health Service aged over than 30 years. For each person with SARS-CoV-2 confirmed infection (case), up to five controls were randomly matched for gender, age and municipality of residence. Odds ratios and 90% confidence intervals for associations between candidate predictors and risk of infection were estimated by means of conditional logistic regression. SARS-CoV-2 Infection Score (SIS) was developed by generating a total aggregate score obtained from assignment of a weight at each selected covariate using coefficients estimated from the model. Finally, the score was categorized by assigning increasing values from 1 to 4. Discriminant power was used to compare SIS performance with that of other comorbidity scores.
Results
Subjects suffering from diabetes, anaemias, Parkinson’s disease, mental disorders, cardiovascular and inflammatory bowel and kidney diseases showed increased risk of SARSCoV-2 infection. Similar estimates were recorded for men and women and younger and older than 65 years. Fifteen conditions significantly contributed to the SIS. As SIS value increases, risk progressively increases, being odds of SARS-CoV-2 infection among people with the highest SIS value (SIS = 4) 1.74 times higher than those unaffected by any SIS contributing conditions (SIS = 1).
Conclusion
Conditions and diseases making people more vulnerable to SARS-CoV-2 infection were identified by the current study. Our results support decision-makers in identifying high-risk people and adopting of preventive measures to minimize the spread of further epidemic waves.
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