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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02/2018 - 01/03/2018
Canuto, C.; Nochetto, R. H.; Stevenson, R.; Verani, M.
A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square | Abstract | | Both practice and analysis of adaptive $p$-FEMs and $hp$-FEMs raise
the question what increment in the current polynomial degree $p$
guarantees a $p$-independent reduction of the Galerkin error. We
answer this question for the $p$-FEM in the simplified context of homogeneous
Dirichlet problems for the Poisson equation in the
two dimensional unit square with polynomial data of
degree $p$. We show that an increment proportional to $p$ yields a
$p$-robust error reduction and provide computational evidence that a
constant increment does not. |
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68/2017 - 12/16/2017
Paolucci, R.; Infantino, M.; Mazzieri, I.; Özcebe, A.G.; Smerzini, C.; Stupazzini, M.
3D physics-based numerical simulations: advantages and current limitations of a new frontier to earthquake ground motion prediction. The Istanbul case study. | Abstract | | In this paper, an overview is presented to motivate the use of 3D physics-based numerical simulations of seismic wave propagation to support enhanced Probabilistic Seismic Hazard Assessment. With reference to the case study of Istanbul, we introduce the activities required to construct a numerical model of the surface geology and topography and to determine the input conditions to trigger future earthquakes in a physically sound way. Owing to the intrinsic frequency limitations of the numerical simulations, a post-processing technique to produce realistic broadband waveforms is introduced, allowing to correlate short-period to long-period spectral ordinates from an Artificial Neural Network. Finally, the results obtained in Istanbul from numerous physics-based ground motion scenarios of M7+ earthquakes allow us to throw light on the potential added value to PSHA of the 3D numerical simulations. Namely, to provide locally constrained probabilistic distributions of ground motion intensity measures, matching the actual footprint of a large earthquake in the specific area under study. |
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67/2017 - 12/16/2017
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 - 12/13/2017
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 - 12/01/2017
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 - 12/01/2017
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 - 11/23/2017
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 - 11/23/2017
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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