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 1287 products
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51/2020 - 07/23/2020
Ferraccioli, F.; Sangalli, L. M.; Arnone, E.,; Finos, L.
A functional data analysis approach to the estimation of densities over complex regions | Abstract | | In this work we propose a nonparametric method for density estimation over two-dimensional domains. Following a functional data analysis approach, we consider a penalized likelihood estimator, with a roughness penalty based on a differential operator. This approach allows for the estimation of densities on any planar domain, including those with complex boundaries or interior holes. We develop an estimation procedure based on fi nite elements. Thanks to the use of this numerical technique, the proposed method has great flexibility and high computational efficiency. |
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50/2020 - 07/23/2020
Bonaventura,L.; Gomez Marmol, M.
The TR-BDF2 method for second order problems in structural mechanics | Abstract | | The application of the TR-BDF2 method to second order problems
typical of structural mechanics and seismic engineering is discussed. A reformulation of this method is presented, that only requires the solution of algebraic systems of size equal to the number of displacement degrees of freedom. A linear analysis and numerical experimentson relevant benchmarks show that the TR-BDF2 method is superiorin terms of accuracy and eciency to the classical Newmark method and to its generalizations. |
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49/2020 - 07/23/2020
Bonaventura,L.; Garres Diaz,J.
Flexible and efficient discretizations of multilayer models with variable density | Abstract | |
We show that the semi-implicit time discretization approaches previously introduced for multilayer shallow water models for the barotropic case can be also applied to the variable density case with Boussinesq approximation. Furthermore, also for the variable density equations, a variable number of layers can be used, so as to achieve greater flexibility and efficiency of the resulting multilayer approach. An analysis of the linearized system is presented, which allows to de- rive linear stability parameters the resulting spatially semi-discretized equations. A number of numerical experiments demonstrate the effectiveness of the proposed approach.
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47/2020 - 07/21/2020
Sangalli, L.M.
A novel approach to the analysis of spatial and functional data over complex domains | Abstract | | Recent years have seen an explosive growth in the recording of increasingly complex and high-dimensional data. Classical statistical methods are often un t to handle such data, whose analysis calls for the definition of new methods merging ideas and approaches from statistics, applied mathematics and engineering. This work in particular focuses on data displaying complex spatial dependencies, where the complexity can for instance be due to the complex physics of the problem or the non-trivial conformation of the domain where the data are observed. |
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48/2020 - 07/21/2020
Clerici, F.; Ferro, N.; Marconi, S.; Micheletti, S.; Negrello, E.; Perotto, S.
Anisotropic adapted meshes for image segmentation: application to 3D medical data | Abstract | | This work focuses on a variational approach to image segmentation based on
the Ambrosio-Tortorelli functional. We propose an efficient algorithm, which combines
the functional minimization with a smart choice of the computational mesh.
With this aim, we resort to an anisotropic mesh adaptation procedure driven by an
a posteriori recovery-based error analysis. We apply the proposed algorithm to a
Computed Tomography dataset of a fractured pelvis, to create a virtual model of
the anatomy. The result is veri fied against a semi-automatic segmentation carried
out using the ITK-SNAP tool. Furthermore, a physical replica of the virtual model
is produced by means of Fused Filament Fabrication technology, to assess the appropriateness
of the proposed solution in terms of resolution-quality balance for 3D
printing production. |
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46/2020 - 07/21/2020
Bucelli, M.; Salvador, M.; Dede', L.; Quarteroni, A.
Multipatch Isogeometric Analysis for Electrophysiology: Simulation in a Human Heart | Abstract | | In the framework of cardiac electrophysiology for the human heart, we apply multipatch NURBS-based Isogeometric Analysis for the space discretization of the Monodomain model. Isogeometric Analysis (IGA) is a technique for the solution of Partial Differential Equations (PDEs) that facilitates encapsulating the exact representation of the computational geometry by using basis functions with high-order continuity. IGA features very small numerical dissipation and dispersion if compared to other methods for the solution of PDEs. The use of multiple patches allows to overcome the conventional limitations of single patch IGA, thanks to the gained flexibility in the design of the computational domain, especially when its representation is quite involved as in bioengineering applications. We propose two algorithms for the preprocessing of CAD models of complex surface and volumetric NURBS geometries with cavities, such as atria and ventricles: our purpose is to obtain geometrically and parametrically conforming NURBS multipatch models starting from CAD models. We employ those algorithms for the construction of an IGA realistic representation of a human heart. We apply IGA for the discretization of the Monodomain equation that describes the evolution in space and time of the cardiac action potential. This PDE is coupled with suitable microscopic models to define the behavior at cellular scale: Courtemanche-Ramirez-Nattel model for the atrial simulation, and Luo-Rudy model for the ventricular one. Numerical simulations on realistic human atria and ventricles geometries are carried out, obtaining accurate and smooth excitation fronts by combining IGA with the multipatch approach for the geometrical representation of the computational domains, either surfaces for the atria or solids for the ventricles. |
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45/2020 - 07/21/2020
Gatti, F.; Menafoglio, A.; Togni, N.; Bonaventura, L.; Brambilla, D.; Papini, M; Longoni, L.
A novel dowscaling procedure for compositional data in the Aitchison geometry with application to soil texture data | Abstract | | In this work, we present a novel downscaling procedure for compositional quantities based on the Aitchison geometry. The method is able to naturally consider compositional constraints, i.e. unit-sum and positivity. We show that the method can be used in a block sequential Gaussian simulation framework in order to assess the variability of downscaled quantities. Finally, to validate the method, we test it first in an idealized scenario and then apply it for the downscaling of digital soil maps on a more realistic case study. The digital soil maps for the realistic case study are obtained from SoilGrids, a system for automated soil mapping based on state-of-the-art spatial predictions methods. |
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44/2020 - 07/21/2020
Masci, C.; Ieva, F.; Paganoni A.M.
EM algorithm for semiparametric multinomial mixed-effects models | Abstract | | This paper proposes an EM algorithm for semiparametric mixed-effects
models dealing with a multinomial response. In multinomial mixed-effects models, in order to obtain the marginal distribution of the response, random effects need to be integrated out. In a full parametric context, where random effects follow a multivariate normal distribution, this is often computationally infeasible. We propose an alternative novel semiparametric approach in which random effects follow a multivariate discrete distribution with an a priori unknown number of support points, that is allowed to differ across categories.
The advantage of this modelling is twofold: the discrete distribution
on random effects allows, first, to express the marginal density as a weighted sum, avoiding numerical problems typical of the integration and, second, to identify a latent structure at the highest level of the hierarchy, where groups are clustered into subpopulations. The paper shows a simulation study to evaluate the method’s performance and applies the proposed algorithm to a real case study for predicting higher education student dropout, comparing the results with the ones of a full parametric method. |
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