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 1275 products
-
MOX 27 - 10/02/2003
Rozza, Gianluigi
Reduced Basis Methods for Elliptic Equations in sub-domains with A-Posteriori Error Bounds and Adaptivity | Abstract | | We present an application in multi-parametrized subdomains based on a technique for the rapid and reliable prediction of linear-functional output of elliptic coercive partial differential equations with affine parameter dependence (reduced basis methods). The essential components are (i) (provably) rapidly convergent global reduce-basis approximation - Galerkin projection onto a space W_N spanned by solutions of the governing partial differential equation at N selected points in parameter space (ii) a posteriori error estimation-relaxations of the error-residual equation that provide inexpensive bounds for the error in the outputs of interest and (iii) off-line/on-line computational procedures-methods wich decouple the generation and projection stages of the approximation process. The operation count for the on-line stage-in Which, given a new parameter value, we calculate the output of interest and associated error bound-depends only on N (typically very small) and the parametric complexity of the problem the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.
In [11] a rigorous a posteriori error bound framework for reduced-basis approximations of elliptic coercive equations is developed. The resulting error estimates are, in some cases, quite sharp: the ratio of the estimated error in the output to the true error in the output, or effectivity, is close to (but always greater than) unity. We use a posteriori bound error estimator applied also to an adaptive procedure in choosing the approximation space and its dimension, minimizing the estimated erro of the effectivity [23].
The application is based on a parametrized geometry, divided in subdomains, each of them depending by geometrical quantities that can be useful for future haemodynamics applications [15], such as the bypass configuration problem (stenosis lenght, graft angle, artery diameter, incoming bypass diameter and outflow lenght). For future development guidelines we suggest to see [19] and [16]. |
-
MOX 26 - 09/29/2003
Saleri, Fausto; Veneziani, Alessandro
Pressure-correction algebraic splitting methods for the incompressible navier-stokes equations | Abstract | | In this paper we present a new family of methods for the effective numerical solution of the incompressible unsteady Navier-Stokes equations. These methods resort to an algebraic splitting of the discretized problem based on inexact LU block-factorizations of the corresponding matrix (following [21]). In particular, we will start from inexact algebraic factorizations of algebraic Chorin-Temam and Yosida type and introduce a pressure correction step aiming at improving the time accuracy. one of the schemes obtained in this way (the Algebraic Chorin-Temam Pressure Correction Method) resembles a method previously introduced in the framework of differential projection schemes (see [24], [19]). The stability and the dependence of splitting error on the time step of the new methods is investigated and tested on several numerical cases. |
-
MOXP1 - 09/10/2003
Formaggia, Luca; Micheletti, Stefano; Savini, Barbara
Modellazione Bidimensionale e Simulazione Numerica del Funzionamento di una Candeletta di Preriscaldo
-
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. |
-
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 |
-
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. |
-
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. |
-
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. |
|
