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 1249 products
-
24/2012 - 05/16/2012
Antonietti, P.F.; Giani, S.; Houston, P.
hp–Version Composite Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains | Abstract | | In this paper we introduce the hp-version discontinuous Galerkin composite finite element method for the discretization of second–order elliptic partial differential equations. This class of methods allows for the approximation of problems posed on computational domains which may contain a huge number of local geometrical features, or micro-structures. While standard numerical methods can be devised for such problems, the computational effort may be extremely high, as the minimal number of elements needed to represent the underlying domain can be very large. In contrast, the minimal dimension of the underlying composite finite element space is independent of the number of geometric features. The key idea in the construction of this latter class of methods is that the computational domain $ Omega$ is no longer resolved by the mesh; instead, the finite element basis (or shape) functions are adapted to the geometric details present in $ Omega$. In this article, we extend these ideas to the discontinuous Galerkin setting, based on employing the hp-version of the finite element method. Numerical experiments highlighting the practical application of the proposed numerical scheme will be presented. |
-
23/2012 - 05/15/2012
Fabio Nobile, Christian Vergara
Partitioned algorithms for fluid-structure interaction problems in haemodynamics | Abstract | | We consider the fluid-structure interaction problem arising in
haemodynamic applications. The finite elasticity equations
for the vessel are written in Lagrangian form,
while the Navier-Stokes equations for the blood in Arbitrary
Lagrangian Eulerian form. The resulting three fields problem
(fluid/ structure/ fluid domain) is formalized via the introduction of
three Lagrange multipliers and consistently discretized by p-th order backward differentiation
formulae (BDFp).
We focus on partitioned algorithms for its numerical solution, which
consist in the successive solution of the three subproblems. We review
several strategies that all rely on the exchange of Robin interface
conditions and review their performances reported recently in the literature.
We also analyze the stability of explicit partitioned procedures and
convergence of iterative implicit partitioned procedures on a simple
linear FSI problem for a general BDFp temporal discretizations. |
-
22/2012 - 05/11/2012
Ettinger, B.; Passerini, T.;Perotto, S.; Sangalli, L.M.
Regression models for data distributed over non-planar domains | Abstract | | We consider the problem of surface estimation and spatial smoothing over non-planar domains. In particular, we deal with the case where the data or signals occur on a domain that is a surface in a three-dimensional space. The application driving our research is the modeling of hemodynamic data, such as the shear stress and the pressure exerted by blood flow on the wall of a carotid artery. The regression model we propose consists of two key phases. First, we conformally map the surface domain to a region in the plane. Then, we apply existing regression methods for planar domains, suitably modified to respect the geometry of the original surface
domain. |
-
21/2012 - 05/01/2012
Guglielmi, A.; Ieva, F.; Paganoni, A.M.; Ruggeri, F.; Soriano, J.
Semiparametric Bayesian models for clustering and classification in presence of unbalanced in-hospital survival | Abstract | | In this work, Bayesian semiparametric logit models are fitted to grouped data related to in-hospital survival outcome of patients hospitalised with ST-segment Elevation Myocardial Infarction diagnosis. Dependent Dirichlet Process priors are considered for modelling the random-effects distribution of the grouping factor (hospital of admission), in order to provide a cluster analysis of the hospitals. The clustering structure is highlighted through the optimal random partition that minimises the posterior expected value of a suitable loss function. Two are the main goals of the work: to provide model-based clustering and ranking of the providers according to the similarity of their effect on patients’ outcome, and to make reliable predictions on the survival outcome at patient’s level, even when the survival rate itself is strongly unbalanced. The study is within a project, named Strategic Program of Regione Lombardia, and is aimed at supporting decisions in healthcare policies. |
-
20/2012 - 04/24/2012
Ieva, F.; Paganoni, A. M.; Zanini, P.
Statistical models for detecting Atrial Fibrillation events | Abstract | | Atrial Fibrillation is the most common cardiac arrhythmia that naturally tends to become a chronic condition and chronic Atrial Fibrillation leads to an increase in the risk of death. The study of time series of time intervals between an R peak in the electrocardiogram and the following one is an effective way to investigate the presence of Atrial Fibrillation and to detect when a single event starts and ends. This work presents a new statistical method to deal with identification of Atrial Fibrillation events. Some simulations in order to assess the performances of the proposed method are detailed and the results
obtained applying this method to real data concerning patients affected by Atrial Fibrillation are discussed. |
-
19/2012 - 04/15/2012
Faggiano, E.; Antiga, L.; Puppini, G.; Quarteroni, A.; Luciani G.B.; Vergara, C.
Helical Flows and Asymmetry of Blood Jet in Dilated Ascending Aorta with Normally Functioning Bicuspid Valve | Abstract | | Bicuspid aortic valve (BAV) is associated with aortic dilatation and aneurysm.
Several studies evidenced an eccentric systolic flow in ascending aorta associated to increased wall shear stresses (WSS) and the occurrence of an helical systolic flow.
This study seeks to elucidate the connections between jet asymmetry and helical flow in patients with normally functioning BAV and dilated ascending aorta.
We performed a computational parametric study by varying, for a patient-specific geometry,
the valve area and the flow rate entering the aorta and drawing also a tricuspid valve (TAV).
We considered also phase contrast magnetic resonance imaging of four BAV and TAV patients.
Measurement of normalized flow asymmetry (NFA) index,
systolic WSS and of a new index (positive helic fraction, PHF) quantifying the presence of a single helical flow, were performed.
In our computation, BAV cases featured higher values of all indices with respect to TAV in both numerical and imaged-based results.
Moreover, all indices increased with decreasing valve area and/or with increasing flow rate.
This allows us to identify two groups for BAV: the former with valve/root area ratio r=0.29 and systolic flow rate F>18 l/min, or for r<0.29, featuring high indices values (NFA>0.45 and PHF>0.8), and the latter featuring intermediate values (0.2 |
-
18/2012 - 04/14/2012
Formaggia, L.; Vergara, C.
Prescription of general defective boundary conditions in fluid-dynamics | Abstract | | This work reviews and extends to a more general setting some strategies
to impose defective boundary conditions to fluid-dynamic problems investigated
by the authors in the last years. We focus here to the steady Stokes
problem as a paradigm for the unsteady and non-linear cases. We show
the well posedness of the proposed approaches and discuss their relative
benefits. |
-
17/2012 - 03/20/2012
Manzoni, A.; Quarteroni, A.; Gianluigi Rozza, G.
Computational reduction for parametrized PDEs: strategies and applications | Abstract | | In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of the reduced basis method, focusing on greedy algorithms for the construction of the reduced spaces. An alternative family of reduction techniques based on surrogate response surface models is briefly recalled too. Then, a simple example dealing with inviscid flows is presented, showing the reliability of the reduced basis method and a comparison between this technique and some surrogate models. |
|
