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 1239 products
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20/2017 - 03/14/2017
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 - 03/14/2017
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 - 03/14/2017
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 - 03/02/2017
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 - 03/02/2017
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 - 03/02/2017
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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13/2017 - 03/02/2017
Gigante, G.; Vergara, C.
Optimized Schwarz Methods for circular flat interfaces and geometric heterogeneous coupled problems | Abstract | | In this work, we focus on the Optimized Schwarz Method for circular flat
interfaces and geometric heterogeneous coupling. In the first case, we pro-
vide a convergence analysis for the diffusion-reaction problem and jumping
coefficients and we apply the general optimization procedure developed in
Gigante and Vergara, Numer. Math., 131(2), 369–404, 2015. In the numer-
ical simulations, we discuss how to choose the range of frequencies in the
optimization and the influence of the Finite Element and projection errors
on the convergence. In the second case, we consider the coupling between
a three-dimensional and a one-dimensional diffusion-reaction problem and
we develop a new optimization procedure. The numerical results highlight
the suitability of the theoretical findings. |
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17/2017 - 03/02/2017
Agosti, A.
Error Analysis of a finite element approximation of a degenerate Cahn-Hilliard equation | Abstract | | This work considers a Cahn-Hilliard type equation with degenerate mobility and single-well potential of Lennard-Jones type, motivated by increasing interest in diffuse interface modelling of solid tumors.
The degeneracy set of the mobility and the singularity set of the potential do not coincide, and the zero of the potential is an unstable equilibrium configuration. This features introduce a nontrivial difference with respect to the Cahn-Hilliard equation analyzed in the literature. In particular, the singularities of the potential do not compensate the degeneracy of the mobility by constraining the solution to be strictly separated from the degeneracy values. The error analysis of a well posed continuous finite element approximation of the problem, where the positivity of the solution is enforced through a discrete variational inequality, is developed. Whilst in previous works the error analysis of suitable finite element approximations has been studied for second order degenerate and fourth order non degenerate parabolic equations, in this work the a-priori estimates of the error between the discrete solution and
the weak solution to which it converges are obtained for a degenerate fourth order parabolic equation.
The theoretical error estimates obtained in the present case state that the norms of the approximation errors, calculated on the support of the solution in the proper functional spaces, are bounded by power laws of the discretization parameters with exponent 1/2, while in the case of the classical Cahn-Hilliard equation with constant mobility the exponent is 1. The estimates are finally succesfully validated by simulation results in one and two space dimensions.
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