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 1322 products
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MOX 48 - 10/20/2004
Perotto, Simona
Adaptive Modeling for free-surface flowm | Abstract | | This work represents a first step towards the adaptive simulation of the motion of water in a complex hydrodynamic configuration, such as a channel network or a river delta by means of different mathematical models. A wide spectrum of space and time scales is involved due to the presence of physical phenomena of different nature. Ideally, moving from a hierarchy of hydrodynamic models, one should solve the most complex model (with solution u_fine) to accurately describe all the physical features of the problems at hand. In more detail, for a user-defined output functional F, we aim to approximate, within a prescribed tolerance (), the value F (u_fine) by means of the quantity F (u_adapted), u_adapted being the adapted solution confining the most complex model only on a restricted region of the computational domain. We aim to provide an efficient tool able to automatically select regions of the domain where to solve the coarse hydrodynamic model rather than the finer one, while guaranteeing |F(u_fine)F (u_adapted)| below the tolerance (). This goal is achieved via a suitable a posteriori modeling error analysis developed in the framework of a goal-oriented theory. We extend the dual-based approach provided in [3] for steady equations to the case of a generic time-dependent problem. Then this analysis is particularized to the case of free-surface flows. In the last part of the paper an exhaustive numerical validation is carried out, while emphasizing the crucial matter of the time discretization for the dual problem. |
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MOX 47 - 09/20/2004
Micheletti, Stefano; Perotto, Simona
Anisotropic mesh adaptivity via a dual-based a posteriori error estimation for semiconductors
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MOXP2 - 09/16/2004
Veneziani, Alessandro; Foa, Erika; Quarteroni, Alfio
Numerical Assessment of Swinsuits Performance
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MOX 46 - 09/13/2004
Quarteroni, Alfio
Modellistica Matematica per la Simulazione, la Progettazione e l Innovazione | Abstract | | Testo della lezione tenuta in occasione della seduta inaugurale del 201° a.a. dell Istituto Lombardo di Scienze e Lettere |
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MOX 45 - 08/30/2004
Deparis, Simone; Discacciati, Marco; Quarteroni, Alfio
A domain decomposition framework for fluid-structure interaction problems | 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. |
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MOX 44 - 06/28/2004
Quarteroni, Alfio; Sala, Marzio; Valli, Alberto
The swiss-carpet domain decomposition preconditioner | 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. |
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MOX 43 - 06/24/2004
Agoshkov, Valery; Quarteroni, Alfio; Rozza, Gianluigi
Shape Design in Aorto-Coronaric Bypass Anastomoses using Perturbation Theory | 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. |
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MOX 42 - 05/21/2004
Rozza, Gianluigi
Optimization, Control and Shape Design of an Arterial Bypass | 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. |
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