Quaderni di Dipartimento

Quaderni MOX

• MOXP2 - 16/09/2004
  Veneziani, Alessandro; Foa, Erika; Quarteroni, Alfio
  Numerical Assessment of Swinsuits Performance

  Abstract

  	Abstract

• MOX 46 - 13/09/2004
  Quarteroni, Alfio
  Modellistica Matematica per la Simulazione, la Progettazione e l Innovazione

  Abstract

  	Abstract
  	Testo della lezione tenuta in occasione della seduta inaugurale del 201° a.a. dell Istituto Lombardo di Scienze e Lettere

• MOX 45 - 30/08/2004
  Deparis, Simone; Discacciati, Marco; Quarteroni, Alfio
  A domain decomposition framework for fluid-structure interaction problems

  Abstract

  	Abstract
  	In this note we review some classical algorithms for fluid-structure interaction problems and we propose an alternative viewpoint mutuated from the domain decomposition theory. This approach yields preconditioned Richardson iteractions on the Steklov-Poincaré nonlinear equation at the fluid-structure interface.

• MOX 44 - 28/06/2004
  Quarteroni, Alfio; Sala, Marzio; Valli, Alberto
  The swiss-carpet domain decomposition preconditioner

  Abstract

  Abstract

  In this paper we consider domain decomposition preconditioners based on a vertex-oriented decomposition of the computational domain. In element-oriented (EO) decompositions, each element of the grid belongs to a different domain, while in vertex-oriented (VO) decompositions each vertex belongs to a different subdomain. Based on VO decompositions, we present several preconditioners for the solution of the original (unreduced) system, as well as for that of the Schur complement system. Theoretical properties are investigated for a finite element approximation of a scalar problem. Numerical results and comparison with state-of-art preconditioners are also reported. The numerical results here presented show the effectiveness of the proposed preconditioners and their good parallel properties.

• MOX 43 - 24/06/2004
  Agoshkov, Valery; Quarteroni, Alfio; Rozza, Gianluigi
  Shape Design in Aorto-Coronaric Bypass Anastomoses using Perturbation Theory

  Abstract

  Abstract

  In this paper we present a new approach in the study of Aorto-Coronaric bypass anastomoses configurations based on small perturbation theory. 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 (the toe) into the coronary (see Figure (1)). The aim is to provide design indications in the perspective of future development for prosthetic bypasses.

• 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.