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 1322 prodotti
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40/2015 - 24/08/2015
Patelli, A.S.; Dedè, L.; Lassila, T.; Bartezzaghi, A.; Quarteroni, A.
Isogeometric approximation of cardiac electrophysiology models on surfaces: an accuracy study with application to the human left atrium | Abstract | | We consider Isogeometric Analysis in the framework of the Galerkin method for the spatial approximation of cardiac electrophysiology models defined on NURBS surfaces; specifically, we perform a numerical comparison between basis functions of degree p ? 1 and globally C^k-continuous, with k = 0 or p ? 1, to find the most accurate approximation of a propagating front with the minimal number of degrees of freedom.We show that B-spline basis functions of degree p ? 1, which are C^(p?1)-continuous capture accurately the front velocity of the transmembrane potential even with moderately refined meshes; similarly, we show that,for accurate tracking of curved fronts, high-order continuous B-spline basis functions should be used. Finally, we apply Isogeometric Analysis to an idealized human left atrial geometry described by NURBS with physiologically sound fiber directions and anisotropic conductivity tensor to demonstrate that the numerical scheme retains its favorable approximation properties also in a more realistic setting. Keywords: Isogeometric Analysis, cardiac electrophysiology, surface PDEs, high-order approximation |
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39/2015 - 10/08/2015
Guglielmi, A.; Ieva, F.; Paganoni, A.M.; Quintana, F.A.
A semiparametric Bayesian joint model for multiple mixed-type outcomes: an Application to Acute Myocardial Infarction | Abstract | | We propose a Bayesian semiparametric regression model to represent mixed-type multiple outcomes concerning patients affected by Acute Myocardial Infarction. Our approach is motivated by data coming from the ST-Elevation Myocardial Infarction(STEMI) Archive, a multi-center observational prospective clinical study planned as part of the Strategic Program of Lombardy, Italy. We specifically consider a joint model for a variable measuring treatment time and in-hospital and 60-day survival indicators.
One of our motivations is to understand how the various hospitals differ in terms of the variety of information collected as part of the study. We are particularly interested in using the available data to detect differences across hospitals. In order to do so we postulate a semiparametric random effects model that incorporates dependence on a location indicator that is used to explicitly differentiate among hospitals in or outside the city of Milano. The model is based on the two parameter Poisson-Dirichlet prior, also known as the Pitman-Yor process prior. We discuss the resulting posterior inference, including sensitivity analysis, and a comparison with the particular sub-model arising when a Dirichlet process prior is assumed. |
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38/2015 - 16/07/2015
Grasso, M.; Menafoglio, A.; Colosimo, B.M.; Secchi, P.
Using Curve Registration Information for Profile Monitoring | Abstract | | The quality characteristics in manufacturing processes are often represented in terms of spatially or time ordered data, called “profiles”, which are characterized by amplitude and phase variability. In this context, curve registration plays a key role, as it allows separating the two kinds of between-profiles variability, and to reduce any undesired inflation of the natural phase variability. In the mainstream literature, registration warping functions are not generally considered in the monitoring process, even though this may cause a significant information loss. We propose a novel approach for profile monitoring, which combines the Functional Principal Component Analysis and the use of parametric warping functions. The key idea is to
jointly monitor the stability over time of the registered profiles (i.e., the information related to amplitude variability) and the registration coefficients (i.e., the information related to phase
variability). This allows improving the capability of detecting unnatural pattern modifications, thanks to a better characterization of the overall natural variability. The benefits of a proper management of functional data registration, together with the advantages over the most common approaches used in the literature, are demonstrated by means of Monte Carlo simulations. The proposed methodology is finally applied to a real industrial case study relying on a dataset acquired in waterjet cutting processes under different health conditions of
the machine tool. |
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37/2015 - 10/07/2015
Aletti, M.; Perotto, S.; Veneziani, A.
Educated bases for the HiMod reduction of advection-diffusion-reaction problems with general boundary conditions | Abstract | | Hierarchical Model (HiMod) reduction is a method introduced in cite{perotto:2008} to effectively solve
advection-diffusion-reaction (ADR) and fluid dynamics problems in pipes. The rationale of the method is to regard
the solution as a mainstream axial dynamics added by transverse components. The mainstream
component is approximated by finite elements as often done in classical 1D models (like the popular Euler equations for gasdynamics). However, the HiMod formulation includes also the transverse dynamics by a spectral expansion.
A few modes are expected to capture the transverse (somehow secondary) dynamics with a good level of approximation. This
drastically reduces the size of the discrete problem, yet preserving accuracy. The method is ``hierarchical'' since the selection of the number of transverse modes can be hierarchically and adaptively performed~cite{perotto:2013}.
