Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1249 prodotti
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22/2017 - 14/04/2017
Bartezzaghi, A.; Dede', L.; Quarteroni, A.
Biomembrane modeling with Isogeometric Analysis | Abstract | | We consider the numerical approximation of lipid biomembranes, including red blood cells, described through the Canham{Helfrich model, according to which the shape minimizes the bending energy under area and volume constraints. Energy minimization is performed via L2-gradient flow of the Canham-Helfrich energy using two Lagrange multipliers to weakly enforce the
constraints. This yields a highly nonlinear, high order, time dependent geometric Partial Differential Equation (PDE). We represent the biomembranes as single-patch NURBS closed surfaces. We discretize the geometric PDEs in space with NURBS-based Isogeometric Analysis and in time with Backward Differentiation Formulas. We tackle the nonlinearity in our formulation through a semi-implicit approach by extrapolating, at each time level, the geometric quantities of interest from previous time steps. We report the numerical results of the approximation of the Canham-Helfrich
problem on ellipsoids of different aspect ratio, which lead to the classical biconcave shape of lipid vesicles at equilibrium. We show that this framework permits an accurate approximation of the Canham-Helfrich problem, while being computationally efficient. |
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21/2017 - 14/04/2017
Talska, R.; Menafoglio, A.; Machalova, J.; Hron, K.; Fiserova, E.
Compositional regression with functional response | Abstract | | This work addresses the problem of performing functional linear regression when the response variable is represented as a probability density function (PDF). PDFs are interpreted as functional compositions, that are objects carrying primarily relative information. In this context, the unit integral constraint allows to single out one of the possible representations of a class of equivalent measures. On these bases, a function-on-scalar regression model with distributional response is proposed, by relying on the theory of Bayes Hilbert spaces. The geometry of Bayes spaces allows capturing all the key inherent feature of distributional data (e.g., scale invariance, relative scale). A B-spline basis expansion combined with a functional version of the centred log-ratio transformation is employed for actual computations. For this purpose, a new key result is proved to characterize B-spline representations in Bayes spaces. We show the potential of the methodological developments on a real case study, dealing with metabolomics data. Here, a bootstrap-based study is also performed for the uncertainty quantification of the obtained estimates.
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20/2017 - 14/03/2017
Albrecht G.; Caliò F.; Miglio E.
Fair surface reconstruction through rational triangular cubic Bézier patches | Abstract | | We consider the problem from reverse engineering to
construct a G^1 continuous interpolant to a triangulated set of 3D
points and corresponding normals by fitting a composite surface
consisting of rational triangular Bézier patches by using the
so--called rational blend technique. The solution depends on free
shape parameters which are fixed by minimizing different functionals
depending on suitable surface metrics. |
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19/2017 - 14/03/2017
Giovanardi, B.; Formaggia, L.; Scotti, A.; Zunino P.
Unfitted FEM for modelling the interaction of multiple fractures in a poroelastic medium | Abstract | | We propose a mathematical model and a discretization strategy for the simulation of pressurized fractures in porous media accounting for the poroelastic effects due to the interaction of pressure and flow with rock deformations. The aim of the work is to develop a numerical scheme suitable to model the interplay among several fractures subject to fluid injection in different geometric configurations, in view of the application of this technique to hydraulic fracturing. The eXtended Fi- nite Element Method, here employed for both the mechanical and fluid-dynamic problems, is particularly useful to analyze different configurations without remesh- ing. In particular, we adopt an ad hoc enrichment for the displacement at the fracture tip and a hybrid dimensional approach for the fluid. After the presentation of the model and discretization details we discuss some test cases to assess the impact of fracture spacing on aperture during injection. |
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18/2017 - 14/03/2017
Ambartsumyan, I.; Khattatov, E.; Yotov, I.; Zunino, P.
