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 1242 products
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34/2019 - 09/04/2019
Antonietti, P. F.; Mazzieri, I.; Melas, L.; Paolucci, R.; Quarteroni, A.; Smerzini, C.; Stupazzini, M.
Three-dimensional physics-based earthquake ground motion simulations for seismic risk assessment in densely populated urban areas | Abstract | | In this paper we introduce a mathematical and numerical approach aiming at coupling the physically simulated ground motion caused by earthquakes with empirical fragility functions introduced to model the structural damages induced to buildings. To simulate earthquake ground motion we solve a three-dimensional differential model at regional scale describing the propagation of seismic waves through the earth layers up to the surface, based on employing the discontinuous Galerkin spectral element method; selected intensity measure, retrieved from the synthetic time histories, are then employed as input for a vulnerability model based on fragility functions, in order to obtain a reliable prediction of buildings damage state.
The main features and effectiveness of the proposed numerical approach are tested on the Beijing metropolitan area (China). |
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32/2019 - 07/29/2019
Fedele, M.; Quarteroni, A.
Polygonal surface processing and mesh generation tools for numerical simulations of the complete cardiac function. | Abstract | | In order to simulate the cardiac function for a patient-specific geometry, the generation of the computational mesh is crucially important.
In practice, the input is typically a set of unprocessed polygonal surfaces coming either from a template geometry or from medical images.
These surfaces need ad-hoc processing to be suitable for a volumetric mesh generation.
In this work we propose a set of new algorithms and tools aiming to facilitate the mesh generation process.
In particular, we focus on different aspects of a cardiac mesh generation pipeline:
a) specific polygonal surface processing for cardiac geometries, like connection of different heart chambers or segmentation outputs;
b) generation of accurate boundary tags;
c) definition of mesh-size functions dependent on relevant geometric quantities;
d) processing and connecting together several volumetric meshes.
The new algorithms - implemented in the open-source software vmtk - can be combined with each other allowing the creation of personalized pipelines, that can be optimized for each cardiac geometry or for each aspect of the cardiac function to be modeled.
Thanks to these features, the proposed tools can significantly speed-up the mesh generation process for a large range of cardiac applications, from single-chamber single-physics simulations to multi-chambers multi-physics simulations.
We detail all the proposed algorithms motivating them in the cardiac context and we highlight their flexibility by showing different examples of cardiac mesh generation pipelines.
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27/2019 - 07/11/2019
Tantardini, M.; Ieva, F.; Tajoli, L.; Piccardi, C.
Comparing methods for comparing networks | Abstract | | With the impressive growth of available data and the flexibility of network modelling, the problem of devising effective quantitative methods for the comparison of networks arises. Plenty of such methods have been designed to accomplish this task: most of them deal with undirected and unweighted networks only, but a few are capable of handling directed and/or weighted networks too, thus properly exploiting richer information. In this work, we contribute to the effort of comparing the different methods for comparing networks and providing a guide for the selection of an appropriate one. First, we review and classify a collection of
network comparison methods, highlighting the criteria they are based on and their advantages and drawbacks. Then, we test
the methods on synthetic networks and we asses their usability and the meaningfulness of the results they provide. Finally, we apply the methods to two real-world datasets, the European Air Transportation Network and the FAO Trade Network, in order to discuss the results that can be drawn from this type of analysis. |
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26/2019 - 07/11/2019
Antonietti, P. F.; Bonaldi, F.; Mazzieri, I.
Simulation of 3D elasto-acoustic wave propagation based on a Discontinuous Galerkin Spectral Element method | Abstract | | In this paper we present a numerical discretization of the coupled elasto-acoustic wave propagation problem based on a Discontinuous Galerkin Spectral Element (DGSE) approach in a three-dimensional setting. The unknowns of the coupled problem are the displacement field and the velocity potential, in the elastic and the acoustic domains, respectively, thereby resulting in a symmetric formulation. After stating the main the- oretical results, we assess the performance of the method by convergence tests carried out on both matching and non-matching grids, and we simulate realistic scenarios where elasto-acoustic coupling occurs. In particular, we consider the case of Scholte waves and the scattering of elastic waves by an underground acoustic cavity. Numerical simulations are carried out by means of the code SPEED, available at http://speed.mox.polimi.it. |
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25/2019 - 07/10/2019
Gigante, G.; Vergara, C.
