Quaderni di Dipartimento

Quaderni MOX

• MOX 42 - 21/05/2004
  Rozza, Gianluigi
  Optimization, Control and Shape Design of an Arterial Bypass

  Abstract

  Abstract

  We present multi-level geometrical approaches in the study of aortocoronaric bypass anastomoses configurations. The theory of optimal control based on adjoint formulation is appliedin order to optimize the shape of the incoming branch of the bypass (the toe) into the coronary. At this level two possibile options are available in shape design: one implements local boundary variations in computational domain, the other is based on a linearized design in a suitable reference domain through the theory of small perturbations. At a coarser level, reduced basis methodologies based on parametrized partial differential equations are developed to provide (a) a sensitivity analysis for geometrical quantities of interest in bypass configurations and (b) rapid and reliable prediction of integral functional outputs. The aims is (i) to provide design indications for arterial surgery in the perspective of future development for prosthetic bypasses, (ii) to develop multi-level numerical methods for optimization and shape design by optimal control, and (iii) to provide an input-output relationship led by models with lower complexity and computational costs. We have numerically investigated a reduced model based on Stokes equations a vorticity cost functional (to be minimized) in the down-field zone of by-pass. In local shape design procedure a Taylor like patch has been found. A feedback procedure with Navier-Stokes fluid model is proposed based on the analysis of wall shear stress and its related indexes of interest.

• MOX41 - 19/05/2004
  Muliere, Pietro; Paganoni, Anna Maria; Secchi, Piercesare
  A two-color, randomly reinforced urn

  Abstract

  Abstract

  We study an urn containing balls of two or more colors. The urn is sequentially sampled. Each time a ball is extracted from the urn it is reintroduced in it togheter with a random number of balls of the same color: the distribution of the number of added balls may depend on the color extracted. We prove asymptotic results for the process of its compositions. Applications to sequential clinical trials are considered as well as connections with adaptive design of experiments in Bayesian framework.

• MOX 40 - 14/05/2004
  de Falco, Carlo; Gatti, Emilio; Lacaita, Andrea L.; Sacco, Riccardo
  Quantum-Corrected Drift-Diffusion Models for Transport in Semiconductor Devices

  Abstract

  Abstract

  In this article, we propose a unified framework for Quantum-Corrected Drift-Diffusion (QCDD) models in nanoscale semiconductor device simulation. QCDD models are presented as a suitable generalization of the classical Drift-Diffusion (DD) system, each particular model being identified by the constitutive relation for the quantum-correction to the electric potential. We examine two special, and relevant, examples of QCDD models the first one is the modified DD model named Schroedinger-Poisson-Drift-Diffusion, and the second one is the Quantum-Drift-Diffusion QDD model. For the decoupled solution of the two models, we introduce a functional iteraction technique that extends the classical Gummel algotithm widely used in the iterative solution of the DD system. We discuss the finite element discretization of the various differential subsystems, with special emphasis on their stability properties, and illustrate the performance of the proposed algorithms and models on the numerical simulation of nanoscale devices in two spatial dimensions.

• MOX 39 - 10/05/2004
  Parolini, Nicola; Quarteroni, Alfio
  Mathematical Models and Numerical Simulation for the America s Cup

  Abstract

  Abstract

  This paper presents a review of the mathematical models which can be adopted to describe the different physical phenomena characterizing the flow around a sailing yacht. The complete model accounting for the laminar-turbulent transition regime, free-surface dynamics and fluid-sails interaction is introduced as long as some simplified models that have been used to reduce the computational complexity. Drawing on the experience of the Ecole Polytechnique Fédérale de Lausanne (EPFL) as Official Scientific Advisor to the Alinghi Team, winner of 2003 America s Cup, we discuss the role of Computational Fluid Dynamics simulations based on Reynolds Averages Navier-Stokes (RANS) equations and their integration in standard yacht design process. Numerical results in different areas (appendages design, free-surface flows, aerodynamics of sails) are presented and discussed.

