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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07/2010 - 02/24/2010
Sangalli, Laura M.; Secchi, Piercesare; Vantini, Simone; Vitelli, Valeria
Functional clustering and alignment methods with applications | Abstract | | We consider the issue of classification of functional data and, in particular, we deal with the problem of curve clustering when curves are misaligned. In the proposed setting, we aim at jointly aligning and clustering the curves, via the solution of an optimization problem. We describe an iterative procedure for the solution of the optimization problem, and we detail two alternative specifications of the procedure, a k-mean version and a k-medoid version. We illustrate via applications to real data the robustness of the alignment and clustering procedure under the different specifications. |
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06/2010 - 02/23/2010
Alastruey, Jordi; Passerini, Tiziano; Formaggia, Luca; Peirò, Joaquim
The effect of visco-elasticity and other physical properties on aortic and cerebral pulse waveforms: an analytical and numerical study | Abstract | | The nonlinear one-dimensional equations of blood flow in Voigttype visco-elastic vessels are numerically solved using both a Taylor-Galerkin and a discontinuous Galerkin scheme to study the effects on aortic and cerebral pulse waveforms of wall visco-elasticity, fluid viscosity, wall compliances and resistances, flow inertia, cardiac ejection, and outflow pressure. A linear analysis of these equations shows that wave dispersion and dissipation is caused by wall viscosity at high frequencies and fluid viscosity at low frequencies. During approximately the last three fourths of diastole the inertial effects of the flow can be neglected, and pressures tend to a space-independent shape dictated by global quantities (cardiac ejection, total peripheral resistance and compliance, and outflow pressure) and the viscous modulus of each arterial segment. During this period, the area-pressure curve reduces to a line whose slope provides a better approximation to the local pulse wave speed than do current techniques based on simultaneous pressure and velocity measurements. The viscous modulus can be estimated from the area of the area-pressure loop. Our findings are important for the identification and estimation of haemodynamic quantities related to the prevention, diagnosis and treatment of disease.
Keywords: Pulse wave propagation; pulse wave speed; circulatory system; circle of Willis; one-dimensional modelling; Voigt-type viscoelasticity; Taylor-Galerkin methods; discontinuous Galerkin methods. |
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05/2010 - 02/22/2010
Longoni, Matteo; Malossi, A.C.I.; Quarteroni, Alfio; Villa, Andrea
A complete model for non-Newtonian sedimentary basins in presence of faults and compaction phenomena | Abstract | | In this paper we present a model and a complete numerical tool for simulating the three-dimensional dynamics of realistic stratified
sedimentary basins. We developed dedicated mathematical algorithms to include most of the key physical aspects such as the movement of
the basement, the non-Newtonian behavior of the sediments, the effects of faults and the presence of compaction phenomena. This approach is mandatory to capture all the three-dimensional effects of realistic evolution dynamics, whose duration is about millions of years and to provide reliable results. In this work we apply our methods to a realistic and topologically complex sedimentary system. |
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04/2010 - 01/18/2010
Discacciati, Marco; Gervasio, Paola; Quarteroni, Alfio
Heterogeneous mathematical models in fluid dynamics and associated solution algorithms | Abstract | | Mathematical models of complex physical problems can be based on heterogeneous differential equations, i.e. on boundary-value problems of
different kind in different subregions of the computational domain. In this presentation we will introduce a few representative examples, we will illustrate the way the coupling conditions between the different models can be devised, then we will address several solution algorithms and discuss their properties of convergence as well as their robustness with respect to the variation of the physical parameters that characterize the submodels. |
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03/2010 - 01/15/2010
Farrell, P.E.; Micheletti, Stefano; Perotto, Simona
A recovery-based error estimator for anisotropic mesh adaptation in CFD | Abstract | | We provide a unifying framework that generalizes the 2D and 3D settings proposed in [32] and [17], respectively. In these two works we propose
a gradient recovery type a posteriori error estimator for finite element approximations
on anisotropic meshes. The novelty is the inclusion of the geometrical features of the computational mesh (size, shape and orientation)
in the estimator itself. Moreover, we preserve the good properties of recovery based error estimators, in particular their computational cheapness and ease of implementation. A metric-based optimization procedure, relying on the estimator, drives the anisotropic adaptation of the mesh. The focus of this work then moves to a goal-oriented framework. In particular,
we extend the idea proposed in [32, 17] to the control of a goal functional.
