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 1249 products
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32/2016 - 09/30/2016
Tarabelloni, N.; Schenone, E.; Collin, A.; Ieva, F.; Paganoni, A.M.; Gerbeau, J.-F.
Statistical Assessment and Calibration of Numerical ECG Models | Abstract | | Objective: Because of the inter-subject variability of ECGs in a healthy
population, it is not straightforward to assess the quality of synthetic ECGs
produced by deterministic mathematical models. We propose a statistical method
to address this question.
Methods: We use a dataset of 1588 healthy, real ECGs and we introduce a way to
calibrate the deterministic model so that its output fits the dataset. Our
approach is based on the concepts of spatial quantiles and spatial depths. These
notions are convenient to manipulate functional data since they provide a
non-parametric way to measure the discrepancy of the model output with a
distribution of data.
Results: The method is successfully applied to two very different models: a
phenomenological model based on ordinary differential equations, and a complex
biophysical model based on partial differential equations set on a
three-dimensional geometry of the heart and the torso. We show in particular
that the proposed calibration strategy allows us to improve the quality of the
ECG obtained with the biophysical model.
Significance: The proposed methodology is to our knowledge the first attempt to
assess the quality of synthetic ECGs with quantitative statistical arguments.
More generally it can be applied to other situations where a deterministic model
produces a functional output that has to be compared with a population of
measurements containing inter-subject variability. |
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31/2016 - 09/09/2016
Antonietti, P.F.; Merlet, B.; Morgan, P.; Verani, M.
Convergence to equilibrium for a second-order time semi-discretization of the Cahn-Hilliard equation | Abstract | | We consider a second-order two-step time semi-discretization of the Cahn-Hilliard equation with an analytic nonlinearity. The time-step is chosen small enough so that the pseudo-energy associated with the discretization is non-increasing at every time iteration. We prove that the sequence generated by the scheme converges to a steady state as time tends to infinity. We also obtain convergence rates in the energy norm. The proof is based on the Lojasiewicz-Simon inequality. |
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30/2016 - 09/09/2016
Abramowicz, K.; Häger, C.; Pini, A.; Schelin, L.; Sjöstedt de Luna, S.; Vantini, S.
Nonparametric inference for functional-on-scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament | Abstract | | Motivated by the analysis of the dependence of knee movement patterns during functional tasks on subject-speci c covariates, we introduce a distribution-free procedure for testing a functional-on-scalar linear model with fixed e ects. The procedure does not only test the global hypothesis on all the domain, but also selects the intervals where statistically signi ficant e ects are detected. We prove that the proposed tests are provided with an asymptotic control of the interval-wise error rate, i.e., the
probability of falsely rejecting any interval of true null hypotheses. The procedure is applied to one-leg hop data from a study on anterior cruciate ligament injury. We compare knee kinematics of three groups of individuals (two injured groups with di erent treatments, and one group of healthy controls), taking individual-speci c covariates into account. |
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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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