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 1152 products
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MOX 25 - 07/29/2003
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 - 06/23/2003
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 - 06/13/2003
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 - 06/09/2003
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 - 05/26/2003
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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MOX 19 - 05/07/2003
Causin, Paola; Sacco, Riccardo
A discontinuous Petrov-Galerkin method with Lagrangian multipliers for second order elliptic problems | Abstract | | We present a discontinuous Petrov-Galerkin method (DPG) for finite element discretization scheme of second order elliptic boundary value problems. The novel approach emanates from a one-element weak formulation of the differential problem (that is typical of Discontinuous Galerkin methods (DG)) which is based on introducing variables defined in the interior and on the boundary of the element. The interface variables are suitable Lagrangian multipliers that enforce interelement continuity of the solution and of its normal derivate, thus providing the proper connection between neighboring elements. The internal variables can be eliminated in favor of the interface variables using static condensation to end up with a system of reduced size having as unknowns the Lagrangian multipliers. A stability and convergence analysis of the novel formulation is carried out and its connection with mixed-hybrid and DG method is explored. Numerical tests on several benchmark problems are included to validate the convergence perfomance and the flux-conservation properties of the DPG method. |
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MOX 18 - 04/16/2003
Causin, Paola; Restelli, Marco; Sacco, Riccardo
A simulation system based on mixed-hybrid finite elements for thermal oxidation in semiconductor technology | Abstract | | In this work we deal with the numerical simulation of thermal oxidation in silicon device technology. This application involves the coupled solution of a diffusion-reaction problem and of a fluid-structure interaction problem. These two problems are mutually dependent through the exchange of stresses and fluxes that are typically post-processed fields in standard finite element approaches, and as such they may suffer form a lack of accuracy and from physical inconsistencies. In this article, we propose a novel approach to the simulation of the thermal oxidation process, that is characterized by the use of mixed and hybrid finite elements. the main advantage of such formulations is that stresses and fluxes are directly computed quantities, rather than obtained from post-processing techniques. We also address the procedures and the techniques that must be devised for handling the coupled interaction problem and the presence of a computational grid moving in time. The numerical approach we propose is eventually validated on a realistic example of the thermal oxidation process in a local oxidation structure (LOCOS) |
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