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 1349 prodotti
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67/2017 - 16/12/2017
Esterhazy, S.; Schneider, F.; Mazzieri, I; Bokelmann, G.
Insights into the modeling of seismic waves for the detection of underground cavities | Abstract | | Motivated by the need to detect an underground cavity within the procedure of an On-Site-Inspection (OSI), of the Comprehensive Nuclear Test Ban Treaty Organization, the aim of this paper is to present results on the comparison of our numerical simulations with an analytic solution. The accurate numerical modeling can facilitate the development of proper analysis techniques to detect the remnants of an underground nuclear test. The larger goal is to help set a rigorous scientific base of OSI and to contribute to bringing the Treaty into force. For our 3D numerical simulations, we use the discontinuous Galerkin Spectral Element Code SPEED jointly developed at MOX (The Laboratory for Modeling and Scientific
Computing, Department of Mathematics) and at DICA (Department of Civil and Environmental Engineering) of the Politecnico di Milano. |
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66/2017 - 13/12/2017
Tamellini, M.; Parolini, N.; Verani, M.
An optimal control problem of two-phase compressible-incompressible flows | Abstract | | In this work two-phase compressible-incompressible flows are studied. In particular, the possibility of driving the gas bubbles moving in a liquid towards a prescribed position is investigated. To this end, first a well-established mathematical model for two-phase compressible-incompressible fluids is briefly introduced, then an adjoint-based optimal control problem is defined. Finally numerical results on the controllability of the system are presented. |
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65/2017 - 01/12/2017
Regazzoni, F.;Parolini, N.;Verani M.
Topology optimization of multiple anisotropic materials, with application to self-assembling diblock copolymers | Abstract | | We propose a solution strategy for a multimaterial minimum compliance topology optimization problem, which consists in finding the optimal allocation of a finite number of candidate (possibly anisotropic) materials inside a reference domain, with the aim of maximizing the stiffness of the body. As a relevant and novel application we consider the optimization of self-assembled structures obtained by means of diblock copolymers. Such polymers are a class of self-assembling materials which spontaneously synthesize periodic microstructures at the nanoscale, whose anisotropic features can be exploited to build structures with optimal elastic response, resembling biological tissues exhibiting microstructures, such as bones and wood. For this purpose we present a new generalization of the classical Optimality Criteria algorithm to encompass a wider class of problems, where multiple candidate materials are considered, the orientation of the anisotropic materials is optimized, and the elastic properties of the materials are assumed to depend on a scalar parameter, which is optimized simultaneously to the material allocation and orientation. Well-posedness of the optimization problem and well-definition of the presented algorithm are narrowly treated and proved. The capabilities of the proposed method are assessed through several numerical tests. |
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64/2017 - 01/12/2017
Fumagalli, I.; Parolini, N.; Verani, M.
Optimal control in ink-jet printing via instantaneous control | Abstract | | This paper concerns the optimal control of a free surface flow with moving contact line, inspired by an application in ink-jet printing. Surface tension, contact angle and wall friction are taken into account by means of the generalized Navier boundary condition. The time-dependent differential system is discretized by an arbitrary Lagrangian-Eulerian finite element method, and a control problem is addressed by an instantaneous control approach, based on the time discretization of the flow equations. The resulting control procedure is computationally highly efficient and its assessment by numerical tests show its effectiveness in deadening the natural oscillations that occur inside the nozzle and reducing significantly the duration of the transient preceding the attainment of the equilibrium configuration. |
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63/2017 - 23/11/2017
Masci, C.; Paganoni, A.M.; Ieva, F.
Non-parametric mixed-effects models for unsupervised classification of Italian schools | Abstract | | This paper proposes an EM algorithm for non-parametric mixed-effects models (NPEM algorithm) and applies it to the National Institute for the Educational Evaluation of Instruction and Training (INVALSI) data of 2013/2014 as a tool for unsupervised clustering of Italian schools. The main novelties introduced by NPEM algorithm, when applied to hierarchical data, are twofold: first NPEM allows the covariates to be group specific; second, it assumes the random effects to be distributed according to a discrete distribution P* with an (a priori) unknown number of support points. In doing so, it induces an automatic clustering of the grouping factor at higher level of hierarchy, enabling the identification of latent groups of schools that differ in their effect on student achievements. The clustering may then be exploited through the use of school level features. |
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62/2017 - 23/11/2017
Barbarotta, L.; Rossi, S.; Dede', L.; Quarteroni, A.
