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 1251 products
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25/2011 - 06/22/2011
de Luca, M.; Ambrosi, D.; Robertson, A.M.; Veneziani, A.; Quarteroni, A.
Finite element analysis for a multi-mechanism damage model of cerebral arterial tissue | Abstract | | We developed a non-linear multi-mechanism model that is suitable to represent the mechanical behavior of the healthy arterial wall and the early stage cerebral aneurism formation. |
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24/2011 - 06/20/2011
Manzoni, A.; Quarteroni, A.; Rozza, G.
Model reduction techniques for fast blood flow simulation in parametrized geometries | Abstract | | In this paper we propose a new model reduction technique aimed at real-time blood flow simulations on a given family of geometrical shapes of arterial vessels. Our approach is based on the combination of a low dimensional shape parametrization of the computational domain and the reduced basis method to solve the associated parametrized flow equations.
We propose a preliminary analysis carried on a set of arterial vessel geometries, described by means of a radial basis functions parametrization. In order to account for patient-specific arterial congurations, we reconstruct the latter by solving a suitable parameter identification problem. Realtime simulation of blood flows are thus performed on each reconstructed parametrized geometry, by means of the reduced basis method. We focus on a family of parametrized carotid artery bifurcations, by modelling blood flows using Navier-Stokes equations and measuring distributed outputs such as viscous energy dissipation or vorticity. The latter are indexes that might be correlated with the assessment of pathological risks. The approach advocated here can be applied to a broad variety of (different) flow problems related with geometry/shape variation, for instance related with shape sensitivity analysis, parametric exploration, and shape design. |
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23/2011 - 05/31/2011
Beck, J.; Nobile, F.; Tamellini, L.; Tempone, R.
On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods | Abstract | | In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by multivariate polynomials. We first consider the Stochastic Galerkin method, and rely on sharp estimates for the decay of the Fourier coefficients of the spectral expansion of u on an orthogonal polynomial basis to build a sequence of polynomial subspaces that features better convergence properties, in terms of error versus
number of degrees of freedom, than standard choices such as Total Degree or Tensor Product subspaces.
We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new class of Sparse Grids, based on the idea of selecting a priori the most
profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids. Numerical results show the effectiveness of the newly introduced polynomial spaces and sparse grids. |
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22/2011 - 05/30/2011
Azzimonti, L.; Ieva, F.; Paganoni, A.M.
Nonlinear nonparametric mixed-effects models for unsupervised classification | Abstract | | In this work we propose a novel estimation method for nonlinear nonparametric mixed-effects models, aimed at unsupervised classification. The proposed method is an iterative algorithm that alternates a nonparametric EM step and a nonlinear Maximum Likelihood step. We perform simulation studies in order to evaluate the algorithm performances and we apply this new procedure to a real dataset.
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21/2011 - 05/29/2011
Ambrosi, D.; Pezzuto, S.
Active stress vs. active strain in mechanobiology: constitutive issues | Abstract | | Many biological tissues exhibit a non--standard continuum mechanics behavior:
they are able to modify their placement in absence of external loads.
The activity of the muscles is usually
represented in solid mechanics in terms of an active stress, to be added to the
standard one. A less popular approach is to introduce a multiplicative decomposition
of the tensor gradient of deformation in two factors: the passive and the active one.
Both approaches should satisfy due mathematical properties, namely frame indifference
and ellipticity of the total stress. At the same time, the constitutive laws should
reproduce the observed physiological behavior of the specific living tissue.
In this paper we focus on cardiac contractility.
We review some constitutive examples of active stress and active strain
taken from the literature and we discuss them in terms of precise mathematical and physiological
properties. These arguments naturally suggest new possible models. |
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20/2011 - 05/04/2011
Antonietti, P.F.; Houston, P.
Preconditioning high--order Discontinuous Galerkin discretizations of elliptic problems | Abstract | | In [P.F. Antonietti, P. Houston, J. Sci. Comp., 2011] it has been proved that the non-overlapping
Schwarz preconditioners can also be successfully employed to reduce the condition number of the stiffness matrices arising from a wide class of high--order DG discretizations of elliptic problems. In this article we aim to validate the theoretical results derived in [P.F. Antonietti, P. Houston, J. Sci. Comp., 2011] for the multiplicative Schwarz preconditioner and for its symmetrized variant by testing their numerical performance. |
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19/2011 - 05/03/2011
Passerini, T.; Sangalli, L.; Vantini, S.; Piccinelli, M.; Bacigaluppi, S.; Antiga, L.; Boccardi, E.; Secchi, P.; Veneziani, A.
An Integrated Statistical Investigation of the Internal Carotid Arteries hosting Cerebral Aneurysms | Abstract | | Cerebral aneurysm formation is the result of a complex interplay of systemic and local factors. Among the latter, the role of the geometry of the vessel hosting an aneurysm (parent vessel) and the induced hemodynamics still needs to be
carefully investigated. In this paper we have considered a data set of 52 patients, reconstructed the geometries of the parent vessel and extracted the relevant morphological
features with image processing methods. We performed the computational fluid dynamics analysis of these patients with a finite element solver. We have collected in this way a set of data including morphology and wall shear stress along the parent vessel. Thanks to a functional principal component analysis we related relevant geometrical and fluid dynamical features to a classification of patients depending on the location of the aneurysms and the rupture status. This analysis is anticipated to provide a contribution for the assessment of an index for the rupture risk. |
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18/2011 - 04/21/2011
Blanco, P.; Gervasio, P.; Quarteroni, A.
Extended variational formulation for heterogeneous partial differential equations | Abstract | | We address the coupling of an advection equation with a diffusion-advection equation, for solutions featuring boundary layers. We consider
non-overlapping domain decompositions and we face up the heterogeneous problem using an extended variational formulation. We will prove the
equivalence between the latter formulation and a treatment based on a singular perturbation theory. An exhaustive comparison in terms of solution and computational efficiency between these formulations is carried out. |
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