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
-
54/2020 - 07/23/2020
Arnone, E.; Bernardi, M. S.; Sangalli, L. M.; Secchi, P.
Analysis of Telecom Italia mobile phone data by space-time regression with differential regularization | Abstract | | We apply spatio-temporal regression with partial differential equation regularization to the Telecom Italia mobile phone data. The technique proposed allows to include specific information on the phenomenon under study through a definition of the non-stationary anisotropy characterizing the spatial regularization based on the texture of the domain on which the data are observed. |
-
53/2020 - 07/23/2020
Arnone, E.; Kneip, A.; Nobile, F.; Sangalli, L. M.
Some numerical test on the convergence rates of regression with differential regularization | Abstract | | We numerically study the bias and the mean square error of the estimator in Spatial Regression with Partial Differential Equation (SR-PDE) regularization.
SR-PDE is a novel smoothing technique for data distributed over two-dimensional domains, which allows to incorporate prior information formalized in term of a partial differential equation. This technique also enables an accurate estimation when the shape of the domain is complex and it strongly influences the phenomenon under study. |
-
52/2020 - 07/23/2020
Arnone, E.; Kneip, A.; Nobile, F.; Sangalli, L. M.
Some first results on the consistency of spatial regression with partial differential equation regularization | Abstract | | We study the consistency of the estimator in spatial regression with partial differential equation (PDE) regularization. This new smoothing technique allows to accurately estimate spatial fields over complex two-dimensional domains, starting from noisy observations; the regularizing term involves a PDE that formalizes problem specific information about the phenomenon at hand. Differently from classical smoothing methods, the solution of the infinite-dimensional estimation
problem cannot be computed analytically. An approximation is obtained via the finite element method, considering a suitable triangulation of the spatial domain. We first consider the consistency of the estimator in the infinite-dimensional setting. We then study the consistency of the finite element estimator, resulting from the approximated PDE. We study the bias and variance of the estimators, with respect to the sample size and to the value of the smoothing parameter. Some final
simulation studies provide numerical evidence of the rates derived for the bias, variance and mean square error. |
-
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. |
-
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. |
-
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.
|
-
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. |
-
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. |
|
