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 1349 products
-
35/2015 - 06/26/2015
Manzoni, A.; Pagani, S.
A certified reduced basis method for PDE-constrained parametric optimization problems by an adjoint-based approach | Abstract | | In this paper we present a certified reduced basis (RB) framework for the efficient solution of PDE-constrained parametric optimization problems. We consider optimization problems (such as optimal control and optimal design) governed by elliptic PDEs and involving possibly non-convex cost functionals, assuming that the control functions are described in terms of a parameters vector. At each optimization step, the high-fidelity approximation of state and adjoint problems is replaced by a certified RB approximation, thus yielding a very efficient solution through an “optimize-then-reduce” approach. We develop a posteriori error estimates for the solutions of state and adjoint problems, for the cost functional, its gradient and the optimal parameters. We confirm our theoretical results in the case of optimal control/design problems dealing with potential and thermal flows. |
-
34/2015 - 06/26/2015
Bernardi, M.S.; Mazza, G.; Ramsay, J.O.; Sangalli, L.M.
A separable model for spatial functional data with application to the analysis of the production of waste in Venice province | Abstract | | We propose a method for the analysis of functional data with complex dependencies, such as spatially dependent curves or time dependent surfaces, over highly textured domains. The models are based on the idea of regression with partial di erential regularizations. We focus in particular on a separable space-time version of the model. Among the various modelling features, the proposed method is able to deal with spatial domains featuring peninsulas, islands and other complex geometries.
Space-varying covariate information is included in the model via a semi-parametric framework. The proposed method is compared via simulation
studies to other spatio-temporal techniques and it is applied to the analysis of the annual production of waste in the towns of Venice province. |
-
33/2015 - 06/26/2015
Fumagalli, A; Pasquale, L; Zonca, S.; Micheletti, S.
An upscaling procedure for fractured reservoirs with non-matching grids | Abstract | | Upscaling of geological models for reservoir simulation is an active and important area of research. In particular, we are interested in reservoirs where the rock matrix exhibits an intricate network of fractures, which usually act as a preferential path to the flow. Accounting for fractures’ contribution in the simulation of a reservoir is of paramount importance. Here, we have focused on obtaining effective parameters (e.g. transmissibility) on a 3D computational grid on the reservoir scale, that account for the presence, at a finer spatial scale, of fractures, and network of fractures. We have, essentially, followed the idea illustrated in Karimi-Fard et al. [2006], yet this work has some notable aspects of innovation in the way the procedure has been implemented, and in its capability to consider rather general corner-point grids, like the ones normally used in reservoir simulations in the industry, and complex and realistic fracture networks. In particular, novel contribution is the employment of EDFM for computing fracture-fracture and matrix-fracture transmissibilities, with a remarkable gain in speed-up. The output is in form of transmissibility that can be used for reservoir simulations with software like Eclipse, Intersect, or GPRS. The results demonstrate the effectiveness and computational efficiency of the numerical procedure, and of the developed software, which is now ready for further testing and industrialization.
|
-
32/2015 - 06/26/2015
Agasisti,T.; Ieva, F.; Masci, C.; Paganoni, A.M.
Does class matter more than school? Evidence from a multilevel statistical analysis on Italian junior secondary school students | Abstract | | This paper assesses the differences in educational attainments between
students across classes and schools they are grouped by, in the context of
Italian educational system. The purpose is to identify a relationship between pupils’ reading test scores and students’ characteristics, stratifying for classes, schools and geographical areas. The dataset contains detailed information about more than 500,000 students at the first year of junior secondary school in the year 2012/2013. By means of multilevel linear models, it is possible to estimate statistically significant school and class effects, after adjusting for pupil’s characteristics, including prior achievement.
The results show that school and class effects are very heterogeneous
across macro-areas (Northern, Central and Southern Italy), and that there are substantial discrepancies between and within schools; overall,
class effects on achievement tend to be larger than school ones. |
-
31/2015 - 06/26/2015
Pini, A.; Vantini, S.; Colombo, D.; Colosimo, B. M.; Previtali, B.
Domain-selective functional ANOVA for process analysis via signal data: the remote monitoring in laser welding | Abstract | | In many application domains, process monitoring and process optimization have to deal with functional responses, also known as profile data.
In these scenarios, a relevant industrial problem consists in discovering which specific parts of the functional response is mostly affected by the process changes. As a matter of fact, knowledge of the specific locations where the curve is more sensitive to process changes can bring several advantages. It can be exploited to design specific monitoring devices directly focusing on the functional data pertaining to the selected intervals. Secondly, the dimensional reduction can eventually bring to an increase of the power to detect process changes.
