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 1251 products
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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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34/2009 - 12/14/2009
Antonietti, Paola F.; Houston, Paul
A Class of Domain Decomposition Preconditioners for hp-Discontinuous Galerkin Finite Element Methods | Abstract | | In this article we address the question of efficiently solving the algebraic linear system of equations arising from the discretization of a symmetric, elliptic boundary value problem using hp-version discontinuous Galerkin finite element methods. In particular, we introduce a class of domain decomposition preconditioners based on the Schwarz framework, and prove bounds on the condition number of the resulting iteration operators. Numerical results con rming the theoretical estimates are also presented. |
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33/2009 - 11/11/2009
Vantini, Simone
On the Definition of Phase and Amplitude Variability in Functional Data Analysis | Abstract | | We introduce a mathematical framework in which a functional data registration problem can be soundly and coherently set. In detail, we show
that the introduction of a metric/semi-metric and of a group of warping function respect to which the metric/semi-metric is invariant is the key to
a clear and not ambiguous de nition of phase and amplitude variability.
Moreover, an amplitude-to-total variability index is proposed. This index turns to be useful in practical situations to measure to what extent amplitude variability a ects the data and to compare the e ectiveness of diff erent
registration methods. |
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32/2009 - 11/10/2009
Micheletti, Stefano; Perotto, Simona
Anisotropic adaptation via a Zienkiewicz-Zhu error estimator for 2D elliptic problems | Abstract | | We propose a Zienkiewicz-Zhu a posteriori error estimator in 2D, which shares the computational advantages typical of the original estimator. The
novelty is the inclusion of the geometrical features of the computational mesh, useful for an anisotropic mesh adaptation. The adapted triangulations are shown numerically to be quasi-optimal with respect to the error-vs-number
of elements behaviour. |
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