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 1152 products
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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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23/2009 - 08/24/2009
Gerardo Giorda, Luca; Nobile, Fabio; Vergara, Christian
Analysis and optimization of Robin-Robin partitioned procedures in Fluid-Structure Interaction Problems | Abstract | | In the solution of Fluid-Structure Interaction problems, partitioned procedures are modular algorithms that involve separate fluid and structure solvers, that interact, in an iterative framework, through the exchange of suitable transmission conditions at the FS interface. In this work we study, using Fourier analysis, the convergence of partitioned algorithms based on
Robin transmission conditions. We derive, for different models of the fluid and the structure, a frequency dependent reduction factor at each iteration of the partitioned algorithm, which is minimized by choosing optimal values of the coefficients in the Robin transmission conditions. Two-dimensional numerical results are also reported, which highlight the effectiveness of the optimization procedure. |
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22/2009 - 08/21/2009
Formaggia, Luca; Minisini, Sara; Zunino, Paolo
Modeling erosion controlled drug release and transport phenomena in the arterial tissue | Abstract | | We introduce and analyze a model for simulating the release of a drug from a polymeric matrix into the arterial tissue, with the aim to describe
the processes which occur after the implantation of a cardiovascular drug eluting stent (DES). The main processes occurring in the polymeric matrix
are drug dissolution and diffusion. Moreover, surface erosion, which consists in mass loss due to the degradation of the polymeric network, is considered as well. The drug eluted from the matrix is released in the arterial wall, modelled as an homogeneous porous medium. By consequence, we assume that drug molecules are transported by diffusion and convection. Moreover, inside the tissue the reversible reaction of the drug with specific binding sites is taken into account and the coupled problem of mass transfer between
matrix and tissue is formulated. It is shown that the mass conservation principle leads to non standard boundary coupling conditions to describe
the transfer of the drug both in the solid and dissolved phases. Then, the problem at hand is solved numerically, highlighting the importance of
enforcing mass conservation and focusing on the influence of the polymer erosion on the drug release profile and drug distribution in the tissue. |
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21/2009 - 08/20/2009
Bonaventura, Luca; Castruccio, Stefano; Sangalli, Laura M.
A Bayesian approach to geostatistical interpolation with exible variogram models | Abstract | | A Bayesian approach to covariance estimation and geostatistical interpolation based on flexible variogram models is introduced. In particular,
we consider black-box kriging models. These variogram models do not require restrictive assumptions on the functional shape of the variogram; furthermore, they can handle quite naturally non isotropic random fields.
The proposed Bayesian approach does not require the computation of an empirical variogram estimator, thus avoiding the arbitrariness implied by the construction of the empirical variogram itself. Moreover, it provides a complete assessment of the uncertainty in the variogram estimation. The advantages of this approach are illustrated via an extensive simulation study and by application to a well known benchmark dataset. |
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