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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29/2016 - 07/30/2016
Miglio, E.; Parolini, N.; Penati, M.; Porcù, R.
GPU parallelization of brownout simulations with a non-interacting particles dynamic model | Abstract | | The term brownout refers to the uplift of sand particles in the air and is
generated when a helicopter is close to a dusty soil. When a brownout occurs the visibility area is remarkably restricted, thus the pilot may be disoriented and the helicopter may dangerously collide with the ground. Simulations of a brownout require tens of millions of particles in order to be significative, so that the execution of a serial program takes a very long time. In order to speedup the computation, the GPU-parallelization of a brownout simulation program is performed in order to obtain a notable speedup. The dynamics of the particles are considered in a Lagrangian way, under the effect of the gravity force and of a precomputed aerodynamic field. The particles are independent from each other since collisions between them are not taken into account. Thus trajectories are independent and the parallelization is very effective. In this paper we discuss in detail the impact of the techniques used for the GPU implementation of the parallel code on the performance. |
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28/2016 - 07/30/2016
Antonietti, P.F.; Dal Santo, N.; Mazzieri, I.; Quarteroni, A.
A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics | Abstract | | The aim of this work is to propose and analyze a new high order discontinuous Galerkin finite element method for the time integration of a Cauchy problem second order ordinary differential equations. These equations typically arise after space semi-discretization of second order hyperbolic-type differential problems, e.g., wave, elastodynamics and acoustics equation. After introducing the new method, we analyze its well-posedness and prove a-priori error estimates in a suitable (mesh-dependent) norm. Numerical results are also presented to verify the theoretical estimates. space-time finite elements, discontinuous Galerkin methods, second order hyperbolic equations. |
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27/2016 - 07/25/2016
Repossi, E.; Rosso, R.; Verani, M.
A phase-field model for liquid-gas mixtures: mathematical modelling and Discontinuous Galerkin discretization | Abstract | | In this article we propose a phase-field approach to model a liquid-gas mixture that might also provide a description of the expansion stage of a metal foam inside a hollow mold. We conceive the mixture as a two-phase incompressible-compressible fluid governed by a Navier-Stokes-Cahn-Hilliard system of equations, and we adapt the Lowengrub-Truskinowsky model to take into account the expansion of the gaseous phase. The resulting system of equations is characterized by a velocity field that fails to be divergence-free, by a logarithmic term for the pressure that enters the Gibbs free-energy expression and by the viscosity that degenerates in the gas phase. In the second part of the article we propose an energy-based numerical scheme that, at the discrete level, preserves the mass conservation property and the energy dissipation law of the original system. We use a Discontinuous Galerkin approximation for the spatial approximation and a modified midpoint based scheme for the time approximation. |
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26/2016 - 07/25/2016
Brunetto, D.; Calderoni, F.; Piccardi, C.
Communities in criminal networks: A case study | Abstract | | Criminal organizations tend to be clustered to reduce risks of detection and information leaks. Yet, the literature exploring the relevance of subgroups for their internal structure is so far very limited. The paper applies methods of community analysis to explore the structure of a criminal network representing the individuals' co-participation in meetings. It draws from a case study on a large law enforcement operation (``Operazione Infinito'') tackling the 'Ndrangheta, a mafia organization from Calabria, a southern Italian region. The results show that the network is indeed clustered and that communities are associated, in a non trivial way, with the internal organization of the 'Ndrangheta into different ``locali'' (similar to mafia families). Furthermore, the results of community analysis can improve the prediction of the ``locale'' membership of the criminals (up to two thirds of any random sample of nodes) and the leadership roles (above 90% precision in classifying nodes as either bosses or non-bosses). The implications of these findings on the interpretation of the structure and functioning of the criminal network are discussed. |
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25/2016 - 07/12/2016
Baroli, D.; Cova, C.M.; Perotto, S.; Sala, L.; Veneziani, A.
