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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33/2011 - 07/26/2011
Antonietti, P.F.; Beirao da Veiga, L.; Lovadina, C.; Verani, M.
Hierarchical a posteriori error estimators for the mimetic discretization of elliptic problems | Abstract | | We present an a posteriori error estimate of hierarchical type for the mimetic discretization of elliptic problems. Under a saturation assumption, the global reliability and efficiency of the proposed a posteriori estimator has been proved.
Several numerical experiments assess the actual performance of the local error indicators in driving adaptive mesh refinement algorithms based on different marking strategies. Finally, we test an heuristic variant of the proposed error estimator which drastically reduces the overall computational cost of the adaptive procedures. |
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32/2011 - 07/25/2011
Aletti, G; Ghiglietti, A; Paganoni, A.
A modified randomly reinforced urn design | Abstract | | We want to construct a response adaptive design, described in terms of two colors urn model targeting fixed asymptotic allocations. We prove asymptotic results for the process of colors generated by the urn and for the process of its compositions. Applications to sequential clinical trials are considered as well as connections with response-adaptive design of experiments. |
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31/2011 - 07/18/2011
Astorino, M.; Becerra Sagredo, J.; Quarteroni, A.
A modular lattice Boltzmann solver for GPU computing processors | Abstract | | During the last decade, the lattice Boltzmann method (LBM) has been increasingly acknowledged as a valuable alternative to classical numerical techniques (e.g. finite elements,finite volumes, etc.) in fluid dynamics. A distinguishing feature of LBM is undoubtedly its highly parallelizable data structure. In this work we present a general parallel LBM framework for graphic processing units (GPUs). After recalling the essential programming principles of the CUDA C language for GPUs, the details of the implementation will be provided. The modular and generic framework here devised guarantees a flexible use of the code both in two- and three-dimensional problems. In addition, a careful implementation of a memory efficient formulation of the LBM algorithm has allowed to limit the high memory consumption that typically affects this computational method. Numerical examples in two and three dimensions illustrate the reliability and the performance of the code. |
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30/2011 - 07/15/2011
Nobile, F.; Pozzoli, M.; Vergara, C.
Time accurate partitioned algorithms for the solution of fluid-structure interaction problems in haemodynamics | Abstract | | In this work we deal with the numerical solution of the fluid-structure
interaction problem arising in the haemodynamic environment. In particular,
we consider BDF and Newmark time discretization schemes, and we
study different methods for the treatment of the fluid-structure interface
position, focusing on partitioned algorithms for the prescription of the continuity
conditions at the fluid-structure interface. We consider explicit and
implicit algorithms, and new hybrid methods. We study numerically the
performances and the accuracy of these schemes, highlighting the best solutions
for haemodynamic applications. We also study numerically their
convergence properties with respect to time discretization, by introducing
an analytical test case |
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29/2011 - 07/14/2011
Morin, P.; Nochetto, R.H.; Pauletti, S.; Verani, M.
AFEM for Shape Optimization | Abstract | | We examine shape optimization problems in the context of inexact sequential
quadratic programming. Inexactness is a consequence of using adaptive
finite element methods (AFEM) to approximate the state
and adjoint equations (via the dual weighted residual method),
update the boundary, and compute the geometric functional.
We present a novel algorithm that equidistributes the errors due to
shape optimization and discretization, thereby leading to
coarse resolution in the early stages and fine resolution upon
convergence, and thus optimizing the computational effort.
We discuss the ability of the algorithm
to detect whether or not geometric singularities such as corners are
genuine to the problem
or simply due to lack of resolution---a new paradigm in adaptivity.
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28/2011 - 07/13/2011
Pischiutta, M.; Formaggia, L.; Nobile, F.
Mathematical modelling for the evolution of aeolian dunes formed by a mixture of sands: entrainment-deposition formulation | Abstract | | In this work we present a mathematical model of the evolution of aeolian sand dunes, in particular we consider the case of dunes formed by a mixture of sands with di erent characteristics. We first recall a basic model
for the evolution of two dimensional sand dune that has been proposed in the literature. Then, we propose a novel type of mathematical formulation for the evolution of sand dunes formed by a mixture of two (or more) sands,
which expresses the temporal variation of sand surface elevation and concentration of each sand type in terms of the balance between entrainment
and deposition rates of sand. We provide some simple but physically based constitutive relationship for the new variables and we present some numerical simulations that clearly demonstrate that our model can be pro fitably
adopted for the study of interesting physical problems such as sand tracking and dunes collision. |
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27/2011 - 07/12/2011
Antonietti, P.F.; Bigoni, N.; Verani, M.
A Mimetic Discretization of Elliptic Control Problems | Abstract | | In this paper we investigate the Mimetic Finite Difference method for the approximation of a constraint optimal control problem governed by an elliptic operator. A priori error estimates of the first order are derived in suitable discrete norms for both the control and the state variables. The theoretical results are confirmed by numerical experiments performed on a set of test cases selected from the literature. |
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26/2011 - 07/02/2011
Secchi, P.; Vantini, S.; Vitelli, V.
Bagging Voronoi classifiers for clustering spatial functional data | Abstract | | We propose a bagging strategy based on random Voronoi tessellations for the exploration of high dimensional spatial data, suitable for different purposes (e.g., classification, regression, ...). In particular, we consider the problem of clustering functional data indexed by the sites of a spatial finite lattice. The analysis is based on local representatives from neighboring data, i.e., belonging to the same element of a tessellation: the proposed algorithm accounts for spatial dependence by repeatedly clustering functional local representatives with respect to a random system of neighborhoods. Due to the resampling of tessellations, classification result is a cluster assignment frequency map, which can be used to define an a-posteriori criterion to choose the most suitable grouping structure. Thanks to spatial dependence, local representatives are expected to be less noisy and less correlated than original data, providing better performances. Moreover, this reduction in the dimension of the dataset permits the handling of high dimensional sets of data otherwise intractable without an explicit model for spatial dependence.
The performance of the proposed approach is tested on simulated data. An application to environmental data contained in Surface Solar Energy database is also illustrated.
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