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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61/2018 - 12/13/2018
Zakerzadeh, R.; Zunino P.
A Computational Framework for Fluid-Porous Structure Interaction with Large Structural Deformation | Abstract | | We study the effect of poroelasticity on fluid-structure interaction. More precisely, we analyze the role of fluid flow through a deformable porous matrix in the energy dissipation behavior of a poroelastic structure. For this purpose, we develop and use a nonlinear poroelastic computational model and apply it to the fluid-structure interaction simulations. We discretize the problem by means of the finite element method for the spatial approximation and using finite differences in time. The numerical discretization leads to a system of non-linear equations that are solved by Newton’s method. We adopt a moving mesh algorithm, based on the Arbitrary Lagrangian Eulerian (ALE) method to handle large deformations of the structure. To reduce the computational cost, the coupled problem of free fluid, porous media flow and solid mechanics is split among its components and solved using a partitioned approach. Numerical results show that the flow through the porous matrix is responsible for generating a hysteresis loop in the stress versus displacement diagrams of the poroelastic structure. The sensitivity of this effect with respect to the parameters of the problem is also analyzed. |
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59/2018 - 11/20/2018
Martino, A.; Guatteri, G.; Paganoni, A. M.
Multivariate Hidden Markov Models for disease progression | Abstract | | Disease progression models are a powerful tool for understanding the development of a disease, given some clinical measurements obtained from longitudinal events related to a sample of patients. These models are able to give some insights about the disease progression through the analysis of patients histories and can be also used to predict the future course of the disease for an individual. In particular, Hidden Markov Models are suitable for disease progression since they model the latent unobservable states of the disease. In this work we introduce a novel HMM where the outcome is multivariate and its components are not independent; to accomplish our aim, since we do not make any usual normality assumptions, we model the outcome using copulas. We first test the performance of our model in a simulation setting and show the validity of the method. Then, we study the course of Heart Failure, applying our model to an administrative dataset from Lombardia Region in Italy, showing how episodes of hospitalization can give information about the disease status of a patient. |
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58/2018 - 11/13/2018
Ferro, N.; Micheletti, S.; Perotto, S.
A sequential coupling of shape and topology optimization for structural design | Abstract | | We consider different algorithms to design lightweight and stiff structures exhibiting free-form features. First we apply a shape optimization and a topology optimization procedure, separately. Then, we couple these two techniques sequentially. Topology optimization is also enhanced by a structure-tailored computational mesh, made it possible by anisotropic mesh adaptation. This allows us to obtain an intrinsically smooth final layout which can be directly moved on to the production manufacturing phase. An extensive numerical assessment corroborates both qualitatively and quantitatively the performances of the proposed algorithms. |
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57/2018 - 11/13/2018
Ferro, N.; Micheletti, S.; Perotto, S.
POD-assisted strategies for structural topology optimization | Abstract | | We propose a new numerical tool for structural optimization design. To cut down the computational burden typical of the Solid Isotropic Material with Penalization method, we apply Proper Orthogonal Decomposition on SIMP snapshots computed on a fixed grid to construct a rough structure (predictor) which becomes the input of a SIMP procedure performed on an anisotropic adapted mesh (corrector). The benefit of the proposed design tool is to deliver smooth and sharp layouts which require a contained computational effort before moving to the 3D printing production phase. |
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56/2018 - 11/13/2018
Antonietti, P.F.; Manzini, G.; Verani, M.
The conforming virtual element method for polyharmonic problems | Abstract | | In this work, we exploit the capability of virtual element methods in accommodating approximation spaces featuring high-order continuity to numerically approximate differential problems of the form $Delta^p u =f$, $pge1$. More specifically, we develop and analyze the conforming virtual element method for the numerical approximation of polyharmonic boundary value problems, and prove an abstract result that states the convergence of the method in the energy norm. |
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55/2018 - 10/30/2018
Cerroni, D.; Laurino, F.; Zunino, P.
Mathematical analysis, finite element approximation and numerical solvers for the interaction of 3D reservoirs with 1D wells | Abstract | | We develop a mathematical model for the interaction of a three-dimensional reservoir with the flow through wells, namely narrow cylindrical channels cutting across the reservoir. Leak off or sink effects are taken into account. To enable the simulation of complex configurations featuring multiple wells, we apply a model reduction technique that represents the wells as one-dimensional channels. The challenge in this case is to account for the interaction of the reservoir with the embedded one- dimensional wells. The resulting problem consists of coupled partial differential equations defined on manifolds with heterogeneous dimensionality. The existence and regularity of weak solutions of such problem is thoroughly addressed. Afterwards, we focus on the numerical discretization of the problem in the framework of the finite element method. We notice that the numerical scheme does not require conformity between the computational mesh of the reservoir and the one of the wells. From the standpoint of the solvers, we discuss the application of multilevel algorithms, such as the algebraic multigrid method. Finally, the reduced mathematical model and the discretization method is applied to a few configurations of reservoir with wells, with the purpose of verifying the theoretical properties and to assess the generality of the approach. |
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54/2018 - 10/30/2018
Dal Santo, N.; Deparis, S.; Manzoni, A.; Quarteroni, A.
Multi space reduced basis preconditioners for parametrized Stokes equations | Abstract | | We introduce a two-level preconditioner for the efficient solution of large scale saddle-point linear systems arising from the finite element (FE) discretization of parametrized Stokes equations. This preconditioner extends the Multi Space Reduced Basis (MSRB) preconditioning method proposed in [Dal Santo et al., 2018]; it combines an approximated block (fine grid) preconditioner with a reduced basis (RB) solver which plays the role of coarse component. A sequence of RB spaces, constructed either with an enriched velocity formulation or a Petrov-Galerkin projection, is built. Each RB coarse component is defined to perform a single iteration of the iterative method at hand. The flexible GMRES (FGMRES) algorithm is employed to solve the resulting preconditioned system and targets small tolerances with a very small iteration count and in a very short time. Numerical test cases for Stokes flows in three dimensional parameter-dependent geometries are considered to assess the numerical properties of the proposed technique in different large scale computational settings. |
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53/2018 - 10/30/2018
Giantesio, G.; Musesti, A.; Riccobelli, D.
A comparison between active strain and active stress in transversely isotropic hyperelastic materials | Abstract | | Active materials are media for which deformations can occur in absence of loads, given an external stimulus. Two approaches to the modeling of such materials are mainly used in literature, both based on the introduction of a new tensor: an additive stress P_act in the active stress case and a multiplicative strain F_a in the active strain one. Aim of this paper is the comparison between the two approaches on simple shears.
Considering an incompressible and transversely isotropic material, we design constitutive relations for P_act and F_a so that they produce the same results for a uniaxial deformation along the symmetry axis. We then study the two approaches in the case of a simple shear deformation. In a hyperelastic setting, we show that the two approaches produce different stress components along a simple shear, unless some necessary conditions on the strain energy density are fulfilled. However, such conditions are very restrictive and rule out the usual elastic strain energy functionals. Active stress and active strain therefore produce different results in shear, even if they both fit uniaxial data.
Our results show that experimental data on the stress-stretch response on uniaxial deformations are not enough to establish which activation approach can capture better the mechanics of active materials. We conclude that other types of deformations, beyond the uniaxial one, should be taken into consideration in the modeling of such materials. |
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