This paper proposes a methodology to inferentially select the parts of the output functions that are more informative in terms of the underlying factors. The procedure is based on a non-parametric domain-selective ANOVA for functional data, which results in the selection of the intervals of the domain presenting statistically significant effects of each factor. To illustrate its potential in industrial applications, the proposed procedure is applied to a case study on remote laser welding, where the main aim is monitoring the gap between the welded plates through the observation of the emission spectra of the welded material. |
-
30/2015 - 06/13/2015
Pini, A.; Vantini, S.
Interval-wise testing for functional data | Abstract | | We propose an inferential procedure for functional data, able to select the intervals of the domain imputable of rejecting a functional null hypothesis.
The procedure is based on three different steps: (i) a functional test is performed on any interval of the domain; (ii) an unadjusted and an adjusted p-value function are defined from the results of the previous tests; (iii) the significant intervals of the domain are selected by thresholding the unadjusted or the adjusted p-value functions, depending on the desired type of control of the family-wise error rate (i.e., point-wise or interval-wise, respectively). In detail, we prove that the newly defined unadjusted p-value function provides a control of the point-wise error rate (i.e., given any point of the domain where the null hypothesis is not violated - in an L2 sense to be suitably defined - the probability of wrongly selecting it as significant is controlled) and that it is point-wise consistent (i.e., given any point of the domain where the null hypothesis is violated - in an L2 sense to be suitably defined - the probability of selecting it as significant goes to one as the sample size goes to infinity). Similarly, we prove that the newly defined adjusted p-value function provides instead a control of the interval-wise error rate (i.e., given any interval of the domain where the null hypothesis is almost-everywhere not violated the probability of wrongly selecting it as significant is controlled) and that it is interval-wise consistent (i.e., given any interval of the domain where the null hypothesis is almost-everywhere violated the probability of selecting it as significant goes to one as the sample size goes to infinity).
The procedure is also applied - together to other two state-of-the-art procedures - to the analysis of of the Canadian daily temperatures, to test for pairwise differences between four climatic regions. In detail, we show how the new procedure hereby proposed is able to give a new deeper and useful insight on the possible rejection of the null hypothesis that consists in the selection of the periods of the years presenting significant differences between each couple of regions. |
-
29/2015 - 06/13/2015
Antonietti, P.F.; Cangiani, A.; Collis, J.; Dong, Z.; Georgoulis, E.H.; Giani, S.; Houston, P.
Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains | Abstract | | The numerical approximation of partial differential equations (PDEs) posed on complicated geometries, which include a large number of small geometrical features or microstructures, represents a challenging computational problem. Indeed, the use of standard mesh generators, employing simplices or tensor product elements, for example, naturally leads to very fine finite element meshes, and hence the computational effort required to numerically approximate the underlying PDE problem may be prohibitively expensive. As an alternative approach, in this article we present a review of composite/agglomerated discontinuous Galerkin finite element methods (DGFEMs) which employ general polytopic elements. Here, the elements are typically constructed as the union of standard element shapes; in this way, the minimal dimension of the underlying composite finite element space is independent of the number of geometrical features. In particular, we provide an overview of hp–version inverse estimates and approximation results for general polytopic elements, which are sharp with respect to element facet degeneration. On the basis of these results, a priori error bounds for the hp–DGFEM approximation of both second–order elliptic and first–order hyperbolic PDEs will be derived. Finally, we present numerical experiments which highlight the practical application of DGFEMs on meshes consisting of general polytopic elements. |
-
28/2015 - 06/13/2015
Taffetani, M.; Ciarletta, P.
Beading instability in soft cylindrical gels with capillary energy: weakly non-linear analysis and numerical simulations | Abstract | | Soft cylindrical gels can develop a long-wavelength peristaltic pattern driven by a competition between surface tension and bulk elastic energy. In contrast to the Rayleigh-Plateau instability for viscous fluids, the macroscopic shape in soft solids evolves toward a stable beading, which strongly differs from the buckling arising in compressed elastic cylinders.
This work proposes a novel theoretical and numerical approach for studying the onset and the non-linear development of the elastocapillary beading in soft cylinders, made of neo-Hookean hyperelastic material with capillary energy at the free surface, subjected to axial stretch. Both a theoretical study, deriving the linear and the weakly non-linear stability analyses for the problem, and numerical simulations, investigating the fully non-linear evolution of the beaded morphology, are performed. The theoretical results prove that an axial elongation can not only favour the onset of beading, but also determine the nature of the elastic bifurcation. The fully non-linear phase diagrams of the beading are also derived from finite element numerical simulations, showing two peculiar morphological transitions when varying either the axial stretch or the material properties of the gel. Since the bifurcation is found to be subcritical for very slender cylinders, an imperfection sensitivity analysis is finally performed. In this case, it is shown that a surface sinusoidal imperfection can resonate with the corresponding marginally stable solution, thus selecting the emerging beading wavelength.
In conclusion, the results of this study provide novel guidelines for controlling the beaded morphology in different experimental conditions, with important applications in micro-fabrication techniques, such as electrospun fibres. |
|