Hi-POD solution of parametrized fluid dynamics problems: preliminary results | Abstract | | Numerical modeling of fluids in pipes or network of pipes (like in the circulatory system) has been recently faced with new methods that exploit the specific nature of the dynamics, so that a one dimensional axial mainstream is enriched by local secondary transverse components. These methods - under the name of Hi-Mod approximation - construct a solution as a finite element axial discretization, completed by a spectral approximation of the transverse dynamics. It has been demonstrated that Hi-Mod reduction significantly accelerates the computations without compromising the accuracy. In view of variational data assimilation procedures (or, more in general, control problems), it is crucial to have efficient model reduction techniques to rapidly solve, for instance, a parametrized problem for several choices of the parameters of interest. In this work, we present some preliminary results merging Hi-Mod techniques with a classical Proper Orthogonal Decomposition (POD) strategy. We name this new approach as Hi-POD model reduction. We demonstrate the efficiency and the reliability of Hi-POD on multiparameter advection-diffusion-reaction problems as well as on the incompressible Navier-Stokes equations, both in a steady and in an unsteady setting.
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24/2016 - 06/12/2016
Pagani, S.; Manzoni, A.; Quarteroni, A.
A Reduced Basis Ensemble Kalman Filter for State/parameter Identification in Large-scale Nonlinear Dynamical Systems | Abstract | | The ensemble Kalman filter is nowadays widely employed to solve state and/or parameter identification problems recast in the framework of Bayesian inversion. Unfortunately its cost becomes prohibitive when dealing with systems described by parametrized partial differential equations, because of the cost entailed by each PDE query. This is even worse for nonlinear time-dependent PDEs. In this paper we propose a reduced basis ensemble Kalman filter technique to speed up the numerical solution of Bayesian inverse problems arising from the discretization of nonlinear time dependent PDEs. The reduction stage yields intrinsic approximation errors, whose propagation through the filtering process might affect the accuracy of the identified state/parameters. Since their evaluation is computationally heavy, we equip our reduced basis ensemble Kalman filter with a reduction error model based on ordinary kriging for functional-valued data, to gauge the effect of state reduction on the whole filtering process. The accuracy and efficiency of our method is then verified on two numerical test cases, dealing with the identification of uncertain parameters or fields for a FitzHugh-Nagumo model and a Fisher-Kolmogorov model. |
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23/2016 - 06/07/2016
Fedele, M.; Faggiano, E.; Dedè, L.; Quarteroni, A.
A Patient-Specific Aortic Valve Model based on Moving Resistive Immersed Implicit Surfaces | Abstract | | In this paper, we propose a full computational pipeline to simulate the hemodynamics in the aorta including the valve. Closed and open valve surfaces, as well as the lumen aorta, are reconstructed directly from medical images using new ad hoc algorithms, allowing a patient-specific simulation. The fluid dynamics problem that accounts from the movement of the valve is solved by a new 3D-0D fluid-structure interaction model in which the valve surface is implicitly represented through level set functions, yielding, in the Navier-Stokes equations, a resistive penalization term enforcing the blood to adhere to the valve leaflets. The dynamics of the valve between its closed and open position is modeled using a reduced geometric 0D model. At the discrete level, a Finite Element formulation is used and the SUPG stabilization is extended to include the resistive term in the Navier-Stokes equations. Then, after time discretization, the 3D fluid and 0D valve models are coupled through a staggered approach. This computational pipeline, applied to a patient specific geometry and data, can reliably reproduce the movement of the valve, the sharp pressure jump occurring across the leaflets, and the blood flow pattern inside the aorta. |
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22/2016 - 05/24/2016
Antonietti, P.F.; Facciola', C.; Russo, A.;Verani, M.
Discontinuous Galerkin approximation of flows in fractured porous media | Abstract | | We present a numerical approximation of Darcy's flow through a fractured porous medium which employs discontinuous Galerkin methods. For simplicity, we consider the case of a single fracture
represented by a (d-1)-dimensional interface between two d-dimensional
subdomains, d = 2; 3. We propose a discontinuous Galerkin Finite
element approximation for the flow in the porous matrix which is
coupled with a conforming finite element scheme for the
flow in the fracture. Suitable (physically consistent) coupling conditions complete the model. We theoretically analyse the resulting formulation and
prove its well-posedness. Moreover, we derive optimal a priori error
estimates in a suitable (mesh-dependent) energy norm and we present
two-dimensional numerical experiments assessing their validity. |
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