On the stability of a loosely-coupled scheme based on a Robin interface condition for fluid-structure interaction | Abstract | | We consider a loosely coupled algorithm for fluid-structure interaction based on a Robin interface condition for the fluid problem (explicit Robin-Neumann scheme). We study the dependence of the stability of this method on the interface parameter in the Robin condition. In particular, for a model problem we find sufficient conditions for instability and stability of the method. In the latter case, we found a stability condition relating the time discretization parameter, the interface parameter, and the added mass effect. Numerical experiments confirm the theoretical findings and highlight optimal choices of the interface parameter that guarantee an accurate solution
with respect to an implicit one. |
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24/2019 - 07/05/2019
Masci, C.; Ieva, F.; Agasisti, T.; Paganoni A.M.
Evaluating class and school effects on the joint achievements in different subjects: a bivariate semi-parametric mixed-effects model | Abstract | | This paper proposes an innovative statistical method to measure the impact of the class/school on its student achievements in multiple subjects. We propose a semi-parametric mixed-effects model with a bivariate response variable, where the random effects are assumed to follow a discrete distribution with an unknown number of support points, together with an Expectation-Maximization algorithm to estimate its parameters. The bivariate setting allows to estimate the distributions of the model coefficients related to each response variable as well as their joint distribution. In the case study, we apply the BSPEM algorithm to data about Italian middle schools, considering students nested within classes, and we identify subpopulations of classes, standing on their effects on student achievements in two different subjects (reading and mathematics). The proposed model is extremely informative in exploring the correlation between multiple class effects, which are typical of the educational production function. The estimated class effects on reading and mathematics student achievements are then explained in terms of various class and school level characteristics selected by means of a LASSO regression. |
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23/2019 - 07/05/2019
Laurino, F; Zunino, P.
Derivation and analysis of coupled PDEs on manifolds with high dimensionality gap arising from topological model reduction | Abstract | | Multiscale methods based on coupled partial differential equations defined on bulk and embedded manifolds are still poorly explored from the theoretical standpoint, although they are successfully used in applications, such as microcirculation and flow in perforated subsurface reservoirs. This work aims at shedding light on some theoretical aspects of a multiscale method consisting of coupled partial differential equations defined on one-dimensional domains embedded into three-dimensional ones. Mathematical issues arise because the dimensionality gap between the bulk and the inclusions is larger than one, that is the high dimensionality gap case. First, we show that such model derives from a system of fully three-dimensional equations, by the application of a topological model reduction approach. Secondly, we rigorously analyze the problem, showing that the averaging operators applied for the model reduction introduce a regularization effect that resolves the issues due to the singularity of solutions and to the ill-posedness of restriction operators. Then, we exploit the structure of the model reduction technique to analyze the modeling error. This study confirms that for infinitesimally small inclusions, the modeling error vanishes. Finally, we discretize the problem by means of the finite element method and we analyze the approximation and the model error by means of numerical experiments. |
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22/2019 - 07/05/2019
Gigante, G.; Sambataro, G.; Vergara, C.
Optimized Schwarz methods for spherical interfaces with application to fluid-structure interaction | Abstract | | In this work we consider the Optimized Schwarz method designed for computational domains that feature spherical or almost spherical interfaces. In the first part, we consider the diffusion-reaction problem. We provide a convergence analysis of the generalized Schwarz method, we discuss an optimization procedure for constant interface parameters leading to a Robin-Robin scheme, and we present some numerical results both in spherical and in ellipsoidal domains. In the second part of the
work, we address the fluid-structure interaction problem. Again, we provide a convergence analysis and discuss optimal choices of constant interface parameters. Finally, we present 3D numerical results inspired by hemodynamic applications, to validate the proposed optimal choices in presence of large added mass effect. In particular, we consider numerical experiments both in an ideal spherical domain and in a realistic abdominal aortic aneurysm. |
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