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 1251 products
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42/2013 - 10/05/2013
Bernardi, M.; Sangalli, L.M.; Secchi, P.; Vantini, S.
Analysis of Juggling Data: an Application of K-mean Alignment | Abstract | | We analyze the juggling data by means of the k-mean alignment algorithm using cycles as the experimental units of the analysis. Allowing for affine warping, we detect two clusters distinguishing between mainly-planar trajectories and trajectories tilted toward the body of the juggler in the lower part of the cycle. In particular we detect an anomalous presence of tilted trajectories among the record third cycles. We also find warping functions to be clustered according to records suggesting that each record is performed at a di fferent pace and thus associated to a diff erent typical cycle-duration. |
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41/2013 - 10/04/2013
Bernardi, M.; Sangalli, L.M.; Secchi, P.; Vantini, S.
Analysis of Proteomics data: Block K-mean Alignment | Abstract | | We analyze the proteomics data introducing a block k-mean alignment procedure. This technique is able to jointly align and cluster the data, accounting appropriately for the block structure of these data, that includes measurement repetitions for each patient. An analysis of area-under-peaks, following the alignment, separates patients who respond and those who do not respond to treatment. |
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40/2013 - 10/03/2013
Pacciarini P.; Rozza G.
Stabilized reduced basis method for parametrized advection-diffusion PDEs | Abstract | | In this work, we propose viable and efficient strategies for the stabilization of the reduced basis
approximation of an advection dominated problem. In particular, we investigate the combination
of a classic stabilization method (SUPG) with the Offline-Online structure of the RB method. We
explain why the stabilization is needed in both stages and we identify, analytically and numerically,
which are the drawbacks of a stabilization performed only during the construction of the reduced
basis (i.e. only in the Offline stage). We carry out numerical tests to assess the performances
of the double stabilization both in steady and unsteady problems, also related to heat transfer
phenomena. |
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39/2013 - 10/02/2013
Ieva, F.; Marra, G.; Paganoni, A.M.; Radice, R.
A semiparametric bivariate probit model for joint modeling of outcomes in STEMI patients | Abstract | | In this work we analyse the relationship among in-hospital mortality and a treatment effectiveness outcome in patients affected by ST-Elevation Myocardial Infarction. The main idea is to carry out a joint modelling of the two outcomes applying a Semiparametric Bivariate Probit Model to data arising from a clinical registry called STEMI Archive. A realistic quantification of the relationship between outcomes can be problematic for various reasons. First, latent factors associated with hospitals organization can affect the treatment efficacy and/or interact with patient s condition at admission time, then they can influence the mortality outcome. Such factors can be hardly measurable. Thus, the use of classical estimation methods will clearly result in inconsistent and biased parameter estimates. Secondly, covariate-outcomes relationships can exhibit non-linear patterns. Provided that proper statistical methods for model fitting in such framework are available, it is possible to employ a simultaneous estimation approach to account for unobservable confounders. Such a framework can also provide flexible covariate structures and model the whole conditional distribution of the response. |
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38/2013 - 09/17/2013
Bonizzoni, F.; Nobile, F.
Perturbation analysis for the Darcy problem with log-normal permeability | Abstract | | We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in the case of a random field parametrized by a finite number of random variables. On the other hand, in the case of an infinite dimensional random field, suitable equations satisfied by the derivatives of the stochastic solution can be derived. We give a theoretical upper bound for the norm of the residual of the Taylor expansion which predicts the divergence of the series as the polynomial degree goes to infinity.
We provide a formula to compute the optimal degree for the Taylor polynomial and the maximum achievable accuracy of the perturbation approach.
Our theoretical findings are confirmed by numerical experiments in the simple case where the permeability field is described using one random variable.
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37/2013 - 08/26/2013
Lever, V.; Porta, G.; Tamellini, L.; Riva, M.
Characterization of basin-scale systems under mechanical and geochemical compaction | Abstract | | We present an inverse modeling procedure for the calibration of uncertain model parameters characterizing basin scale sandstone compaction due to mechanical and geochemical processes. Unknown model parameters include geophysical and geochemical system attributes as well as pressure and temperature boundary conditions. We derive a reduced model of the system based on the generalized polynomial chaos expansion (gPCE) approximation method and compute the variance-based Sobol indices for the selected uncertain parameters. The gPCE is used to
approximate the model response at a low computational cost and the Sobol indices quantify the effect of each uncertain parameter on the state variables. Parameter estimation is performed
within a Maximum Likelihood framework. Results are illustrated on a one-dimensional test case
involving quartz cementation and mechanical compaction in sandstones. The reliability of the
gPCE approximation in the context of an inverse modeling framework is assessed. The effects of
(a) the strategy adopted in building the gPCE and (b) the type and spatial location of calibration
data (such as temperature and porosity) on the goodness of the parameter estimates are explored
by means of classical estimation error analysis and model selection criteria. |
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36/2013 - 08/25/2013
Ferran Garcia, Luca Bonaventura, Marta Net, Juan Sanchez
Exponential versus IMEX high-order time integrators for thermal convection in rotating spherical shells | Abstract | | We assess the accuracy and efficiency of several exponential time integration methods coupled to a spectral discretization of the three-dimensional
Boussinesq thermal convection equations in rotating spherical shells. Exponential methods are compared to implicit-explicit (IMEX) multi-step methods. The results of a wide range of numerical simulations highlight the superior accuracy of exponential methods for a given time step, especially when employed with large time steps and at low Ekman number. However, presently available implementations of exponential methods appear to be in general computationally more expensive than those of IMEX methods and further research is needed to reduce their computational cost per time step. A physically justified extrapolation argument suggests that some exponential methods could be the most
efficient option for integrating flows near Earth’s outer core conditions.
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35/2013 - 08/24/2013
Cattaneo, L.; Formaggia, L.; Iori G. F.; Scotti, A,; Zunino, P.
Stabilized extended finite elements for the approximation of saddle point problems with unfitted interfaces | Abstract | | We address a two-phase Stokes problem, namely the coupling of two fluids with different kinematic viscosities.
The domain is crossed by an interface corresponding to the surface separating the two fluids.
We observe that the interface conditions allow the pressure and the velocity gradients to be discontinuous across the interface. The eXtended Finite Element Method is applied to accommodate the weak discontinuity of the velocity field across the interface and the jump in pressure on computational meshes that do not fit the interface. Numerical evidence shows that the discrete pressure approximation may be unstable in the neighborhood of the interface, even though the spatial approximation is based on inf-sup stable finite elements. It means that XFEM enrichment locally violates the satisfaction of the stability condition for mixed problems.
For this reason, resorting to pressure stabilization techniques in the region of elements cut by the unfitted interface is mandatory. In alternative, we consider the application of stabilized equal order pressure / velocity XFEM discretizations and we analyze their approximation properties. On one side, this strategy increases the flexibility on the choice of velocity and pressure approximation spaces. On the other side, symmetric pressure stabilization operators, such as local pressure projection methods or the Brezzi-Pitkaranta scheme, seem to be effective to cure the additional source of instability arising from the XFEM approximation. We will show that these operators can be applied either locally, namely only in proximity of the interface, or globally, that is on the whole domain when combined with equal order approximations. After analyzing the stability, approximation properties and the conditioning of the scheme, numerical results on benchmark cases will be discussed, in order to thoroughly compare the performance of different variants of the method. |
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