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 1268 prodotti
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56/2020 - 07/08/2020
Botti, L.; Botti, M.; Di Pietro, D. A.;
A Hybrid High-Order method for multiple-network poroelasticity | Abstract | | We develop Hybrid High-Order methods for multiple-network poroelasticity, modelling seepage through deformable fissured porous media. The proposed methods are designed to support general polygonal and polyhedral elements. This is a crucial feature in geological modelling, where the need for general elements arises, e.g., due to the presence of fracture and faults, to the onset of degenerate elements to account for compaction or erosion, or when nonconforming mesh adaptation is performed. We use as a starting point a mixed weak formulation where an additional total pressure variable is added, that ensures the fulfilment of a discrete inf-sup condition. A complete theoretical analysis is performed, and the results are demonstrated on a panel of numerical tests. |
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55/2020 - 07/08/2020
Botti, M.; Castanon Quiroz, D.; Di Pietro, D.A.; Harnist, A.
A Hybrid High-Order method for creeping flows of non-Newtonian fluids | Abstract | | In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of convergence that match those obtained for Leray--Lions scalar problems.
A complete well-posedness and convergence analysis of the method is carried out under new, general assumptions on the strain rate-shear stress law, which encompass several common examples such as the power-law and Carreau--Yasuda models. Numerical examples complete the exposition. |
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54/2020 - 23/07/2020
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. |
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53/2020 - 23/07/2020
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. |
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52/2020 - 23/07/2020
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. |
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51/2020 - 23/07/2020
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 - 23/07/2020
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 - 23/07/2020
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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