The preliminary results are promising, since it is shown numerically to yield quasi-optimal triangulations with respect to the error-vs-number of elements behaviour. |
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02/2010 - 01/14/2010
Barbieri, P.; Grieco, N.; Ieva, F.; Paganoni, A. M.; Secchi, P.
Exploitation, integration and statistical analysis of Public Health Database and STEMI archive in Lombardia Region | Abstract | | In this work we describe nature and aims of the Strategic Program Exploitation, integration and study of current and future health databases in
Lombardia for Acute Myocardial Infarction . The main goal of the Program is the construction and statistical analysis of data coming from the integration of complex clinical and administrative databases concerning patients
with Acute Coronary Syndromes treated in Lombardia Region. Clinical data sets arise from observational studies about specific diseases, while administrative data arise from standardized and on-going procedures of data collection. The linkage between clinical and administrative databases enables Lombardia Region to create an efficient global system for collecting
and storing integrated longitudinal data, to check them, to guarantee for their quality and to study them from a statistical perspective. |
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01/2010 - 01/13/2010
Porta, G.M.; Perotto, S.; Ballio, F.
Anisotropic Mesh Adaptation Driven by a Recovery-Based Error Estimator for Shallow Water Flow Modeling | Abstract | | Focus of the paper is to propose an e ffective anisotropic mesh adaptation procedure for the solution of the shallow water equations. The hyperbolic partial di fferential equation system is solved via the streamline diff usion
finite element method, suitably corrected by a shock capturing contribution.
The proposed adaptation procedure relies on a recovery-based error estimator. In particular we look for an anisotropic error estimator able to
select not only the size, but also the shape and the orientation of the mesh elements, with the aim of optimizing the computational advantages yielded by mesh adaptation. The robustness of the proposed estimator is tested fi rst in a purely diffusive setting and then on two steady shallow water problems, with known analytical solution. Finally we discuss the reliability
of the adaptation procedure on a real-scale unsteady confi guration. |
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35/2009 - 12/15/2009
D'Angelo, Carlo; Zunino, Paolo
Robust numerical approximation of coupled Stokes and Darcy flows applied to vascular hemodynamics and biochemical transport | Abstract | | The fully coupled description of blood flow and mass transport in blood vessels requires extremely robust numerical methods. In order to handle the heterogeneous coupling between blood flow and plasma filtration, addressed by
means of Navier-Stokes and Darcy’s equations, we need to develop a numerical scheme capable to deal with extremely variable parameters, such as the blood viscosity and Darcy’s permeability of the arterial walls.
In this paper, we describe a finite element method for the approximation of incompressible flow coupled problems. We exploit stabilized mixed finite elements together with Nitsche type matching conditions that automatically
adapt to the coupling of different combinations of coefficients. We study in details the stability of the method using weighted norms, emphasizing the robustness of the stability estimate with respect to the coefficients. We also
consider an iterative method to split the coupled heterogeneous problem in possibly homogeneous local problems, and we investigate the spectral properties of suitable preconditioners for the solution of the global as well as local
problems.
Finally, we present the simulation of the fully coupled blood flow and plasma filtration problems on a realistic geometry of a cardiovascular artery
after the implantation of a drug eluting stent (DES). A similar finite element method for mass transport is then employed to study the evolution of the drug released by the DES in the blood stream and in the arterial walls, and the role of plasma filtration on the drug deposition is investigated.
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