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 1238 prodotti
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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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13/2017 - 02/03/2017
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 - 02/03/2017
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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12/2017 - 20/02/2017
Gasperoni, F.; Ieva, F.; Barbati, G.; Scagnetto, A.; Iorio, A.; Sinagra, G.; Di Lenarda, A.
Multi state modelling of heart failure care path: a population-based investigation from Italy | Abstract | | Background: How different risk profiles of Heart Failure (HF) patients can influence multiple readmission rate and outpatients management is widely unknown. To date, several models for predicting adverse outcomes have been developed, but they are mainly focused on a single outcome We propose the application of two different multi state models in real world setting to jointly evaluate the impact of different risk factors on multiple hospital admissions, on Integrated Home Care (IHC) activations, on Intermediate Care Unit (ICU) admissions and on death.
Methods and findings: We propose two multi state models. Each multi state model is characterized by a state space and an intensity transition matrix. A transition is defined as a possible passage from one state to another (in our case, we consider readmission, discharge and death as possible transitions).
The first model (Model 1) concerns only hospitalizations as possible events in patients’ clinical history. In the second one (Model 2), we consider both hospitalizations and ICU admission and IHC activation. Through Model 1, we want to detect the determinants of repeated hospitalizations, while, through Model 2, we want to evaluate which patients’ profiles are associated with transitions in intermediate care with respect to repeated hospitalizations or death. Both models are characterized by transition specific covariates, adjusting for patient’s risk factors.
We identified 4,904 patients (4,129 De Novo and 775 Worsening Heart Failure, WHF) hospitalized for HF from 2009 to 2014, corresponding to 23, 665 events. Among these events, 7, 634 (32%) were HF hospitalizations, 8, 329 (35%) were hospitalization for any cause, 2, 303
(10%) were admission in ICU and 5, 399 (23%) were activation of IHC. 2, 714 (55%) patients died, of these 407 deaths (8% out of the whole cohort) occurred during a HF hospitalization. 1, 316 De Novo HF patients had only one hospitalization and 520 (40% out of 1, 316 ) died after or during the first, and unique, hospitalization. Advanced age and higher morbidity load, measured by Charlson score, increased the rate of dying and of being rehospitalized
(Model 1). Increasing age was also correlated with a longer staying in the hospital (Model 1 and Model 2). Instead, age was inversely related to time spent in IHC (Model 2). The increasing comorbidity load was related to a longer hospital stay and a shorter time spent in IHC (Model 2). WHF condition did not increase the risk of being admitted in ICU/IHC significantly, whereas it was still an important risk factor associated with hospital readmission.
Conclusions: The application of multi state models enables a better identification of two patterns of HF patients. In fact, once adjusted for age and comorbidity load, the WHF condition identifies patients who are more likely to be readmitted several times to hospital, but does not represent an increasing risk factor for activating ICU/IHC. This highlights different ways to manage specific patients patterns of care. In so doing, the results of the paper provide useful healthcare support to patients management in real word context. Our study suggests that the epidemiology of the considered clinical characteristics are more nuanced than traditionally presented with single event by demonstrating their important and versatile role on different patterns of care.
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