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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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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21/2016 - 05/12/2016
Ambrosi, D.; Zanzottera, A.
Mechanics and polarity in cell motility | Abstract | | The motility of a fish keratocyte on a flat substrate exhibits two distinct regimes: the non- migrating and the migrating one. In both configurations the shape is fixed in time and, when the cell is moving, the velocity is constant in magnitude and direction. Transition from a stable configuration to the other one can be produced by a mechanical or chemotactic perturbation. In order to point out the mechanical nature of such a bistable behaviour, we focus on the actin dynamics inside the cell using a minimal mathematical model. While the protein diffusion, recruitment and segregation govern the polarization process, we show that the free actin mass balance, driven by diffusion, and the polymerized actin retrograde flow, regulated by the active stress, are sufficient ingredients to account for the motile bistability. The length and velocity of the cell are predicted on the basis of the parameters of the substrate and of the cell itself. The key physical ingredient of the theory is the exchange among actin phases at the edges of the cell, that plays a central role both in kinematics and in dynamics. |
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20/2016 - 05/05/2016
Wilhelm, M.; Sangalli, L.M.
Generalized Spatial Regression with Differential Regularization | Abstract | | We aim at analyzing geostatistical and areal data observed over irregularly shaped spatial domains and having a distribution within the exponential family. We propose a generalized additive model that allows to account for spatially-varying covariate information. The model is fitted by maximizing a penalized log-likelihood function, with a roughness penalty term that involves a differential quantity of the spatial field, computed over the domain of interest. Efficient estimation of the spatial field is achieved resorting to the finite element method, which provides a basis for piecewise polynomial surfaces. The proposed model is illustrated by an application to the study of criminality in the city of Portland, Oregon, USA. |
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19/2016 - 05/05/2016
Guerciotti, B.; Vergara, C.
Computational comparison between Newtonian and non-Newtonian blood rheologies in stenotic vessels | Abstract | | This work aims at investigating the influence of non-Newtonian blood rheology on the hemodynamics of 3D patient-specific stenotic vessels, by means of a comparison of some numerical results with the Newtonian case. In particular, we consider two carotid arteries with severe stenosis and a stenotic coronary artery treated with a bypass graft, in which we virtually vary the degree of stenosis. We perform unsteady numerical simulations based on the Finite Element method using the Carreau-Yasuda model to describe the non-Newtonian blood rheology. Our results show that velocity, vorticity and wall shear stress distributions are moderately influenced by the non-Newtonian model in case of stenotic carotid arteries. On the other hand, we observed that a non-Newtonian model seems to be important in case of stenotic coronary arteries, in particular to compute the relative residence time which is greatly affected by the rheological model. |
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18/2016 - 04/11/2016
Ferroni, A.; Antonietti, P.F.; Mazzieri, I.; Quarteroni, A.
Dispersion-dissipation analysis of 3D continuous and discontinuous spectral element methods for the elastodynamics equation | Abstract | | In this paper we present a three dimensional dispersion and dissipation analysis for both the semi-discrete and the fully discrete approximation of the elastodynamics equation based on the plane wave method. For space discretization we compare different approximation strategies, namely the continuous and discontinuous spectral element method on both tetrahedral and hexahedral elements. The fully discrete scheme is then obtained exploiting a leap-frog time integration scheme. Several numerical results are presented and discussed. |
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17/2016 - 04/08/2016
Penati, M.; Miglio, E.
A new mixed method for the Stokes equations based on stress-velocity-vorticity formulation | Abstract | | In this paper, we develop and analyze a mixed finite element method for the Stokes flow. This method is based on a stress-velocity-vorticity formulation. A new discretization is proposed: the stress is approximated using the Raviart-Thomas elements, the velocity and the vorticity by piecewise discontinuous polynomials. It is shown that if the orders of these spaces are properly chosen then the advocated method is stable. We derive error estimates for the Stokes problem, showing optimal accuracy for both the velocity and vorticity. |
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