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
-
42/2014 - 10/21/2014
Canale, A.; Vantini, S.
Constrained Functional Time Series: an Application to Demand and Supply Curves in the Italian Natural Gas Balancing Platform | Abstract | | In Italy we have assisted to the recent introduction of the natural gas balancing platform, a system in which gas operators virtually sell and buy natural gas in order to balance the common pipelines network. Basically, the operators daily submit demand bids and supply offers which are eventually sorted according to price. Demand and supply curves are hence obtained by cumulating the corresponding quantities. Motivated by market dynamic modeling in the Italian Natural Gas Balancing Platform, we propose a model to analyze time series of bounded and monotonic functions. In detail, we provide the constrained functions with a suitable pre-Hilbert structure and introduce a useful isometric bijective map associating each possible bounded and monotonic function to an unconstrained. We then introduce a functional-to-functional autoregressive model that we use to predict the entire demand/supply function. We estimate the model by minimizing the squared $L^2$ distance between functional data and functional predictions with a penalty term based on the Hilbert-Schmidt squared norm of autoregressive lagged operators. We have proved that the solution always exist, unique and that it is linear on the data with respect to the introduced geometry thus guaranteeing that the plug-in predictions of future entire demand/supply functions satisfy all required constraints. We also provide an explicit expression for estimates and predictions. The approach is of general interest and can be generalized in any situation in which one has to deal with constrained monotonic functions (strictly positive or bounded) which evolve through time (e.g., dose response functions right-censored survival curves or cumulative distribution functions). |
-
41/2014 - 10/16/2014
Esfandiar, B.; Porta, G.; Perotto, S.; Guadagnini, A.
Impact of space-time mesh adaptation on solute transport modeling in porous media | Abstract | | We implement a space-time grid adaptation procedure to efficiently improve the accuracy of numerical simulations of solute transport in porous media in the context of model parameter estimation. We focus on the Advection Dispersion Equation (ADE) for the interpretation of non-reactive transport experiments in laboratory-scale heterogeneous porous media. When compared to a numerical approximation based on a fixed space-time discretization, our approach is grounded on a joint automatic selection of the spatial grid and the time step to capture the main (space-time) system dynamics. Spatial mesh adaptation is driven by an anisotropic recovery-based error estimator which enables us to properly select the size, shape and orientation of the mesh elements. Adaptation of the time step is performed through an ad-hoc local reconstruction of the temporal derivative of the solution via a recovery-based approach. The impact of the proposed adaptation strategy on the capability to provide reliable estimates of the key parameters of an ADE model is assessed on the basis of experimental solute breakthrough data measured following tracer injection in a non-uniform porous system. Model calibration is performed in a Maximum Likelihood (ML) framework upon relying on the representation of the ADE solution through a generalized Polynomial Chaos Expansion (gPCE). Our results show that the proposed anisotropic space-time grid adaptation leads to ML parameter estimates and to model results of markedly improved quality when compared to classical inversion approaches based on a uniform space-time discretization. |
-
40/2014 - 10/15/2014
Antonietti, P.F.; Mazzieri, I.; Quarteroni, A.
Improving seismic risk protection through mathematical modeling
-
39/2014 - 10/14/2014
Ghiglietti, A.; Paganoni, A.M.
Statistical inference for functional data based on a generalization of Mahalanobis distance | Abstract | | In this paper we propose a generalization of Mahalanobis distance that extends the usual multivariate one to functional data generated by stochastic processes. We show that this distance is well defined in L2 and achieves both the goals of (i) considering all the infinite components of data basis expansion and (ii) keeping the same ideas on which is based the Mahalanobis distance. This new mathematical tool is adopted in an inferential context to construct tests on the mean of Gaussian processes for one and two populations. The tests are constructed assuming the covariance structure to be either know or unknown. The power of all the critical regions has been computed analytically. A wide discussion on the behavior of these tests in terms of their power functions is realized, supported by some simulation studies. |
-
38/2014 - 10/13/2014
Shen, H.; Truong, Y.; Zanini, P.
Independent Component Analysis for Spatial Stochastic Processes on a Lattice | Abstract | | Independent Component Analysis (ICA) is a widespread data-driven methodology used to solve Blind Source Separation problems. A lot of algorithms have been proposed to perform ICA, but few of them take into account the dependence within the mixtures and not only the dependence between the mixtures. Some algorithms deal with the temporal ICA (tICA) approach exploiting the temporal autocorrelation of the mixtures (and the sources). In particular, colored ICA (cICA), that works in the spectral domain, is an effective method to perform ICA through a Whittle likelihood procedure assuming the sources to be temporal stochastic process. However spatial ICA (sICA) approach is becoming dominant in several field, like fMRI analysis or geo-referred imaging. In this paper we present an extension of cICA algorithm, called spatial colored ICA (scICA), where sources are assumed to be spatial stochastic processes on a lattice. We exploit the Whittle likelihood and a kernel based nonparametric algorithm to estimate the spectral density of a spatial process on a lattice. We illustrate the performance of the proposed method through different simulation studies and a real application using a geo-referred dataset about mobile-phone traffic on the urban area of Milan, Italy. Simulations and the real application showed the improvements provided by scICA method due to take into account the spatial autocorrelation of the mixtures and the sources. |
-
37/2014 - 10/12/2014
Giuliani, N.; Mola, A.; Heltai, L.; Formaggia,L.
FEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows | Abstract | | In finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov-Galerkin(SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes. |
-
36/2014 - 10/11/2014
Abbà,A.;Bonaventura,L.; Nini, M.;Restelli,M.;
Anisotropic dynamic models for Large Eddy Simulation of compressible flows with a high order DG method | Abstract | | The impact of anisotropic dynamic models for applications to LES of compressible flows is assessed in the framework of a numerical model based on high order discontinuous finite elements. The projections onto lower dimensional subspaces associated to lower degree basis function are used as LES filter, along the lines proposed in Variational Multiscale templates. Comparisons with DNS results available in the literature for channel flows at Mach numbers 0.2, 0.7 and 1.5 show clearly that the anisotropic model is able to reproduce well some key features of the flow, especially close to the wall, where the flow anisotropy plays a major role. |
-
35/2014 - 10/07/2014
Tricerri, P.; Dedè, L.; Deparis, S.; Quarteroni, A.; Robertson, A.M.; Sequeira, A.
Fluid-structure interaction simulations of cerebral arteries modeled by isotropic and anisotropic constitutive laws | Abstract | | This paper considers numerical simulations of fluid-structure interaction (FSI) problems in hemodynamics for idealized geometries of healthy cerebral arteries modeled by means of both nonlinear isotropic and anisotropic material constitutive laws. In particular, it focuses on an anisotropic model initially proposed for cerebral arteries, to characterize the activation of collagen fibers at finite strains. In the current work, this constitutive model is implemented for the first time in the context of an FSI formulation. In this framework, we investigate the influence of the material model on the numerical results and, in the case of the anisotropic laws, the importance of the collagen fibers on the overall mechanical behavior of the tissue. With this aim, we compare our numerical results by analyzing fluid dynamic indicators, vessel wall displacement, Von Mises stress, and deformations of the collagen fibers. Specifically, for an anisotropic model with collagen fiber recruitment at finite strains, we highlight the progressive activation and deactivation processes of the fibrous component of the tissue throughout the wall thickness during the cardiac cycle. The inclusion of collagen recruitment is found to have a substantial impact on the intramural stress, which will in turn impact the biological response of the intramural cells. Hence, the methodology presented here will be particularly useful for studies of mechanobiological processes in the healthy and diseased vascular wall. |
|
