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 1251 products
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07/2014 - 01/31/2014
Agasisti, T.; Ieva, F.; Paganoni, A.M.
Heterogeneity, school-effects and achievement gaps across Italian regions: further evidence from statistical modeling | Abstract | | Catching the differences in educational attainments between groups of students and across schools is becoming increasingly interesting. With the aim of assessing the extent of these differences in the context of Italian educational system, the paper applies multilevel modeling to a new administrative dataset, containing detailed information for more than 500,000 students at grade 6 in the year 2011/12, provided by the Italian Institute for the Evaluation of Educational System. The results show that the national averages hide considerable heterogeneity both within and between schools, and that it is possible to estimate statistically significant school effects , i.e. the positive/negative impact of attending a specific school on the student s test score, after a case-mix adjustment. Therefore, the paper s most important message is that school effects are different in terms of magnitude and types in the three geographical macro-areas (Northern, Central and Southern Italy) and are dependent upon specific students characteristics. |
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06/2014 - 01/28/2014
Benzi, M.; Deparis, S.; Grandperrin, G.; Quarteroni, A.
Parameter estimates for the relaxed dimensional factorization preconditioner and application to hemodynamics | Abstract | | We present new results on the Relaxed Dimensional Factorization (RDF) preconditioner for solving saddle point problems, first introduced in [5]. This method contains a parameter α > 0, to be chosen by the user. Previous works provided an estimate of α in the 2D case using Local Fourier Analysis. Novel algebraic estimation techniques for finding a suitable value of the RDF parameter in both the 2D and the 3D case with arbitrary geometries are proposed. These techniques are tested on a variety of discrete saddle point problems arising from the approximation of the Navier–Stokes equations using a Marker-and-Cell scheme and a finite element one. We also show results for a large-scale problem relevant for hemodynamics simulation that we solve in parallel using up to 8196 cores.
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05/2014 - 01/27/2014
Rozza, G.; Koshakji, A.; Quarteroni, A.
Free Form Deformation Techniques Applied to 3D Shape Optimization Problems | Abstract | | The purpose of this work is to analyse and study an efficient parametrization technique for a 3D shape optimization problem. After a brief review of the techniques and approaches already available in literature, we recall the Free Form Deformation parametrization, a technique which proved to be efficient and at the same time versatile, allowing to manage complex shapes even with few parameters. We tested and studied the FFD technique by establishing a path, from the geometry definition, to the method implementation, and finally to the simulation and to the optimization of the shape. In particular, we have studied a bulb and a rudder of a race sailing boat as model applications, where we have tested a complete procedure from Computer-Aided-Design to build the geometrical model to discretization and mesh generation. |
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04/2014 - 01/26/2014
Palamara, S.; Vergara, C.; Catanzariti, D.; Faggiano, E.; Centonze, M.; Pangrazzi, C.; Maines, M.; Quarteroni, A.
Patient-specific generation of the Purkinje network driven by clinical measurements: The case of pathological propagations | Abstract | | To describe the electrical activity of the left ventricle is necessary to take into account the Purkinje fibers, responsible for the fast and coordinate ventricular activation, and their interaction with the muscular propagation. The aim of this work is to propose a methodology for the generation of a patient-specific Purkinje network driven by clinical measurements of the activation times acquired during pathological propagations. In particular, we consider clinical data acquired on four subjects suffering from pathologies with different origins, from conduction problems in the muscle or in the Purkinje fibers to a pre-excitation ventricular syndrome. To assess the accuracy of the proposed method, we compare the results obtained by using the patient-specific Purkinje network with the ones obtained by using a not patient-specific network. The results showed that the mean absolute errors are reduced by a factor in the range 27%-54%, highlighting the importance of including a patient-specific Purkinje network in computational models. |
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03/2014 - 01/25/2014
Kashiwabara, T.; Colciago, C.M.; Dede, L.; Quarteroni, A.
Well-posedness, regulariy, and convergence analysis of the Finite Element approximation of a Generalized Robin boundary value problem | Abstract | | In this paper, we propose the mathematical and finite element analysis of a second order Partial Differential Equation endowed with a generalized Robin boundary condition which involves the Laplace–Beltrami operator, by introducing a function space H 1 (Ω; Γ) of H 1 (Ω)-functions with H 1 (Γ)-traces, where Γ ⊆ ∂Ω. Based on a variational method, we prove that the solution of the generalized Robin boundary value problem possesses a better regularity property on the boundary than in the case of the standard Robin problem. We numerically solve generalized Robin problems by means of the finite element method with the aim of validating the theoretical rates of convergence of the error in the norms associated to the space H 1 (Ω; Γ).
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02/2014 - 01/23/2014
Antonietti, P.F.; Sarti, M.; Verani, M.
Multigrid algorithms for high order discontinuous Galerkin methods | Abstract | | In this paper we study the performance of a W-cycle multigrid algorithm for high order Discontinuous Galerkin discretizations of the Poisson problem. We recover the well known uniformity of the rate of convergence with respect to the mesh size and the number of levels and study the dependence on the polyonomial order p employed. The theoretical estimates are verified by two- and three-dimensional numerical tests. |
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01/2014 - 01/13/2014
Secchi, P.; Vantini, S.; Zanini, P.
Hierarchical Independent Component Analysis: a multi-resolution non-orthogonal data-driven basis | Abstract | | We introduce a new method, named HICA (Hierarchical Independent Component Analysis), suited to the dimensional reduction and the multi-resolution analysis of high dimensional and complex data. HICA solves a Blind Source
Separation problem by integrating Treelets with Independent Component Analysis and provides a multi-scale non-orthogonal data-driven basis apt
to meaningful data representations in reduced spaces. We describe some theoretical properties of HICA and we test the method on synthetic data. Finally, we apply HICA to the analysis of EEG traces. |
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67/2013 - 12/24/2013
Canuto, C.; Simoncini, V.; Verani, M.
On the decay of the inverse of matrices that are sum of Kronecker products | Abstract | | Decay patterns of
matrix inverses have recently attracted considerable interest,
due to their relevance in numerical analysis,
and in applications requiring matrix
function approximations.
In this paper we analyze the decay pattern of the inverse of banded matrices in the form
$S=M otimes I_n + I_n otimes M$ where $M$ is tridiagonal, symmetric and positive definite, $I_n$ is the identity matrix, and $ otimes$ stands for the Kronecker product.
It is well known that the inverses of banded matrices exhibit an exponential
decay pattern away from the main diagonal. However, the entries in $S^{-1}$
show a non-monotonic decay, which is not caught
by classical bounds. By using an alternative expression for $S^{-1}$, we
derive computable upper bounds that
closely capture the actual behavior of its entries. We also show that similar estimates
can be obtained when $M$ has a larger bandwidth, or when the sum of Kronecker
products involves two different matrices.
Numerical experiments illustrating the new bounds are also reported.
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