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 1238 products
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34/2009 - 12/14/2009
Antonietti, Paola F.; Houston, Paul
A Class of Domain Decomposition Preconditioners for hp-Discontinuous Galerkin Finite Element Methods | Abstract | | In this article we address the question of efficiently solving the algebraic linear system of equations arising from the discretization of a symmetric, elliptic boundary value problem using hp-version discontinuous Galerkin finite element methods. In particular, we introduce a class of domain decomposition preconditioners based on the Schwarz framework, and prove bounds on the condition number of the resulting iteration operators. Numerical results con rming the theoretical estimates are also presented. |
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33/2009 - 11/11/2009
Vantini, Simone
On the Definition of Phase and Amplitude Variability in Functional Data Analysis | Abstract | | We introduce a mathematical framework in which a functional data registration problem can be soundly and coherently set. In detail, we show
that the introduction of a metric/semi-metric and of a group of warping function respect to which the metric/semi-metric is invariant is the key to
a clear and not ambiguous de nition of phase and amplitude variability.
Moreover, an amplitude-to-total variability index is proposed. This index turns to be useful in practical situations to measure to what extent amplitude variability a ects the data and to compare the e ectiveness of diff erent
registration methods. |
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32/2009 - 11/10/2009
Micheletti, Stefano; Perotto, Simona
Anisotropic adaptation via a Zienkiewicz-Zhu error estimator for 2D elliptic problems | Abstract | | We propose a Zienkiewicz-Zhu a posteriori error estimator in 2D, which shares the computational advantages typical of the original estimator. The
novelty is the inclusion of the geometrical features of the computational mesh, useful for an anisotropic mesh adaptation. The adapted triangulations are shown numerically to be quasi-optimal with respect to the error-vs-number
of elements behaviour. |
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31/2009 - 11/06/2009
Antonietti, Paola F.; Biscari, Paolo; Tavakoli, Alaleh; Verani, Marco; Vianello, Maurizio
Theoretical study and numerical simulation of textiles | Abstract | | We propose a new approach for developing continuum models fit to describe the mechanical behavior of textiles. We develop a physically mo-
tivated model, based on the properties of the yarns, which can predict and simulate the textile behavior. The approach relies on the selection of a suitable topological model for the patch of the textile, coupled with constitutive models for the yarn behavior. The textile structural con guration is related to the deformation through an energy functional, which depends on both the macroscopic deformation and the distribution of internal nodes.
We determine the equilibrium positions of these latter, constrained to an assigned macroscopic deformation. As a result, we derive a macroscopic
strain energy function, which reflects the possibly nonlinear character of the yarns as well as the anisotropy induced by the microscopic topological pattern. By means of both analytical estimates and numerical experiments, we show that our model is well suited for both academic test cases and real industrial textiles, with particular emphasis on the tricot textile.
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30/2009 - 10/22/2009
Xuan , Z. C.; Lassilla, T.; Rozza, Gianluigi; Quarteroni, Alfio
On computing upper and lower bounds on the outputs of linear elasticity problems approximated by the smoothed finite element method | Abstract | | Verification of the computation of local quantities of interest, e.g. the displacements at a point, the stresses in a local area and the stress intensity factors at crack tips, plays an important role in improving the structural design
for safety. In this paper, the smoothed finite element method (SFEM) is used for finding upper and lower bounds on the local quantities of interest that are outputs of the displacement field for linear elasticity problems,
based on bounds on strain energy in both the primal and dual problems.
One important feature of SFEM is that it bounds the strain energy of the structure from above without needing the solutions of different subproblems that are based on elements or patches but only requires the direct finite element computation. Upper and lower bounds on two linear outputs and one quadratic output related with elasticity – the local reaction, the local displacement, and the J-integral – are computed by the proposed method in two different examples. Some issues with SFEM that remain to be resolved are also discussed. |
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29/2009 - 10/21/2009
Antonietti, Paola F.; Pratelli, Aldo
Finite Element Approximation of the Sobolev Constant | Abstract | | Denoting by $S$ the sharp constant in the Sobolev inequality in $W^{1,2}_0(B)$, being $B$ the unit ball in $R3$, and denoting by $S_h$ its approximation in a suitable finite element space, we show that $S_h$ converges to $S$ as $h->0$ with a polynomial rate of convergence. We provide both an upper and a lower bound on the rate of convergence, and present some numerical results. |
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28/2009 - 09/11/2009
Gaudio, Loredana; Quarteroni, Alfio
Spectral Element Discretization of Optimal Control Problems | Abstract | | In this work we consider the numerical solution of a distributed optimal control problem associated with an elliptic partial differential equation.
We approximate the optimality system by the spectral element method and derive a posteriori error estimates with respect to the cost functional.
Then we use an hN adaptive refinement technique to reduce this error: the error indicator is used to mark what elements must be refined. The
choice between an h or N refinement is based on the use of a predicted error reduction algorithm. Numerical results show the way this algorithm
works. |
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27/2009 - 09/10/2009
Mirabella, Lucia; Nobile, Fabio; Veneziani, Alessandro
An a posteriori error estimator for model adaptivity in electrocardiology | Abstract | | We introduce an a posteriori modeling error estimator for the effective computation of electric potential propagation in the heart. Starting from the Bidomain problem and an extended formulation of the simplified Monodomain
system, we build a hybrid model, called Hybridomain, which is dynamically adapted to be either Bi- or Mono-domain ones in different regions of the computational domain according to the error estimator. We show that accurate results can be obtained with the adaptive Hybridomain model with a reduced computational cost compared to the full Bidomain model. We discuss the effectivity of the estimator and the reliability of results on simulations performed on real human left ventricle geometries retrieved from healthy subjects. |
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