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 1249 products
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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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16/2011 - 03/31/2011
Mesin, L; Ambrosi, D.
Spiral waves on a contractile tissue | Abstract | | In a healthy cardiac tissue, electric waves propagate in the form of a travelling pulse, from the apex to the base, and activate the contraction of the heart. Defects in the propagation can destabilize travelling fronts and originate possible new periodic solutions, as spiral waves. Spiral waves are quite stable, but the interplay between currents and strain can distort the periodic pattern, provided the coupling is strong enough.
In this paper we investigate the stability of spiral waves on a contractile medium in a non--standard framework, in which the electrical potential dictates the active strain (not stress) of the muscle. The role of conducting and contracting fibers is included in the model and periodic boundary conditions are adopted. A correlation analysis allows to evaluate numerically the range of stability of the parameters for the spiral waves, depending on the strain of the contracted fibers and on the magnitude of the stretch activated current.
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17/2011 - 03/31/2011
Quarteroni, A.; Rozza, G.; Manzoni, A.
Certified Reduced Basis Approximation for Parametrized Partial Differential Equations and Applications | Abstract | | Reduction strategies, such as model order reduction (MOR) or reduced basis (RB) methods, in scientific computing may become crucial in applications of increasing complexity. In this paper we review the reduced basis method (built upon a high-fidelity “truth” finite element approximation) for a rapid and reliable approximation of parametrized partial differential
equations, and comment on their potential impact on applications of industrial interest. The essential ingredients of RB methodology are: a Galerkin projection onto a low-dimensional space of basis functions properly selected, an affine parametric dependence enabling to perform a competitive Offline-Online splitting in the computational procedure, and a rigorous a posteriori error estimation used for both the basis selection and the certification of the
solution. The combination of these three factors yields substantial computational savings which are at the basis of an efficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identification). After a brief excursus on the methodology, we focus on linear elliptic and parabolic problems, discussing some extensions to more general classes of problems and several perspectives of the ongoing research. We present some results from applications dealing with heat and mass transfer, conduction-convection phenomena, and thermal treatments. |
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