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 1249 prodotti
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08/2013 - 22/02/2013
Chen, P.; Quarteroni, A.; Rozza, G.
A Weighted Reduced Basis Method for Elliptic Partial Differential Equations with Random Input Data | Abstract | | In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equation (PDE) with random input data. The PDE is first transformed into a weighted parametric elliptic problem depending on a finite number of parameters. Distinctive importance at different values of the parameters are taken into account by assigning different weight to the samples in the greedy sampling procedure. A priori convergence analysis is carried out by constructive approximation of the exact solution with respect to the weighted parameters. Numerical examples are provided for the assessment of the advantages of the proposed method over the reduced basis method and stochastic collocation method in both univariate and multivariate stochastic problems. Keywords: weighted reduced basis method, stochastic partial differential equation, uncertainty quantication, stochastic collocation method, Kolmogorov N-width, exponential convergence |
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07/2013 - 21/02/2013
Chen, P.; Quarteroni, A.; Rozza, G.
A Weighted Empirical Interpolation Method: A-priori Convergence Analysis and Applications | Abstract | | We extend the conventional empirical interpolation method to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work. We apply our method to geometric Brownian motion, exponential Karhunen-Loeve expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method. Keywords: empirical interpolation method, a priori convergence analysis, greedy algorithm, Kolmogorov N-width, geometric Brownian motion, Karhunen-Loeve expansion, reduced basis method |
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06/2013 - 18/02/2013
Dedè, L.; Quarteroni, A.
Isogeometric Analysis for second order Partial Differential Equations on surfaces | Abstract | | We consider the numerical solution of second order Partial Differential Equations (PDEs) on lower dimensional manifolds, specifically on surfaces
in three dimensional spaces. For the spatial approximation, we consider Isogeometric Analysis which facilitates the encapsulation of the exact
geometrical description of the manifold in the analysis when this is represented by B–splines or NURBS. Our analysis addresses linear, nonlinear,
time dependent, and eigenvalues problems involving the Laplace–Beltrami operator on surfaces. Moreover, we propose a priori error estimates
under h–refinement in the general case of second order PDEs on the lower dimensional manifolds. We highlight the accuracy and efficiency of Isogeometric Analysis with respect to the exactness of the geometrical representations of the surfaces. |
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05/2013 - 16/02/2013
Caputo, M.; Chiastra, C.; Cianciolo, C.; Cutri , E.; Dubini, G.; Gunn, J.; Keller, B.; Zunino, P.;
Simulation of oxygen transfer in stented arteries and correlation with in-stent restenosis | Abstract | | Computational models are used to study the combined effect of biomechanical and biochemical factors on coronary in-stent restenosis, which is a post-operative remodeling and regrowth of the stented artery tissue. More precisely, we address numerical simulations based on Navier-Stokes and mass transport equations to study the role of perturbed wall shear stresses and reduced oxygen concentration in a geometrical model reconstructed from a real porcine artery treated with a stent. Joining emph{in vivo} and emph{in silico} tools of investigation has multiple benefits in this case. On one hand, the geometry of the arterial wall and of the stent closely correspond to a real implanted configuration. On the other hand, the inspection of histological tissue samples informs us on the location and intensity of in-stent restenosis. As a result of that, we are able to correlate geometrical factors, such as the axial variation of the artery diameter and its curvature, the numerical quantification of biochemical stimuli, such as wall shear stresses, and the availability of oxygen to the inner layers of the artery, with the appearance of in-stent restenosis. This study shows that the perturbation of the vessel curvature could induce hemodynamic conditions that stimulate an undesired arterial remodeling. |
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04/2013 - 21/01/2013
Morlacchi, S.; Chiastra, C.; Cutrì, E.; Zunino, P.; Burzotta, F.; Formaggia, L.; Dubini, G.; Migliavacca, F.
Stent deformation, physical stress, and drug elution obtained with provisional stenting, conventional culotte and Tryton-based culotte to treat bifurcations: a virtual simulation study | Abstract | | Aims: To investigate the possible influence of different bifurcation stenting techniques on stent deformation, physical stress, and drug elution using an implemented virtual tool that comprehends structural, fluid dynamics and drug-eluting numerical models. Methods and results: A virtual bench test based on explicit dynamic modelling was used to simulate procedures
on bifurcated coronary vessels performed according to three different stenting techniques: provisional side branch stenting, culotte and Tryton-based culotte. Geometrical configurations obtained after stenting were used to perform fluid dynamics and drug elution analyses. Results show that major different pattern of mechanical deformation, shear stress and theoretical
drug elution are obtained using different techniques. Compared with conventional culotte, the dedicated Tryton seems to facilitate the intervention in terms of improved access to the main branch and lowers its biomechanical influence on the coronary bifurcation in terms of mechanical and hemodynamic parameters. However, since the Tryton stent is a bare metal stent, the drug elution obtained is lower. Conclusion: Numerical models might successfully complement the information on stenting procedures obtained
with traditional approaches as in vitro bench testing or clinical trials. Devices dedicated to bifurcations may facilitate procedure completion and may result in specific patterns of mechanical stress, regional blood flow and drug elution. |
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03/2013 - 20/01/2013
Antonietti, P.F.; Ayuso de Dios, B.; Bertoluzza, S.; Pennacchio, M.
Substructuring preconditioners for an $h-p$ Nitsche-type method | Abstract | | We propose and study an iterative substructuring method for an $h-p$ Nitsche-type discretization, following the original approach introduced in [Bramble, Pasciak, Schatz, Math. Comp., 1986] for conforming methods. We prove quasi-optimality with respect to the mesh size and the polynomial degree for the proposed preconditioner. Numerical experiments asses the performance of the preconditioner and verify the theory. |
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02/2013 - 11/01/2013
Brugiapaglia, S.; Gemignani, L.
On the simultaneous refinement of the zeros of H-palindromic polynomials | Abstract | | In this paper we propose a variation of the Ehrlich–Aberth method for the simultaneous refinement of the zeros of H-palindromic polynomials.
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01/2013 - 04/01/2013
Arnold, D.N.; Boffi, D.; Bonizzoni,F.
Tensor product finite element differential forms and their approximation properties | Abstract | | We discuss the tensor product construction for complexes of differential forms and show how it can be applied to define shape functions and degrees of freedom for finite element differential forms on cubes in n dimensions. These may be extended to curvilinear cubic elements, obtained as images of a reference cube under diffeomorphisms, by using the pullback transformation for differential forms to map the shape functions and degrees of freedom from the reference cube to the image finite element. This construction recovers and unifies several known finite element approximations in two and three dimensions. In this context, we study the approximation properties of the resulting finite element spaces in two particular cases: when the maps from the reference cube are affine, and when they are multilinear. In the former case the rate of convergence depends only on the degree of polynomials contained in the reference space of shape functions. In the latter case, the rate of approximation is degraded, with the loss more severe for differential forms of higher form degree. |
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