We have previously considered only Dirichlet boundary conditions for the lateral walls of the pipe and the procedure was tested only in 2D domains. With an appropriate selection of the spectral basis functions,
here we extend our formulation to 3D problems with general boundary conditions, still pursuing an essential approach.
The modal basis functions fulfill by construction the (homogeneous) boundary conditions associated with the solution.
This is achieved
by solving a Sturm-Liouville eigenpair problem.
We analyze this approach and provide a convergence analysis for the numerical error in the case of a linear ADR problem in rectangles (2D) and slabs (3D). Numerical results confirm the theory. |
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36/2015 - 10/07/2015
Fedele, M.; Faggiano, E.; Barbarotta, L.; Cremonesi, F.; Formaggia, L.; Perotto, S.
Semi-Automatic Three-Dimensional Vessel Segmentation Using a Connected Component Localization of the Region-Scalable Fitting Energy | Abstract | | Segmentation of patient-specific vascular segments of interest from
medical images is an important topic for numerous applications. De-
spite the great importance of having semi-automatic segmentation meth-
ods in this field, the process of image segmentation is still based on
several operator-dependent steps which make large-scale segmentation
a non trivial and time consuming task. In this work we present a
semi-automatic segmentation method to reconstruct vascular struc-
tures from three-dimensional medical images. We start from the mini-
mization of the Region Scalable Fitting Energy using the Split-Bregman
method and we modify the resulting algorithm adding a connected
component extraction of the solution starting from a point that identi-
fies the vascular structure of interest. In this way, we add a constraint
to the algorithm focusing it only on the vascular structure we want
to reconstruct and avoiding the attachment with the nearby objects.
Finally, we describe a strategy to minimize the number of involved
parameters in order to limit the user effort. The results obtained on
two different images (a Magnetic Resonance and a Computed Tomog-
raphy) demonstrate that our method outperforms the original method
in segmenting the vascular region of interest without the inclusion of
nearby objects in the result. |
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35/2015 - 26/06/2015
Manzoni, A.; Pagani, S.
A certified reduced basis method for PDE-constrained parametric optimization problems by an adjoint-based approach | Abstract | | In this paper we present a certified reduced basis (RB) framework for the efficient solution of PDE-constrained parametric optimization problems. We consider optimization problems (such as optimal control and optimal design) governed by elliptic PDEs and involving possibly non-convex cost functionals, assuming that the control functions are described in terms of a parameters vector. At each optimization step, the high-fidelity approximation of state and adjoint problems is replaced by a certified RB approximation, thus yielding a very efficient solution through an “optimize-then-reduce” approach. We develop a posteriori error estimates for the solutions of state and adjoint problems, for the cost functional, its gradient and the optimal parameters. We confirm our theoretical results in the case of optimal control/design problems dealing with potential and thermal flows. |
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34/2015 - 26/06/2015
Bernardi, M.S.; Mazza, G.; Ramsay, J.O.; Sangalli, L.M.
A separable model for spatial functional data with application to the analysis of the production of waste in Venice province | Abstract | | We propose a method for the analysis of functional data with complex dependencies, such as spatially dependent curves or time dependent surfaces, over highly textured domains. The models are based on the idea of regression with partial di erential regularizations. We focus in particular on a separable space-time version of the model. Among the various modelling features, the proposed method is able to deal with spatial domains featuring peninsulas, islands and other complex geometries.
Space-varying covariate information is included in the model via a semi-parametric framework. The proposed method is compared via simulation
studies to other spatio-temporal techniques and it is applied to the analysis of the annual production of waste in the towns of Venice province. |
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33/2015 - 26/06/2015
Fumagalli, A; Pasquale, L; Zonca, S.; Micheletti, S.
An upscaling procedure for fractured reservoirs with non-matching grids | Abstract | | Upscaling of geological models for reservoir simulation is an active and important area of research. In particular, we are interested in reservoirs where the rock matrix exhibits an intricate network of fractures, which usually act as a preferential path to the flow. Accounting for fractures’ contribution in the simulation of a reservoir is of paramount importance. Here, we have focused on obtaining effective parameters (e.g. transmissibility) on a 3D computational grid on the reservoir scale, that account for the presence, at a finer spatial scale, of fractures, and network of fractures. We have, essentially, followed the idea illustrated in Karimi-Fard et al. [2006], yet this work has some notable aspects of innovation in the way the procedure has been implemented, and in its capability to consider rather general corner-point grids, like the ones normally used in reservoir simulations in the industry, and complex and realistic fracture networks. In particular, novel contribution is the employment of EDFM for computing fracture-fracture and matrix-fracture transmissibilities, with a remarkable gain in speed-up. The output is in form of transmissibility that can be used for reservoir simulations with software like Eclipse, Intersect, or GPRS. The results demonstrate the effectiveness and computational efficiency of the numerical procedure, and of the developed software, which is now ready for further testing and industrialization.
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