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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MOX 26 - 29/09/2003
Saleri, Fausto; Veneziani, Alessandro
Pressure-correction algebraic splitting methods for the incompressible navier-stokes equations | Abstract | | In this paper we present a new family of methods for the effective numerical solution of the incompressible unsteady Navier-Stokes equations. These methods resort to an algebraic splitting of the discretized problem based on inexact LU block-factorizations of the corresponding matrix (following [21]). In particular, we will start from inexact algebraic factorizations of algebraic Chorin-Temam and Yosida type and introduce a pressure correction step aiming at improving the time accuracy. one of the schemes obtained in this way (the Algebraic Chorin-Temam Pressure Correction Method) resembles a method previously introduced in the framework of differential projection schemes (see [24], [19]). The stability and the dependence of splitting error on the time step of the new methods is investigated and tested on several numerical cases. |
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MOXP1 - 10/09/2003
Formaggia, Luca; Micheletti, Stefano; Savini, Barbara
Modellazione Bidimensionale e Simulazione Numerica del Funzionamento di una Candeletta di Preriscaldo
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MOX 25 - 29/07/2003
Ballestra, Luca V.; Sacco, Riccardo
Numerical Problems in Semiconductor Simulation Using the Hydrodynamical Model: a Second-Order Finite Difference Scheme | Abstract | | In this paper a second-order Total Variation Diminuishing (TVD) finite diffence scheme of upwind type is employed for the numerical approximation of the classical hydrodynamic model for semiconductors proposed byB. and Baccarani-Wordeman. In particular, the high-order hyperbolic fluxes are evaluated by a suitable extrapolation on adjacent cell of the first-order fluxes of Roe, while total variation diminuishing is achieved by limiting th slopes of the discrete Riemann invariants using the so-called Flux Corrected Transport approach.
Extensive numerical simulations are performed on a submicron n^+ - n - n^+ ballistic diode. The numerical experiments show that the spurious oscillations arising in the electron current are not completely suppressed by the TVD scheme, and can lead to serious numerical instabilities when the solution of the hydrodynamic model is non-smooth and the computational mesh is coarse.
The accuracy of the numerical method is investigated in terms of conservation of the steady electron current. The Obtained results show that the second-order scheme does not behave much better than a corresponding first-order one due to a poor performance of the slope limiters caused by the presence of local extrema of the Riemann invariant associated with the hyperbolic system. |
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MOX 24 - 07/07/2003
Quarteroni, Alfio; Rozza, Gianluigi
Optimal Control and Shape Optimization of Aorto-Coronaric Bypass | Abstract | | In this paper we present a new approach in the study of
Aorto-Coronaric bypass anastomoses configurations. The theory of
optimal control based on adjoint formulation is applied in order
to optimize the shape of the zone of the incoming branch of the
bypass into the coronary.
The aim is to provide design indications in the perspective of
future development for prosthetic bypasses. With a reduced model
based on Stokes equations and a vorticity functional in the down
field zone of bypass, a Taylor like patch is found. A feedback
procedure with Navier-Stokes fluid model is proposed, based on the
analysis of wall shear stress and its related indexes such as OSI |
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MOX 23 - 23/06/2003
Paganoni, Anna Maria; Secchi Piercesare
Interacting reinforced urn systems | Abstract | | We introduce a class of a discrete time stochastic processes generated by interacting systems of reinforced urns. We show that such processes are asymptotically partially exchangeable and we prove a strong law of large numbers. Examples and the analysis of particular cases show that interacting reinforced urn systems are very flexible representations for modelling countable collections of dependents and asymptotically exchangeable sequences of random variables. First published in: Advances in Applied Probability - Vol. 36 No.3 (September 2004) by The Applied Probability Trust. |
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MOX 22 - 13/06/2003
Formaggia, Luca; Nobile, Fabio
Stability analysis of second ordr time accurate schemes for ALE-FEM | Abstract | | In this work we will introduce and analyze the Arbitrary Lagrangian Eulerian formulation for a model problem of a scalar advection diffusion equation defined on a moving domain. Moving from the results illustrated in our previous work of the same authors we will consider first and second order time advancing schemes and analyze how the movement of the domain might affect accuracy and stability properties of the numerical schemes with respect to their counterpart on fixed domains. Theoretical and numerical results will be presented, showing that stability properties are not, in general preserved while accuracy is maintained. |
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MOX 21 - 09/06/2003
Formaggia, Luca; Veneziani, Alessandro
Reduced and multiscale models for the human cardiovascular system | Abstract | | This report collects the notes of two lectures given by L. Formaggia at VKI Lecture Series on Biological Fluid Dynamics held at the Von Karman Institute, Belgium, on May 2003.
Tyhey give a summary of some aspects of the research activity carried out by the authors at Politecnico di Milano and at EPFL, Lausanne, under the direction of prof. Alfio Quarteroni, aimed at providing mathematical models and numerical techniques for the simulation of the human cardiovascular system.
This report is subdivided in two chapters, in correspondence with the two lectures. The first deals with the derivation of one dimensional models for blood flow in arteries. The second is more specifically devoted to the description and analysis of the geometrical multiscale technique. |
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MOX 20 - 26/05/2003
Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo
A multiscale formulation of the discontinuous Petrov-Galerkin method for advective-diffusive problems | Abstract | | We consider the Discontinuous Petrov-Galerkin method for the advection-diffusion model problem and we investigate the application of the variational multiscale method to this formulation. We show the exact modeling of the fine scale modes at the element level for the linear case, and we discuss the approximate modeling both in the linear and in the non-linear cases. Furthermore, we highlight the existing link between this multiscale formulation and the $p$ version of the finite element method. Numerical examples illustrate the behavior of the proposed scheme. |
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