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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13/2012 - 02/14/2012
Formaggia, L.; Guadagnini, A.; Imperiali, I.; Lever, V.; Porta, G.; Riva, M.; Scotti, A.; Tamellini, L.
Global Sensitivity Analysis through Polynomial Chaos Expansion of a basin-scale geochemical compaction model | Abstract | | We present a model-driven uncertainty quantification methodology based on the use of sparse grids sampling techniques in the context
of a generalized Polynomial Chaos Expansion (GPCE) approximation of a basin-scale geochemical evolution scenario. The approach is illustrated through a one-dimensional example involving the process of quartz cementation in sandstones and the resulting effects on the dynamics of the vertical distribution of porosity, pressure and
temperature. The proposed theoretical framework and computational tools allow performing an efficient and accurate Global Sensitivity Analysis (GSA) of the system states (i.e., porosity, temperature, pressure and fluxes) in the presence of uncertain key mechanical and geochemical model parameters as well as boundary conditions. GSA is grounded on the use of the variance-based Sobol indices. These allow
discriminating the relative weights of uncertain quantities on the global model variance and can be computed through the GPCE of the model response surface. Evaluation of the GPCE of the random model response is performed through the implementation of a sparse grid interpolation technique in the space of the selected uncertain
quantities. As opposed to a standard Monte Carlo sampling, the use of sparse grids polynomial interpolants renders computationally affordable and reliable evaluations of the required indices. GPCE can then be employed as a surrogate model of the system states to quantify uncertainty propagation through the model in terms of the
probability distribution (and its statistical moments) of target system states. |
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12/2012 - 02/13/2012
Guglielmi, A.; Ieva, F.; Paganoni, A.M.; Ruggeri, F.
Hospital clustering in the treatment of acute myocardial infarction patients via a Bayesian semiparametric approach | Abstract | | In this work, we develop Bayes rules for several families of loss functions for hospital report cards under a Bayesian semiparametric hierarchical
model. Moreover, we present some robustness analysis with respect to the choice of the loss function, focusing on the number of hospitals our procedure identifies as unacceptably performing . The analysis is carried out on
a case study dataset arising from MOMI2 (Month MOnitoring Myocardial Infarction in MIlan) survey on patients admitted with ST-Elevation Myocardial Infarction to the hospitals of Milan Cardiological Network. The major aim of this work is the ranking of the health care providers performances, together with the assessment of the role of patients and providers characteristics on survival outcome.
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11/2012 - 02/10/2012
Bonnemain, J.; Faggiano, E.; Quarteroni A.; Deparis S.
A Patient-Specific Framework for the Analysis of the Haemodynamics in Patients with Ventricular Assist Device | Abstract | | Nowadays ventricular assist devices play an important role in the treatment of terminal heart failure. While the devices themselves have been widely studied there are no studies of patient-specific numerical simulation in this context. This could be explained by the fact that the presence of the device induces metallic artifacts and noise in the acquired images so that conventional segmentation techniques fail. The aim of our work is to propose a robust framework for the segmentation of medical images of poor quality, the generation of high quality meshes and for the patient-specific analysis of the collected data via fluid-structure interaction (FSI) numerical simulations. First images are processed using histogram adjustment, histogram equalization, and gradient anisotropic diffusion filter. The watershed algorithm is then applied and the result is refined by the use of morphological operators. Then our framework allows the generation of two conforming meshes, one for the arterial lumen and the other for the arterial wall, ready for FSI simulations.
We also describe the numerical model and methods used to perform FSI simulations. Final results performed on two patients demonstrate the ability of our methods: the whole strategy results suitable, robust, and accurate for patient-specific data. |
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10/2012 - 02/09/2012
Lassila, T.; Manzoni, A.; Quarteroni, A.; Rozza, G.
Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty | Abstract | | We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the the worst-case in terms of recirculation effects is inferred to correspond to a residual strong orifice flow through near-complete occlusion. Worst-case optimization is performed to identify an anastomosis angle and a cuffed shape that are robust with respect to a possible range of residual flows. We also consider a reduced order modelling framework based on reduced basis methods
in order to make the robust design problem computationally feasible. Keywords: optimal control, shape optimization, arterial bypass grafts, uncertainty, worst-case design, reduced order modelling, Navier-Stokes equations. |
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09/2012 - 01/30/2012
Mauri, L.; Perotto, S.; Veneziani, A.
Adaptive geometrical multiscale modeling for hydrodynamic problems | Abstract | | Hydrodynamic problems often feature geometrical configurations that allow a suitable dimensional model reduction. One-dimensional models may be
sometimes accurate enough for describing a dynamic of interest. In other cases, localized relevant phenomena require more precise models. To improve the computational efficiency, geometrical multiscale models have been proposed,
where reduced (1D) and complete (2D-3D) models are coupled in a unique numerical solver. In this paper we consider an adaptive geometrical multiscale modeling: the regions of the computational domain requiring more or less
accurate models are automatically and dynamically selected via a heuristic criterion. To the best of our knowledge, this is a first example of automatic geometrical multiscale model reduction. |
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08/2012 - 01/29/2012
Sangalli, L.M.; Ramsay, J.O.; Ramsay, T.O.
Spatial Spline Regression Models | Abstract | | We describe a model for the analysis of data distributed over irregularly shaped spatial domains with complex boundaries, strong concavities and interior holes. Adopting an approach typical of functional data analysis, we propose a Spatial Spline Regression model that is computationally efficient, allows for spatially distributed covariate information and can impose various conditions over the boundaries of the domain. Accurate surface estimation is achieved by the use of finite elements, which provide a basis for piecewise polynomial surfaces. |
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07/2012 - 01/28/2012
Perotto, S; Zilio, A.
Hierarchical model reduction: three different approaches | Abstract | | We present three different approaches to model, in a computationally cheap way, problems characterized by strong horizontal dynamics, even though
in the presence of transverse heterogeneities.
The three approaches move from the hierarchical model reduction setting introduced in S. Perotto, A. Ern, A. Veneziani 2010. |
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06/2012 - 01/27/2012
Micheletti, S.; Perotto, S.
Anisotropic recovery-based a posteriori error estimators for advection-diffusion-reaction problems | Abstract | | We combine the good properties of recovery-based error estimators with the richness of information typical of an anisotropic a posteriori analysis.
This merging yields error estimators which are general purpose yet simple and easy to implement, and automatically incorporate detailed geometric information about the computational mesh.
This allows us to devise an effective anisotropic mesh adaptation procedure suited to control the discretization error both in the energy norm and in a goal-oriented framework.
The advection-diffusion-reaction problem is considered as a computational paradigm.
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