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 1275 prodotti
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20/2010 - 09/06/2010
Nobile, Fabio; Quarteroni, Alfio; Ruiz Baier, Ricardo
Numerical solution of an active strain formulation for the electromechanical activity in the heart | Abstract | | We propose a finite element method for solving a system of equations describing the coupling
between cardiac mechanics and electrical signalling. The model is based on a multiplicative
decomposition of the deformation tensor into a passive and active part, the latter carrying
the information of the electrical potential propagation and anisotropy of the cardiac tissue into the equations of incompressible or nearly incompressible nonlinear elasticity, governing the
mechanical response of the biological material. Moreover, by changing from an Eulerian to
a Lagrangian configuration, the underlying problem exhibits a nonlinear diffusion term in the
equations of the electrical propagation (namely, the bidomain and monodomain equations).
Piecewise quadratic finite elements are used to approximate the displacements field, while for
pressure, electrical potentials and ionic variables, we use piecewise linear elements. Various test cases show that the proposed method is able to capture some important features of the
studied phenomenon, and illustrate the behavior of the global model. |
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19/2010 - 08/06/2010
Gaudio, Loredana; Quarteroni, Alfio
hN-adaptive spectral element discretization of optimal control problems for environmental applications | Abstract | | In this work, we propose an hN adaptive algorithm for optimal control problems whose space discretization is based on the spectral element method.
We focus on a special class of problems described by quadratic cost functional and linear advection-di ffusion state equation. This model has been
employed to forecast and suitably reduce, by an optimization process, the pollutant concentration in air on a speci c area of interest. Moreover, a
local adaptive algorithm is employed to achieve a desired accuracy on the cost functional by reducing the computational cost of the problem. |
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18/2010 - 07/06/2010
Antonietti, P.F.; Fadel, N.A.; Verani, M.
Modelling and numerical simulation of the polymeric extrusion process in textile products | Abstract | | We present the mathematical modelling and the numerical simulation of the polymer extrusion process of hollow and non-hollow yarns. In particular, the polymeric material flow has been modelled as non-Newtonian, incompressible, isothermal and steady. We attempt to develop a possible strategy for effective die design in profile extrusion and we numerically asses the validity of the model on both academic and real industrial test cases. Keywords:Free boundary flow, Die-swell, Hollow yarn. 2000 Mathematics Subject Classification. 76D07, 35Q30. |
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17/2010 - 05/06/2010
Guglielmi, Alessandra; Ieva, Francesca; Paganoni, Anna Maria; Ruggeri, Fabrizio
A Bayesian random-effects model for survival probabilities after acute myocardial infarction | Abstract | | Studies of variations in health care utilization and outcome involve the analysis of multilevel clustered data, considering in particular the estimation of a cluster-specific adjusted response, covariates effect and components of variance. Besides reporting on the extent of observed variations, those studies quantify the role of contributing factors including patients
and providers characteristics. In addition, they may assess the relationship between health-care process and outcomes. In this article we present
a case-study, considering a Bayesian hierarchical generalized linear model, to analyze MOMI2 (MOnth MOnitoring Myocardial Infarction in MIlan)
data on patients admitted with ST-Elevation Myocardial Infarction diagnosis, in order to predict survival probabilities. We obtain posterior estimates of the regression parameters, as well as of the random-effects parameters
(the grouping factor is the hospital the patients were admitted to), through an MCMC algorithm. The choice of covariates is achieved in a Bayesian
fashion as a preliminary step. Some issues about model fitting are discussed through the use of predictive tail probabilities and Bayesian residuals.
Keywords:
Bayesian hierarchical models,
Multilevel data analysis,
Bayesian generalized linear mixed models, Logistic regression,
Health services research.
AMS Subject Classi¯cation: 62F15, 62P10, 62J12 |
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16/2010 - 04/06/2010
Formaggia, Luca; Scotti, Anna
Positivity and conservation properties of some integration schemes for mass action kinetics | Abstract | | The numerical schemes approximating chemical reactions according to the mass action law should reproduce at least two properties of the corresponding physical system: mass conservation and nonnegativity of the concentrations.
This paper analyzes the equations of mass action kinetics providing a proof of the existence, uniqueness, and positivity of the solution under
mild hypothesis on the reaction rate and the stoichiometric coefficients.
We then consider some classic integration schemes in terms of conservation, positivity and accuracy compared to schemes tailored for production-destruction systems, and propose an original scheme which guarantees conservation,
nonnegativity of the solution and has order of convergence between two and three. |
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15/2010 - 03/06/2010
Quarteroni, A.; Formaggia, L.
Domain Decomposition (DD) Methods | Abstract | | This short paper gives a review of domain decomposition methods for parallel computations of large scale problems, with a focus on computational geology. |
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14/2010 - 02/06/2010
Antonietti, Paola F. ; Beirao da Veiga, Lourenco; Verani, Marco
A Mimetic Discretization of Elliptic Obstacle Problems | Abstract | | We develop a Finite Element method (FEM) which can adopt very general meshes with polygonal elements for the numerical approximation of elliptic obstacle problems. This kind of methods are also known as mimetic discretization schemes,
which stem from the Mimetic Finite Difference (MFD) method. The first-order convergence estimate in a suitable (mesh-dependent) energy norm is established.
Numerical experiments con firming the theoretical results are also presented.
Keywords: Mimetic Finite Difference Methods, obstacle problem.
2000 Mathematics Subject Classi cation. Primary 65N30; Secondary 35R35. |
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13/2010 - 01/06/2010
Porta, G.M.; Perotto, S.; Ballio, F.
A Space-Time Adaptation Scheme for Unsteady Shallow Water Problems | Abstract | | We provide a space-time adaptation procedure for the approximation of the Shallow Water Equations (SWE). This approach relies on a recovery
based estimator for the global discretization error, where space and time contributions are kept separate. In particular we propose an ad hoc procedure for the recovery of the time derivative of the numerical solution and then employ this reconstruction to de ne the error estimator in time. Concerning the space adaptation, we move from an anisotropic error estimator, i.e., able to automatically identify the density, the shape and the orientation of the elements of the computational mesh. The proposed global error estimator turns out to share the good properties of each recovery based error estimator. The whole adaptive procedure is then combined with a suitable stabilized nite element SW solver. Finally the reliability of the coupled
solution-adaptation procedure is successfully assessed on two unsteady test cases of interest for hydraulics applications. |
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