Quaderni di Dipartimento

Quaderni MOX

• MOX 70 - 28/10/2005
  Veneziani, Alessandro; Vergara, Christian
  An approximate method for solving incompressible Navier-Stokes problem with flow rate conditions

  Abstract

  Abstract

  We consider the incompressible Navier-Stokes problem with flow rate boundary conditions. This problem has been investigated in [2] and [12], following a Langrage multiplier approach. This approach has the drawback of high computational costs. In this paper, we propose an approximate formulation of the problem, yielding a strong reduction of the computational cost. The error analysis shows that the error introduced by this approximate formulation is confined in a smoll region of the boundary. This is a confirmed by the numerical simulations

• MOXP5 - 20/10/2005
  Olgiati, Emanuela; Paglieri, Luca; Salvati, Simonetta; Secchi, Piercesare
  Storia di un Caso: Intervalli di Confidenza per una Proporzione per la regolazione della qualità del servizio nel settore energetico nazionale

  Abstract

  	Abstract
  	Si descrive il processo di costruzione di un metodo di controllo campionario della qualita' dei servizi di distribuzione misura e vendita dell'energia elettrica e del gas attualmente adottato dall'Autorita' per l'energia elettrica e il gas italiana

• MOX 69 - 27/09/2005
  Quarteroni, A.; Rozza, G.; Dede', L.; Quaini, A.
  Numerical Approximation of a Control Problem for Advection-Diffusion Processes

  Abstract

  Abstract

  Two different approaches are proposed to enhance the efficiency of the numerical resolution of optimal control problems governed by a linear advection-diffusion equation. In the framework of Galerkin-Finite Element (FE) method, we adopt a novel a posteriori error estimate of the discretization error in the cost functional this estimated is used in the course of a numerical adaptive strategy for the generation of efficient grids for the resolution of the optimal control problem. Moreover, we propose to solve the control problem by adopting a reduced basis (RB) technique, hence ensuring rapid, reliable and repeated evaluations of input-output relationship. Our numerical tests show that by this technique a substantial saving of computational costs can be achieved.

• MOX 68 - 07/09/2005
  Micheletti, Stefano; Perotto, Simona
  Nested dual-residual a posteriori error estimators for advection-diffusion-reaction problems

  Abstract

  Abstract

  In this work we introduce a fully computable dual-based a posteriori error estimator for standard scalar advection-diffusion-reaction problems. In particular, such an estimator does not depend on neither the primal nor the dual exact solution, but only on the corresponding Galerkin finite element approximations. This new approach merges the main advantages of the dual-based and of the residual-based error analysis, being devised as a residual-based estimator nested in a dual-based one. This allows us to explicitly approximate suitable functionals of the solution, in the spirit of a classical goal-oriented analysis, at the same cost as a dual-based strategy, the solution of two differential problems being involved. The related issue of optimal mesh adaptivity is also addressed. Several two-dimensional numerical test cases validate the proposed theory as well as the employed adaptive procedure.

• MOX 67 - 06/09/2005
  Quarteroni, Alfio; Rozza, Gianluigi
  Tecniche a Basi Ridotte per l Ottimizzazione di Configurazioni di Innesto per Bypass Coronarici

  Abstract

  Abstract

  Viene applicato un metodo a basi ridotte per equazioni alle derivate parziali su domini parametrizzati allo scopo di approssimare il flusso del sangue attraverso un bypass aorto-coronarico. L obiettivo del lavoro è quello di fornire (a) un analisi di sensività per grandezze geometriche rilevanti nella caratterizzazione della configurazione di innesto di un bypass e (b) una rapida e affidabile previsione del valore di certi funzionali integrali, denominati outputs (quali, per esempio, indici legati a grandezze fluidodinamiche). Le linee guida del lavoro sono finalizzate a (i) ottenere valide indicazioni circa le procedure di progetto e innesto chirurgico di un bypass, nella prospettiva futura dello sviluppo e dell uso di protesi bioartificiali, (ii) sviluppare metodi numerici per l ottimizzazione e la progettazione biomeccanica e, (iii) fornire una relazione di tipo input-output retta da modelli con complessità matematica e costi computazionali inferiori rispetto a quelli che si avrebbero risolvendo le equazioni della fluidodinamica mediante il metodo classico degli elementi finiti.

• MOX 66 - 29/07/2005
  Montano, Antonio; Restelli, Marco; Sacco, Riccardo
  Modeling and Numerical Simulation of Tethered Buoy Dynamics

  Abstract

  Abstract

  In this article we deal with the numerical simulation of the dynamics of a tethered buoy, which is a mechanical system for marine applications consisting of a rigid floating bonding (buoy) connected by an elastic cable to the bottom of the fluid environment. A novel mixed finite element formulation is proposed for the spatial numerical approximation of the equations governing the dynamics of the elastic cable. This is done to allow a robust modeling of the cable, event in the limit of an infinite value of the Young modulus, in a way that is similar to mixed formulations for incompressible fluid-mechanics. The dynamics of the floating bodyis described by the classical Euler equations of motion, written using quaternion variables to end up with a numerically robust algorithm in presence of large rotations. For the time discretization of the resulting coupled system of nonlinear differential equations, the Backward Euler implicit method is adopted due to the stability requirements of the problem at hand, while a damped Newton method is used for linearization. Finally, the accuracy and robustness of the proposed numerical procedure are validated in the simulation of the tethered buoy system under various static and dynamic working conditions.

• MOX 65 - 26/07/2005
  Paganoni, Anna Maria; Secchi, Piercesare
  A numerical study for comparing two response-adaptive designs for continuous treatment effects

  Abstract

  Abstract

  We study two sequential, response-adaptive randomized designs for clinical trials one has been proposed in Bandy-opadhyay and Biswas (2001) and Biswas and Basu (2001), the other stems from randomly reinforced urn introduced and studied in Muliere et al.(2005). Both designs can be used in clinical trials where the response from each patient is a continuous variable. Comparison is conducted through numerical studies and along a new guideline for the evaluation of a response-adaptive design

• MOX 64 - 24/06/2005
  Formaggia, Luca; Sala, Marzio; Saleri, Fausto
  Domain decomposition techniques

  Abstract

  Abstract

  We introduce some parallel domain decomposition preconditioners for iterative solution of sparse linear systems like those arising from the approximation of partial differential equations by finite elements or finite volumes. We first give an overview of algebraic domain decomposition techniques. We then introduce a preconditioner based on a multilevel approximate Schurcomplement system. Then we present a Schwarz-based preconditioner augmented by an algebraic coarse correction operator. Being the definition of a coarse grid a difficult task on unstructured meshes, we propose a general framework to build a coarse operator by using an agglomeration procedure that operates directly on the matrix entries. Numerical results are presented aimed at assessing and comparing the effectiveness of the two methodologies. The main application will concern computational fluid dynamics (CFD), and in particular the simulation of compressible flow around aeronautical configurations.