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 1349 prodotti
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MOX 80 - 31/01/2006
Ponzini, R.; Vergara, Christian; Redaelli, A.; Veneziani, Alessandro
Reliable CFD-based estimation of flow rate in haemodynamics measures | Abstract | | Physical useful measures in current clinical practice refer often to the blood ow rate, that is related to the mean velocity. However, the direct measure of the latter is currently not possible using a Doppler velocimetry technique. Therefore, the usual approach to calculate the
ow rate with this technique consists in measuring the maximum velocity and in estimating the
mean velocity, making the hypothesis of parabolic profile, that in realistic situations brings to strongly inaccurate estimates. In this paper, we propose a different way for estimating the
ow rate regarded as a function of maximum velocity and Womersley number. This relation is obtained by fixing a parametrized representation and by evaluating the parameters by means of a least square approach working on the numerical results of CFD simulations (about 200). Numerical simulations are carried out by prescribing the
ow rate, not the velocity profile. In this way, no bias are implicitly induced in prescribing boundary conditions. Validation tests based on numerical simulations show that the proposed
relation improves the flow rate estimation. |
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MOX 79 - 30/01/2006
Quarteroni, Alfio; Rozza, Gianluigi; Quaini, Annalisa
Reduced basis methods for optimal control of advection-diffusion problems | Abstract | | The reduced basis (RB) method is proposed for the
approximation of multiparametrized
equations governing an optimal control problem. The idea
behind the RB method is to project the solution onto a space of small
dimension, specifically designed on the problem at hand, and to decouple
the generation and projection stages (off-line/on-line computational
procedures)
of the approximation process in order to solve parametrized equations
in a rapid and not expensive way.
The application that we investigate is an air pollution control problem: we
aim at regulating the emissions of industrial chimneys in order to keep the
pollutant concentration below a certain threshold over an observation area,
like a town. Adopting the RB method for both state and adjoint equations
of the optimal control problem leads to important computational savings
with respect to the use of the Galerkin-finite element method. We consider
different parametrization (control, physical and geometrical input
parameters)
so that we are able to solve the control problem from a global and
decisional point of view.
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MOX 78 - 23/01/2006
Agoshkov, Valery; Gervasio, Paola; Quarteroni, Alfio
Optimal Control in Heterogeneous Domain Decomposition Methods for Advection-Diffusion Equations | Abstract | | New domain decomposition methods (DDM) based on optimal control approach are introduced for the coupling of first and second order equations on overlapping subdomains. Several cost functionals and control functions are proposed. Uniqueness and existence results are proved for the coupled problem, and the convergence of iterative processes is analyzed.
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MOX 77 - 16/01/2006
Quarteroni, Alfio
What mathematics can do for the simulation of blood circulation | Abstract | | In this paper we introduce some basic differential models for the description of blood flow in the circulatory system. We comment on their mathematical properties, their meaningfulness and their limitation to yield realistic and accurate numerical simulations, and their contribution for a better understanding of cardiovascular physio-pathology.
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MOX 76 - 13/01/2006
Formaggia, Luca; Micheletti, Stefano; Sacco, Riccardo; Veneziani, Alessandro
Mathematical modelling and numerical simulation of a glow-plug | Abstract | | In this work we derive a mathematical model that
describes the working of a glow-plug of the type used in Diesel engines
to preheat the air-diesel fuel mixture.
The proposed model consists of a time dependent one dimensional
partial differential equation which incorporates the electro-thermal
interaction between the electric current flowing in the plug and the
temperature.
It has been obtained by integrating the heat
equation on each section of the plug, assuming axial symmetry and using
thermal equilibrium relation in the radial direction. The problem is
highly non-linear because of the radiation boundary conditions and the
dependence on temperature of several parameters. In particular, heat
is generated by an electric resistance whose characteristic strongly
depends on temperature.
We have adopted a quasi-Newton treatment of the non-linear term and a
mixed finite element formulation for the linearized problem. Time
advancing has been carried out using a semi-implicit Euler scheme.
Several numerical simulations have been carried in order to assess the
validity of the model, whose predictions have been compared with
available experimental data.
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MOX 75 - 12/01/2006
Baudisch, J.; Bonaventura, Luca; Iske, A.; Miglio, Edie
Matrix valued Radial Basis Functions for local vector field reconstruction: applications to computational fluid dynamic models | Abstract | | Matrix valued radial basis functions
are applied to achieve accurate local vector field reconstructions of smooth vector fields from normal components assigned at the edges of a computational mesh. The theory underlying this reconstruction approach is reviewed and reformulated so as to allow for more straightforward application.
The accuracy of the locally reconstructed fields is assessed by appropriate numerical tests. Applications to numerical models for geophysical fluid dynamics problems show that such reconstruction techniques can usefully complement low order discretization approaches with important discrete conservation properties.
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MOX 74 - 14/12/2005
Aletti, G.; May, C.; Secchi, Piercesare
On the distribution of the limit proportion for a two-color, randomly reinforced urn with equal reinforcement distributions | Abstract | | We consider a two-color randomly reinforced urn with equal reinforcement distributions and we characterize the distribution of the urn s limit proportions as the unique continous solution of a functional equation involving unknown probability distributions on [0.1]. |
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MOX 73 - 13/12/2005
Caliò, Franca Miglio, Edie Moroni, G. Rasella, M.
Curve fairing using integral spline operators | Abstract | | In this paper a local automatic planar curve fairing algorithm based parametric B-spline class is presented. In particular we employ a particular class of spline characterized by a shape parameterer lambda: for this family of spline it has been shown (see [9]) that the value of the parameter affects the shape of the whole spline curve. We have exploited this last property locally in order to move a subset of the control points defining the given curve. In our approach the value of lambda is chosen in order
to minimize a functional related to the fairness of the curve and in particular we have considered a functional involving the second derivative of the curvature. The numerical test cases we have performed showed the effectiveness of algorithm both in academic and real-world situations.
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