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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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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26/2009 - 09/09/2009
Longoni, Matteo; Malossi, A.C.I.; Villa, Andrea
A robust and efficient conservative technique for simulating three-dimensional sedimentary basins dynamics | Abstract | | The development of new efficient numerical techniques is a key point in computational fluid dynamics, and as a consequence in geological simulations. In this paper we present a model for simulating the dynamic of a three-dimensional stratified sedimentary basins. This kind of problem contains several numerical complexities such as the presence of high viscosity jumps, or the necessity of tracking multiple surfaces of interface (horizons) independently. To overcome these difficulties, we introduce a new preconditioner, that reduces significantly
the amount of time required to solve the finite element linear system resulting from the Stokes problem, and a new tracking method. Using
a coupled Level Set–Volume Tracking method, indeed, an unlimited number of layers can be tracked with good mass conservation properties. To prove the efficiency of these new techniques, we present finally the results and the computation performances obtained in simulations
of a realistic case with four horizons, together with a complete description of the main physical quantities involved. |
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25/2009 - 08/26/2009
Farrell, P.E.; Micheletti, Stefano; Perotto, Simona
An anisotropic Zienkiewicz-Zhu a posteriori error estimator for 3D applications | Abstract | | We extend the anisotropic Zienkiewicz-Zhu a posteriori error estimator of [1] to three dimensions. Like the standard Zienkiewicz-Zhu estimator, the proposed estimator is designed to be independent of the problem at hand, is cheap to compute and easy to implement. In contrast to the standard Zienkiewicz-Zhu estimator, the elementwise counterpart of the proposed
estimator explicitly takes into account the geometrical properties of the actual tetrahedron. Thus, in a wide variety of applications, the estimator is able to detect the anisotropic features exhibited by the solution of the
governing equations. A metric-based optimization procedure, rigorously addressed, drives the adaptation of the mesh. It is shown numerically
to yield quasi-optimal triangulations, dictating the accuracy-vs-number of elements behaviour. Despite being heuristic to some extent, in practice the overall anisotropic adaptation procedure turns out to be effective. |
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24/2009 - 08/25/2009
Di Maio, Francesco; Secchi, Piercesare; Vantini, Simone; Zio, Enrico
Optimized Fuzzy C-Means Clustering and Functional Principal Components for Post-Processing Dynamic Scenarios in the Reliability Analysis of a Nuclear System | Abstract | | This paper deals with the processing of accident scenarios generated from a dynamic reliability analysis of a Nuclear Power Plant (NPP). A large number of scenarios are simulated to account for the influence of the timing and magnitudes of fault events on the accident end states; post-simulation processing is then required for retrieving the safety-relevant information.
For classifying the final system state reached at the end of the accident scenarios, Fuzzy C-Means clustering is performed with different sets of Functional Principal Components (FPCs) of a selected relevant process variable. The approach allows capturing the characteristics of the process evolution determined by the occurrence,
timing, and magnitudes of the fault events.
An illustrative case study is considered, regarding the fault scenarios of the digital I&C
of the Lead Bismuth Eutectic eXperimental Accelerator Driven System (LBE-XADS).
The results obtained are compared with those of the Kth Nearest Neighbor (KNN) and Classification and Regression Tree (CART) classifiers. |
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