• MOX 38 - 20/04/2004
  Fumagalli, Elena; Lo Schiavo,Luca; Salvati, Simonetta; Secchi,Piercesare
  Statistical Identification of Major Event Days: An Application to Continuity Of Supply Regulation In Italy

  Abstract

  Abstract

  The Italian regulatory mechanism for quality of service in electricity distribution links the tariff to the SAIDI indicator of average duration of interruptions per consumer. In order to separate major interruption events data from normal operation data the regulator introduced, in the year 2000, a criterion based on a given definition of Force Majeure. For the new regulatory period, beginning in 2004, the authors studied the possibility of substituting this criterion with one based on a statistical definition of major event days. The statistical two step methodology proposed here was tested using real data, compared with other statistical criteria found in the literature, and proposed to interested parties in the consultation process. It was found to be at the same time equitable, unambiguous and simple to implement. This criterion was thus adopted in the new regulatoy framework.

• MOX 36 - 16/04/2004
  Miglio, Edie; Perotto, Simona; Saleri, Fausto
  Strategies of model coupling: application to free surface flow problems

  Abstract

  Abstract

  The motion of water in a complex hydrodynamic configuration is characterized by a wide spectrum of space and time scales, due to coexistence of physical phenomena of different nature. Consequently, the numerical simulation of a hydrodynamic system of this type is characterized by a large computational cost. In this paper, after introducing a quite general setting for model coupling, we discuss two techniques to reduce such a computational effort by suitably coupling different hydrodynamic models. The first approach is based on a dimensionally heterogeneous-physically homogeneous coupling strategy driven a priori physical considerations. As second strategy we suggest a dimensionally homogeneous-physically heterogeneous coupling. This time the subdomain-to-model correspondence is identified automatically thanks to a suitable a posteriori modeling error estimator. The range of applicability of both the approaches is finally examined on some test cases.

• MOX 37 - 16/04/2004
  Micheletti, Stefano; Perotto, Simona
  Reliability and efficiency of an anisotropic Zienkiewicz-Zhu error estimator

  Abstract

  Abstract

  In this paper we study the efficiency and the reliability of an anisotropic a posteriori error estimator in the case of the Poisson problem supplied with mixed boundary conditions. The error estimator may be classified as a residual-basedone, but its novelty is twofold: firstly, it employs anisotropic estimates of the interpolation error for linear triangular finite elements and, secondly, it makes use of the Zienkiewicz-Zhu recovery procedure to approximate the gradient of the exact solution. Finally, we describe the adaptive procedure used to obtain a numerical solution satisfying a given accuracy, and we include some numerical test cases to assess the robustness of the proposed numerical algorithm.

• MOX 35 - 08/04/2004
  Veneziani, Alessandro; Vergara, Christian
  Flow rate defective boundary conditions in haemodynamics simulations

  Abstract

  Abstract

  In the numerical simulation of blood flow problems it might happen that the only available boundary conditions prescribe the flow rate incoming/outcoming the vascular district at hand. In order to have a well posed Navier-Stokes problem, these conditions need to be completed. In the bioengineering community, this problem is usually faced by choosing a priori a velocity profile on the inflow/outflow sections, to be fitted with the assigned flow rates. This approach strongly influences the accuracy of the numerical solutions. A less perturbative strategy is based on the so-called do-nothing approach, advocated in Heywood, Rannacher, turek, Int. J. Num. Fl, 1996. An equivalent approach, but easier from the numerical discretization viewpoint, has been proposed in Formaggia, Gerbeau, Nobile, Quarteroni, SIAM J Num An, 2002. It is based on an augmented formulation of the problem, in which the conditions on the flow rates are prescribed in a weak sense by means of Lagrangian multipliers. In this paper we analyze the unsteady augmented Navier-Stokes problem, proving a well posedness result. Moreover, we present some numerical methods for solving the augmented problem, based on a splitting of the computation of velocity and pressure on one side and the Lagrangian multiplier on the other one. In this way, we show how it is possible to solve the augmented problem resorting to available Navier-Stokes solvers.