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 1349 prodotti
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01/2020 - 05/01/2020
Pozzi, S.; Vergara, C.
Mathematical and numerical models of atherosclerotic plaque progression in carotid arteries | Abstract | | We propose a mathematical model for the description of plaque progression in carotid arteries.
This is based on the coupling of a fluid-structure interaction problem, arising between blood and vessel wall,
and differential problems for the cellular evolution. A numerical model is also proposed. This is based on
the splitting of the coupled problem based on a suitable strategy to manage the multiscale-in-time
nature of the problem. We present some preliminary numerical results both in ideal and real scenarios. |
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60/2019 - 30/12/2019
Ieva, F; Paganoni, A.M.; Romo, J.; Tarabelloni, N.
roahd Package: Robust Analysis of High Dimensional Data | Abstract | | The focus of this paper is on the open-source R package roahd (RObust Analysis
of High dimensional Data), see Tarabelloni et al. (2017). roahd has been developed to gather
recently proposed statistical methods that deal with the robust inferential analysis of univariate
and multivariate functional data. In particular, efficient methods for outlier detection and related
graphical tools, methods to represent and simulate functional data, as well as inferential tools for
testing differences and dependency among families of curves will be discussed, and the associated
functions of the package will be described in details. |
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58/2019 - 30/12/2019
Antonietti, P.F; Manzini, G.; Mourad, H.M.; Verani, M.
The virtual element method for linear elastodynamics models. Design, analysis, and implementation | Abstract | | We design the conforming virtual element method for the numerical simulation of two dimensional time-dependent elastodynamics problems. We investigate the performance of the method both theoretically and numerically. We prove the stability and the convergence of the semi-discrete approximation in the energy norm and derive optimal error estimates. We also show the convergence in the $L^2$ norm.
The performance of the virtual element method is assessed on a set
of different computational meshes, including non-convex cells up to order four in the $h$-refinement setting. Exponential convergence is also experimentally seen in the $p$-refinement setting. |
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57/2019 - 30/12/2019
Antonietti, P.F.; Bertoluzza, S.; Prada, D.; Verani M.
The Virtual Element Method for a Minimal Surface Problem | Abstract | | In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surface subject to a prescribed boundary condition. We derive optimal error estimate and present several numerical tests assessing the validity of the theoretical results. |
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56/2019 - 30/12/2019
Antonietti, P.F.; Berrone, S.; Borio A.; D'Auria A.; Verani, M.; Weisser, S.
Anisotropic a posteriori error estimate for the Virtual Element Method | Abstract | | We derive an anisotropic a posteriori error estimate for the adaptive conforming Virtual Element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its approximation results to prove the reliability of the error indicator. We design and implement the corresponding adaptive polygonal anisotropic algorithm. Several numerical tests assess the superiority of the proposed algorithm in comparison with standard polygonal isotropic mesh refinement schemes. |
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55/2019 - 18/12/2019
Agosti, A.; Ciarletta, P.; Garcke, H.; Hinze, M.
Learning patient-specific parameters for a diffuse interface glioblastoma model from neuroimaging data | Abstract | | Parameters in mathematical models for glioblastoma multiforme (GBM) tumour growth
are highly patient specific. Here we aim to estimate parameters in a Cahn-Hilliard type
diffuse interface model in an optimised way using model order reduction (MOR) based on
proper orthogonal decomposition (POD). Based on snapshots derived from finite element
simulations for the full order model (FOM) we use POD for dimension reduction and solve
the parameter estimation for the reduced order model (ROM). Neuroimaging data are used
to define the highly inhomogeneous diffusion tensors as well as to define a target functional in
a patient specific manner. The reduced order model heavily relies on the discrete empirical
interpolation method (DEIM) which has to be appropriately adapted in order to deal with
the highly nonlinear and degenerate parabolic PDEs. A feature of the approach is that
we iterate between full order solves with new parameters to compute a POD basis function
and sensitivity based parameter estimation for the ROM problems. The algorithm is applied
using neuroimaging data for two clinical test cases and we can demonstrate that the reduced
order approach drastically decreases the computational effort. |
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54/2019 - 18/12/2019
Simona, A.; Bonaventura, L; de Falco, C.; Schoeps, S.
IsoGeometric Approximations for Electromagnetic Problems in Axisymmetric Domains | Abstract | | We propose a numerical method for the solution of electromagnetic problems on axisymmetric domains, based on a combination of a spectral Fourier approximation in the azimuthal direction with an IsoGeometric Analysis (IGA) approach in the radial and axial directions. This combination allows to blend the flexibility and
accuracy of IGA approaches with the advantages of a Fourier representation on axisymmetric domains. It also allows to reduce significantly the computational cost by decoupling of the computations required for each Fourier mode. We prove that
the discrete approximation spaces employed functional space constitute a closed and exact de Rham sequence. Numerical simulations of relevant benchmarks confirm the high order convergence and other computational advantages of the proposed
method. |
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53/2019 - 12/12/2019
Cerroni, D., Penati, M.; Porta, G.; Miglio, E.; Zunino, P.; Ruffo, P.
Multiscale modeling of glacial loading by a 3D Thermo-Hydro-Mechanical approach including erosion and isostasy | Abstract | | We present a computational framework that allows investigating the Thermo-Hydro-Mechanical response of a representative part of a sedimentary basin during a glaciation cycle. We tackle the complexity of the problem, arising by the mutual interaction among several phenomena, by means of a multi-physics, multi-scale model with respect to both space and time. Our contribution addresses both the generation of the computational grid and the algorithm for the numerical solution of the problem. In particular we present a multi-scale approach accounting for the global deformation field of the lithosphere coupled with the Thermo-Hydro-Mechanical feedback of the ice load on a representative part of the domain at a finer scale. In the fine scale model we also include the erosion possibly caused by the ice melting. This methodology allows investigating the evolution of the sedimentary basin as a response to glaciation cycle at a fine scale, taking also into account the large spatial scale movement of the lithosphere due to isostasy. The numerical experiments are based on the analysis of simple scenario, and show the emergence of effects due to the multi-physics nature of the problem that are barely captured by simpler approaches.
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