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 1288 products
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17/2010 - 06/05/2010
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 - 06/04/2010
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 - 06/03/2010
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 - 06/02/2010
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 - 06/01/2010
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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12/2010 - 04/21/2010
Sacco, Riccardo; Causin, Paola; Zunino, Paolo; Raimondi, Manuela T.
A multiphysics/multiscale numerical simulation of scaffold-based cartilage regeneration under interstitial perfusion in a bioreactor | Abstract | | Articular cartilage is a connective tissue consisting of a relatively few number of cells, the chondrocytes (CCs), that are immersed in an extensive hydrated matrix, composed primarily of proteoglycans and collagens.
In vitro tissue engineering has been investigated as a potential source of functional tissue constructs for cartilage repair, as well as a model system for controlled studies of cartilage development and function. Among the different kinds of devices for the cultivation of 3D cartilage cell colonies, we consider here polymeric scaffold-based perfusion bioreactors. The perfusion fluid supplies nutrients and oxygen to the growing biomass. At the same time, the fluid-induced shear acts as a physiologically relevant stimulus for the metabolic activity of CCs, because it may enhance cell proliferation and
metabolism, provided that the shear stress level is moderate. In this complex environment, mathematical and computational modeling may help in the optimal design of the bioreactor configuration. In this perspective, we propose a computational model for the simulation of the biomass growth, under given inlet and geometrical conditions. Precisely, we consider a two-step approach. First, we perform a simplified short term analysis in which only biomass growth is taken into account, the nutrient concentration and
the fluid-induced shear stress being assumed constant in time and uniform in space. This allows us to calibrate the biomass growth model with respect to the shear stress dependence on experimental data. Then, we carry out a full analysis where the nutrient concentration and perfusion velocity change in time and space and the growing biomass modifies the porosity
of the scaffold matrix, altering the fluid flow. The model parameters are consistently derived from volume averaging techniques that allow us to upscale the microscopic structural properties to the macroscopic level. The predictions we obtain in this way are significant for long times of culture. |
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11/2010 - 04/20/2010
Biscari, Paolo; Minisini, Sara; Pierotti, Dario; Verzini, Gianmaria; Zunino, Paolo
Controlled release with finite dissolution rate | Abstract | | We consider a two-phase generalization of the classical Higuchi’s model for controlled drug release. The drug is assumed to be prepared in a drug eluting stent in its solid phase by immersion in a polymeric matrix which eventually delivers the drug when it reaches the free end. We derive a single effective evolution equation, which we prove to be equivalent to the original system of two coupled PDE’s. We provide analytical estimates for the asymptotic regimes of large and small diffusion. Results from numerical simulations allow then to fill up the gap, and understand the behavior of the system in intermediate regimes. |
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10/2010 - 03/22/2010
Quarteroni, Alfio; Ruiz Baier, Ricardo
Analysis of a fi nite volume element method for the Stokes problem | Abstract | | In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in
di fferent norms are obtained by establishing the adequate connection between the finite volume
and stabilized finite element formulations. A superconvergence result is also derived by using a
postprocessing projection method. The stabilization of the continuous lowest equal order pair fi nite volume element discretization (P1 - P1) is achieved by enriching the velocity space with bubble-like functions. Finally, some numerical experiments that con firm the predicted behavior of the method are provided. |
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