A Transmurally Heterogeneous Orthotropic Activation Model for Ventricular Contraction and its Numerical Validation | Abstract | | Models for cardiac mechanics require an activation mechanism properly representing the stress-strain relations in the contracting myocardium. In this paper, we propose a new activation model which accounts for the transmural heterogeneities observed in myocardial strain measurements. In order to take into account the anisotropy of the active mechanics, our model is based on an active strain formulation. Thanks to its multiplicative decomposition of the deformation gradient tensor, in this formulation the active strains orthogonal to the fibers can be naturally described. We compare the results of our novel orthotropic formulation against different anisotropic models of the active contraction of the cardiac muscle and, moreover, against experimental data available in the literature. We show that the currently available models can represent only some global quantities, but the strain distributions are not in agreement
with the reported experimental measurements. Conversely, we show that our new transmurally heterogeneous orthotropic activation model improves the accuracy of shear strains related to in-plane rotations and torsion. |
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61/2017 - 22/11/2017
Vadacca, L.; Colciago, C. M.; Micheletti, S.; Scotti, A.
Three-dimensional fault representation by interface and solid elements: effects of the anisotropy of the fault zone permeability on the timing of triggered earthquakes | Abstract | | In the last years numerous seismological evidences have shown a strict correlation between fluid injection and seismicity. An important topic that is currently under discussion in the scientific community concerns the prediction of the earthquake magnitude that may be triggered by fluid injection activities. Coupled fluid flow and geomechanical deformation models can aim at understand the evolution of pore pressure and rock deformation due to fluid injection in the subsurface. To perform an accurate numerical study of the correlation among fluid injection, seismicity rates and maximum earthquake magnitude, it is necessary to characterize the model with two fundamental features: first, the presence of a system of faults possibly intersecting among each other; second, the variability of the hydro-mechanical properties across the region surrounding each fault plane (fault zone). The novelty of this work is to account for these two aspects combining together two different numerical techniques that have been proposed in literature for the fault's modelling: for the first feature, interface elements are used to describe the frictional contacts occurring on the faults surfaces; for the second feature, solid elements are adopted to describe the heterogeneous hydro-mechanical behavior across the fault zone. Moreover, we account for a spatial variation of the permeability in the fault zone both along the dip and the normal direction with respect to the fault plane. We compute the numerical solution for six models among which we vary the permeability contrasts between protolith rocks and damage zone and between damage zone and fault core. We demonstrate that the anisotropy of permeability of the fault zone has a strong impact both on the timing and on the magnitude of triggered earthquakes. We suggest that a similar approach, which includes the entire architecture of the fault zone, shall be included in fluid-flow-geomechanical simulations to improve fault stability analysis during fluid injection. |
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60/2017 - 07/11/2017
Bonaldi, F.; Di Pietro, D. A.; Geymonat, G.; Krasucki, F.
A Hybrid High-Order method for Kirchhoff-Love plate bending problems | Abstract | | We present a novel Hybrid High-Order (HHO) discretization of fourth-order elliptic problems arising from the mechanical modeling of the bending behavior of Kirchhoff--Love plates, including the biharmonic equation as a particular case. The proposed HHO method supports arbitrary approximation orders on general polygonal meshes, and reproduces the key mechanical equilibrium relations locally inside each element. When polynomials of degree $kge 1$ are used as unknowns, we prove convergence in $h^{k+1}$ (with $h$ denoting, as usual, the meshsize) in an energy-like norm. A key ingredient in the proof are novel approximation results for the oblique biharmonic projector on local polynomial spaces. Under biharmonic regularity assumptions, a sharp estimate in $h^{k+3}$ is also derived for the $L^2$-norm of the error on the deflection. The theoretical results are supported by numerical experiments, which additionally show the robustness of the method with respect to the choice of the stabilization. |
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