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 1238 products
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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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15/2011 - 03/30/2011
Argiento, R.; Guglielmi, A.; Soriano J.
A semiparametric Bayesian generalized linear mixed model for the reliability of Kevlar fibres | Abstract | | We analyze the reliability of NASA composite pressure vessels using a new Bayesian semiparametric model. The dataset consists of lifetimes of pressure vessels, wrapped with a Kevlar fiber, grouped by spool, subject to different stress levels; 10% of data are right censored. The model we consider is a regression on the log-scale for the lifetimes, with fixed (stress) and random (spool) effects. The prior of the spool parameters is nonparametric, namely they are a sample from a normalized generalized gamma process, which encompasses the well-known Dirichlet process. The nonparametric prior is assumed to robustify inferences to mispecification of the parametric prior. Here, this choice of likelihood and prior yields a new Bayesian model in reliability analysis. Via a Bayesian hierarchical approach, it is easy to analyze the reliability of the Kevlar fiber by predicting quantiles of the failure time when a new spool is selected at random from the population of spools. Moreover, for comparative purposes we review the most interesting frequentist and Bayesian models analyzing this dataset. Our credibility intervals of the quantiles of interest for a new random spool are narrower than those derived by previous Bayesian parametric literature. Additionally, the discreteness of the random-effects distribution induces a natural clustering of the spools into three different groups, which is in accordance with the frequentist spool rankings.
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14/2011 - 03/29/2011
Antonietti, P.F.; Mazzieri, I.; Quarteroni, A.; Rapetti, F.
Non-Conforming High Order Approximations for the Elastic Wave Equation | Abstract | | In this paper we formulate and analyze two non conforming high order strategies for approximating the solution of elastic wave problems in heterogeneous media, namely the Mortar Spectral Element Method and the Discontinuous Galerkin Spectral Element Method.
Starting from a common variational formulation we make a full comparison of the two techniques from the points of view of accuracy, convergence, grid dispersion and stability. |
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13/2011 - 03/15/2011
Lombardi, M.; Parolini, N.; Quarteroni, A.; Rozza, G.
Numerical simulation of sailing boats: dynamics, FSI, and shape optimization | Abstract | | The numerical simulation of free-surface flows around sailing boats is a complex topic that addresses multiple mathematical tasks: the correct study of the flow field around a rigid hull, the numerical simulation of the hull dynamics, the deformation of the sails and appendages under transient external conditions like gusts of wind or wave patterns and, overall, the coupling among all these components. In this paper, we present some recent advances that have been achieved in different research topics related to yacht design and performance prediction. In particular, we describe the numerical algorithms that have been developed in the framework of open-source libraries for the simulation of free-surface hydrodynamics and boat dynamics, as well as for the analysis of the fluid-structure interaction between wind and sails. Moreover, an algorithm for shape optimization, based on the solution of the adjoint problem and combined with the Free Form Deformation (FFD) method for the shape parametrization and mesh motion, is presented and discussed. Theoretical and methodological aspects are described and the first preliminary results are reported. |
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