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 1238 products
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31/2010 - 11/06/2010
Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi
Shape optimization for viscous flows by reduced basis methods and free-form deformation | Abstract | | In this paper we present a new approach for shape optimization that combines two different types of model reduction: a suitable low-dimensional
parametrization of the geometry (yielding a geometrical reduction) combined with reduced basis methods (yielding a reduction of computational complexity). More precisely, free-form deformation techniques are introduced
for the geometry description and its parametrization, while reduced basis methods are used upon a finite element discretization to solve systems of parametrized partial differential equations. This allows an efficient flow field computation and cost functional evaluation during the iterative optimization
procedure, resulting in effective computational savings with respect to usual shape optimization strategies. This approach is very general
and can be applied for a broad variety of problems. To prove its effectivity, in this paper we apply it to find the optimal shape of aorto-coronaric bypass anastomoses based on vorticity minimization in the down-field region.
Stokes equations are used to model blood flow in the coronary arteries. |
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30/2010 - 11/05/2010
Blanco, Pablo J.; Discacciati, Marco; Quarteroni, Alfio
Modeling dimensionally-heterogeneous problems: analysis, approximation and applications | Abstract | | In the present work a general theoretical framework for coupled dimensionally-heterogeneous partial differential equations is developed. This isdone by recasting the variational formulation in terms of coupling interface variables. In such a general setting we analyze existence and uniqueness of solutions for both the continuous problem and its finite dimensional approximation. This approach also allows the development of different iterative substructuring solution methodologies involving dimensionallyhomogeneous
subproblems. Numerical experiments are carried out to test our theoretical results.
Keywords: Multiphysics, Heterogeneous PDE models, Augmented formulation,Domain decomposition, Finite elements. |
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29/2010 - 11/04/2010
Lesinigo, Matteo; D'Angelo, Carlo; Quarteroni, Alfio
A multiscale Darcy-Brinkman model for fluid flow in fractured porous media | Abstract | | The aim of this work is to present a reduced mathematical model for describing fluid flow in porous media featuring open channels or fractures.
The Darcy s law is assumed in the porous domain while the Stokes-Brinkman equations are considered in the fractures. We address the case of fractures whose thickness is very small compared to the characteristic diameter of the
computational domain, and describe the fracture as if it were an interface between porous regions. We derive the corresponding interface model governing the fluid flow in the fracture and in the porous media, and establish the
well-posedness of the coupled problem. Further, we introduce a finite element scheme for the approximation of the coupled problem, and discuss solution strategies. We conclude by showing the numerical results related to several test cases and compare the accuracy of the reduced model compared with the non-reduced one. |
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28/2010 - 11/03/2010
Crosetto, Paolo; Reymond, Philippe; Deparis, Simone; Kontaxakis, Dimitrios; Stergiopulos, Nikolaos; Quarteroni, Alfio
Fluid Structure Interaction Simulations of Physiological Blood Flow in the Aorta | Abstract | | The numerical tools to simulate blood flow in the cardiovascular system are constantly developing due to the great clinical interest and to scientifi c advances in mathematical models and computational power. The present work aims to address and validate new algorithms to efficiently predict the hemodynamics in large arteries. The latter rely on fi nite elements simulation of the fluid-structure interaction between blood flow and arterial wall deformation of a healthy aorta. Di fferent sets of boundary conditions are devised and tested. The mean velocity and pressure time evolution is plotted
on di erent sections of the aorta and the wall shear stress distribution is computed. The results are compared with those obtained with a rigid wall simulation. Pulse wave velocity is computed and compared with the values available from the literature. The flow boundary conditions used for the outlets are obtained using the solution of as one dimensional model. The results of the simulations are in agreement with the physiological data in terms of wall shear stress, wall displacement, pressure waveforms and velocities. |
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27/2010 - 11/02/2010
Bruggi, Matteo; Verani, Marco
An adaptive algorithm for topology optimization with goal-oriented error control | Abstract | | We present an adaptive scheme, named ATOPT algorithm, to address volume–constrained compliance minimization, a benchmark problem in topology optimization.
The algorithm performs a set of optimization loops on an underlying grid that is iteratively adapted to improve the description quality of the topology of the structure and the accuracy of the finite element compliance approximation of the
evolving solution. Two suitable error estimators are defined in order to address both the issues. Numerical simulations show that ATOPT algorithm achieves optimal layouts that are in full agreement with standard results obtained by employing large scale uniformly refined grids. However, the ATOPT algorithm turns out to be more
accurate in terms of the approximation of both the elastic behavior and the topology, while the computational cost spent in the minimization algorithm is remarkably reduced.
Keywords: topology optimization, minimum compliance, adaptive mesh refinement.
2000 Mathematics Subject Classification. 65N30, 93B40 |
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26/2010 - 07/16/2010
Ieva, Francesca; Paganoni, Anna Maria
Designing and mining a multicenter observational clinical registry concerning patients with Acute Coronary Syndromes | Abstract | | In this work we describe design, aims and contents of the ST-segment Elevation Myocardial Infarction (STEMI) Archive, which is a multicenter
observational clinical registry planned within the Strategic Program Exploitation, integration and study of current and future health databases
in Lombardia for Acute Myocardial Infarction . This is an observational disease registry that collects clinical indicators, process indicators and outcomes concerning STEMI patients admitted to any hospital in Lombardia Region.
This registry is arranged to be automatically linked to the Public Health Database, the on going administrative databank of Lombardia
Region. In this work we also provide an example of statistical tools implemented on a pilot integrated database in order to explore and model such an informative database. |
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25/2010 - 07/15/2010
Pena, G.; Prud'homme, C.; Quarteroni, A.
High Order Methods for the Approximation of the Incompressible Navier-Stokes Equations in a Moving Domain | Abstract | | In this paper we address the numerical approximation of the incompressible Navier-Stokes
equations in a moving domain by the spectral element method and high order time integrators. We present the Arbitrary Lagrangian Eulerian (ALE) formulation of the incompressible
Navier-Stokes equations and propose a numerical method based on the following kernels: a Lagrange basis associated with Fekete points in the spectral element method context, BDF time integrators, an ALE map of high degree, and a robust algebraic linear solver.
In particular, the high degree ALE map is appropriate to deal with a computational domain whose boundary is described with curved elements. Finally, we apply the proposed strategy to a
test case. |
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24/2010 - 07/14/2010
Tamellini, Lorenzo; Formaggia, Luca; Miglio, Edie; Scotti, Anna
An Uzawa iterative scheme for the simulation of floating boats | Abstract | | The numerical simulation of a floating boat requires to solve a complex interaction between free surface flow and the dynamics of the boat. In this work we focus on solution schemes with an explicit representation of the fluid surface and on the speci c problem of the imposition of the presence of a floating object. The floating object represents an unilateral constraint on
the fluid surface, which cannot rise above a the level de ned by the floating object itself.
We propose an Uzawa type iterative scheme for this type of situations and we describe an efficient implementation in the context of a
particular finite element discretization and algebraic splitting procedure. |
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