A Lagrange multiplier method for a Stokes-Biot fluid-poroelastic structure interaction model | Abstract | | We study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium. The free fluid is governed by the Stokes equations, while the flow in the poroelastic medium is modeled using the Biot poroelasticity system. Equilibrium and kinematic conditions are imposed on the interface. A mixed Darcy formu- lation is employed, resulting in continuity of flux condition of essential type. A Lagrange multiplier method is employed to impose weakly this condition. A stability and error analysis is performed for the semi-discrete continuous-in-time and the fully discrete formulations. A series of numerical experiments is presented to confirm the theoretical convergence rates and to study the applicability of the method to modeling physical phenomena and the sensitivity of the model with respect to its parameters. |
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16/2017 - 02/03/2017
Ghiglietti, A.; Scarale, M.G.; Miceli, R.; Ieva, F.; Mariani, L.; Gavazzi, C.; Paganoni, A.M.; Edefonti, V.
Urn models for response-adaptive randomized designs: a simulation study based on a non-adaptive randomized trial | Abstract | | Recently, response-adaptive designs have been proposed in randomized clinical trials to achieve ethical and/or cost advantages by using sequential accrual information collected during the trial to dynamically update the probabilities of treatment assignments. In this context, urn models - where the probability to assign patients to treatments is interpreted as the proportion of balls of different colors available in a virtual urn - have
been used as response-adaptive randomization rules. We propose the use of Randomly Reinforced Urn (RRU) models in a simulation study based on a published randomized clinical trial on the efficacy of home enteral nutrition in cancer patients after major gastrointestinal surgery.
We compare results with the RRU design with those previously published with the non-adaptive approach.
We also provide a code written with the R software to implement the RRU design in practice. In detail, we simulate 10,000 trials based on the RRU model in three setups of different total sample sizes. We report information on the number of patients allocated to the inferior treatment and on the empirical power of the t-test for the treatment coefficient in the ANOVA model. We carry out a sensitivity analysis to assess the effect of different urn compositions. For each sample size, in approximately 75% of the simulation runs, the number of patients allocated to the inferior treatment by the RRU design is lower, as compared to the non-adaptive design. The empirical power of the t-test for the treatment effect is similar in the two designs. Accettato per la pubblicazione su Journal of Biopharmaceutical Statistics |
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15/2017 - 02/03/2017
Tagliabue, A; Dede', L.; Quarteroni A.
Complex blood flow patterns in an idealized left ventricle: a numerical study | Abstract | | In this paper, we study the blood flow dynamics in a three-dimensional (3D)
idealized left ventricle of the human heart whose deformation is driven by muscle contraction and relaxation in coordination with the action of the mitral and aortic valves. We propose a simplified but realistic mathematical treatment of the valves function based on mixed time-varying boundary conditions (BCs) for the Navier-Stokes equations modeling the
ow. These switching in time BCs, from natural to essential and viceversa, model either the open or the closed configurations of the valves. At the numerical level these BCs are enforced by means of the extended Nitsche's method [A. Tagliabue et al., MATHICSE report, 2015]. Numerical results for 3D idealized left ventricle obtained by means of Isogeometric Analysis are presented, discussed in terms of both instantaneous and phase-averaged quantities of interest and validated against those available in literature, both experimental and computational. The complex blood flow patterns are analysed to describe the characteristic fluid properties, to show the transitional nature of the flow, and to highlight its main features inside the left ventricle. The sensitivity of the intraventricular flow patterns to the mitral valve properties is also investigated. |
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14/2017 - 02/03/2017
Bruggi, M.; Parolini, N.; Regazzoni, F.; Verani, M.
Finite Element approximation of an evolutionary Topology Optimization problem | Abstract | | We present a topology optimization based procedure aiming at the optimal placement (and design) of the supports in problems characterized by a time dependent construction process. More precisely, we focus on the solution of a time-dependent minimal compliance problem based on the classical Solid Isotropic Material with Penalization (SIMP) method. In particular, a continuous optimization problem with the state equation
defined as the time-integral of a linear elasticity problem on a space-time domain is firstly introduced and the mean compliance over a time interval objective functional is then selected as objective function. The optimality conditions are derived and a fixed-point algorithm is introduced for the iterative computation of the optimal solution. Numerical examples showing the differences between a standard SIMP method, which only optimizes the shape at the final time, and the proposed time-dependent approach are presented and discussed. |
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