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 1148 prodotti
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14/2007 - 06/09/2007
Dede', L.
Reduced Basis Method for Parametrized Advection-Reaction Problems | Abstract | | In this work we consider the Reduced Basis method for the solution of parametrized advection-reaction partial differential equations. For generation of the basis we adopt a stabilized Finite Element method and we define the Reduced Basis method in the primal-dual formulation for this stabilized problem. We provide both a priori and a posteriori Reduced Basis error estimates and we discuss the effects of the Finite Element approximation on the Reduced Basis error. We propose an adaptive algorithm for the selection of the sample sets upon which thew basis are built. The basis idea of this algorithm is the minimization of the computational costs associated with the solution of the Reduced Basis problem. Numerical tests shows the convenience, in terms of computational costs, of the prime-dual Reduced Basis approach. |
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13/2007 - 30/08/2007
Zunino Paolo
Discontinuous Galerkin methods based on weighted interior penalties for second order PDEs with non-smooth coefficients | Abstract | | We develop and analyze a Discontinuous Galerkin (DG) method based on weighted interior penalties (WIP) applied to second order PDEs and in particular to advection-diffusion-reaction equations featuring non-smooth and possibly vanishing diffusivity.
First of all, looking at the derivation of a DG scheme with a bias to domain decomposition methods, we carefully discuss the set up of the discretization scheme in a general framework putting into evidence the helpful role of the weights and the connection with the well known Local Discontinuous Galerkin schemes (LDG).
Then, we address the a-priori and the a-posteriori error analysis of the method, recovering optimal error estimates in suitable norms. By virtue of the introduction of the weighted penalties, these results turn out to be robust with respect to the diffusion parameter.
Furthermore, we discuss the derivation of an a-posteriori local error indicator suitable for advection-diffusion-reaction problems with higly variable, locally small diffusivity.
Finally, all the theoretical results are illustrated and discussed by means of numerical experiments.
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12/2007 - 27/07/2007
Deponti, Alberto; Bonaventura, Luca; Rosatti; Giorgio, Garegnani, Giulia
An Accurate and Efficient Semi-Implicit Method for Section Averaged Free Surface Flow Modelling | Abstract | | An accurate, efficient and robust numerical method for the
solution of the section averaged equations of open channel flow is
presented and discussed.
The method allows for river sections of arbitrary shape and for arbitrary bottom topography. The continuity equation is formulated in a conservative fashion, while a non conservative form is chosen for the momentum equation, thus avoiding the need for well balanced schemes to handle rapidly varying bathymetry.
In order to achieve unconditional stability with respect to flow celerity, a semi-implicit time discretization is introduced, which requires the solution of a weakly nonlinear system for the free surface at each time step by a fixed point iteration technique.
A semi-Lagrangian discretization is introduced, to achieve full unconditional stability and increase efficiency at no accuracy loss in subcritical flow regimes.
An appropriate upwind discretization is also introduced for the momentum equation, which allows to recover correct solutions also in presence of discontinuities and strong gradients. Numerical experiments show that the semi-Lagrangian method yields indeed accurate results also in the case of stationary hydraulic jumps.
The model is validated in a wide range of
idealised test cases, highlighting its accuracy and efficiency
characteristics, especially for long time range simulations of subcritical river
flow. Finally, a first model validation on realistic data is presented, concerning simulations of flooding events of the Adda river.
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11/2007 - 26/07/2007
Badia, Santiago; Nobile, Fabio; Vergara, Christian
Fluid-structure partitioned procedures based on Robin transmission conditions | Abstract | | In this article we design new partitioned procedures for fluid-structure
interaction problems, based on Robin-type transmission conditions. The
choice of the coefficient in the Robin conditions is justified via simplified
models. The strategy is effective whenever an incompressible fluid interacts
with a relatively thin membrane, as in haemodynamics applications. We
analyze theoretically the new iterative procedures on a model problem,
which represents a simplified blood-vessel system. In particular, the Robin-
Neumann scheme exhibits enhanced convergence properties with respect to
the existing partitioned procedures. The theoretical results are checked
using numerical experimentation.
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10/2007 - 28/04/2007
Parolini, Nicola; Quarteroni, Alfio
Modelling and Numerical Simulation for Yacht Engineering | Abstract | | In the past few years, Computational Fluid Dynamics (CFD) has become an essential tool in the design and optimization of racing sailboats and in particular America s Cup yachts.
The prevalent role of CFD in the design
process is demonstrated by the number of numerical simulations on different boat features, ranging from hull and appendage design to sail optimization, that each America s Cup syndicate carries on during the boat design and its further development.
In this work, we report some of the numerical results obtained in the framework of the research partnership between the Ecole Polytechnique Fédérale de Lausanne (EPFL) and the Alinghi Team, in preparation to the 32nd edition of the America s Cup.
A particular attention is devoted to the innovative aspects of the numerical models that have been recently developed. |
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09/2007 - 21/04/2007
May, Caterina; Flournoy, Nancy
Asymptotics in response-adaptive designs generated by a two-colors, randomly reinforced urn | Abstract | | This paper illustrates asymptotic properties for a response-adaptive
design generated by a two-color, randomly reinforced urn model. The
design considered is optimal in the sense that it assigns patients to
the best treatment with probability converging to one. An approach
to show the joint asymptotic normality of the estimators of the mean
responses to the treatments is provided in spite of the fact that allocation
proportions converge to zero and one. Results on the rate of
convergence of the number of patients assigned to each treatment are
also obtained. Finally, we study the asymptotic behavior of a suitable
test statistic.
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08/2007 - 14/04/2007
Formaggia, Luca; Miglio, Edie; Mola, Andrea; Parolini, Nicola
Fluid-structure interaction problems in free surface flows: application to boat dynamics | Abstract | | We present some recent studies on fluid-structure
interaction problems in the presence of free surface flow. We consider
the dynamics of boats simulated as rigid bodies. Several hydrodynamic
models are presented, ranging from full Reynolds Averaged
Navier-Stokes equations down to reduced models based on potential flow
theory.
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07/2007 - 22/03/2007
Ern, Alexandre; Stephansen, Annette F.; Zunino, Paolo
A Discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally vanishing and anisotropic diffusivity | Abstract | | We consider Discontinuous Galerkin approximations of advection-diffusion equations with anisotropic and discontinuous diffusivity, and propose the symmetric weighted interior penalty (SWIP) method for better coping with locally vanishing diffusivity. The analysis yields convergence results for the natural energy norm that are optimal (with respect to mesh-size) and robust (fully independent of the diffusivity). The convergence results for the advective derivative are optimal with respect to mesh-size and robust for isotropic diffusivity, as well as for anisotropic diffusivity in the dominant advection regime. In the dominant diffusivity regime, an optimal convergence result for the the $L^2$-norm is also recovered.
Numerical results are presented to illustrate the performance of the scheme.
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