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 1242 products
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26/2008 - 11/24/2008
Aletti, Giacomo; May, Caterina; Secchi, Piercesare
A Central Limit Theorem, and related results, for two-color randomly reinforced urn | Abstract | | We prove a Central Limit Theorem for the sequence of random compositions of a two-color randomly reinforced urn. As a consequence, we are
able to show that the distribution of the urn limit composition has no point
masses. |
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25/2008 - 11/20/2008
Detomi, Davide; Parolini, Nicola; Quarteroni, Alfio
Mathematics in the wind
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24/2008 - 11/19/2008
Bacchelli, Valeria; Veneziani, Alessandro; Vessella, Sergio
Corrosion detection in a 2D domain with a polygonal boundary | Abstract | | We consider the problem of quantitative non-destructive evaluation
of corrosion in a 2D domain representing a thin metallic plate. Corro-
sion damage is assumed to occur in an inaccessible part of the domain.
Reconstruction of the damaged profile is possible by measuring an electro-
static current properly induced by a potential in an accessible part of the
boundary (electrical impedance tomography). We present here numerical
methods and results based on a formulation of the problem introduced
and analyzed in Bacchelli-Vessella, Inverse Problems, 22 (2006), where
the corroded profile is represented by a polygonal boundary. We resort
in particular to the Landweber method and the Brakhage semi-iterative
scheme. Numerical results show the reliability of this approach in general
situations, including nongraph corroded boundaries |
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23/2008 - 10/28/2008
Hysing, Shu-Ren; Turek, Stefan; Kuzmin, Dmitri; Parolini, Nicola; Burman, Erik; Ganesan, Sashikumaar; Tobiska, Lutz
Quantitative benchmark computations of two-dimensional bubble dynamics | Abstract | | Benchmark configurations for quantitative validation and comparison of incompressible interfacial flow
codes, which model two-dimensional bubbles rising in liquid columns, are proposed. The benchmark
quantities: circularity, center of mass, and mean rise velocity are defined and measured to monitor
convergence towards a reference solution. Comprehensive studies are undertaken by three independent
research groups, two representing Eulerian level set finite element codes, and one representing an ALE
moving grid approach.
The first benchmark test case considers a bubble with small density and viscosity ratios which
undergoes moderate shape deformation. The results from all codes agree very well allowing for target
reference values to be established. For the second test case, a bubble with a very low density compared
to that of the surrounding fluid, the results for all groups are in good agreement up to the point of
break up, after which all three codes predict different bubble shapes. This highlights the need for the
research community to invest more effort in obtaining reference solutions to problems involving break
up and coalescence.
Other research groups are encouraged to participate in these benchmarks by contacting the authors
and submitting their own data. The reference data for the computed benchmark quantities can also
be supplied for validation purposes |
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22/2008 - 10/23/2008
Nobile, Fabio; Tempone, Raul
Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients | Abstract | | We consider the problem of numerically approximating statistical moments
of the solution of a time dependent linear parabolic partial differential
equation (PDE), whose coefficients and/or forcing terms are spatially
correlated random fields. The stochastic coefficients of the PDE are approximated
by truncated Karhunen-Lo eve expansions driven by a finite number
of uncorrelated random variables. After approximating the stochastic coefficients
the original stochastic PDE turns into a new deterministic parametric
PDE of the same type, the dimension of the parameter set being
equal to the number of random variables introduced.
After proving that the solution of the parametric PDE problem is analytic
with respect to the parameters, we consider global polynomial approximations
based on tensor product, total degree or sparse polynomial spaces
and constructed by either a Stochastic Galerkin or a Stochastic Collocation
approach. We derive convergence rates for the different cases and present
numerical results that show how these approaches are a valid alternative to
the more traditional Monte Carlo Method for this class of problems |
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21/2008 - 09/29/2008
Antonietti, Paola; Suli, Endre
Domain Decomposition Preconditioning for Discontinuous Galerkin Approximation of Convection-Diffusion Problems | Abstract | | We study a class of nonoverlapping Schwarz preconditioners for DG ap- proximations of convection-di usion equations. The generalized minimal residual (GMRES) Krylov space-based iterative solver is accelerated with the proposed preconditioners. We discuss the issue of convergence of the re- sulting preconditioned iterative method, and demonstrate through numer- ical computations that the classical Schwarz convergence theory for non- symmetric and indefinite problems developed by Cai and Widlund [SIAM J. Sci. Statist. Comput. 13 (1992) 243--258], [SIAM J. Numer. Anal.
30 (1993) 936--952] cannot be applied to explain theoretically the converge observed numerically |
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20/2008 - 09/24/2008
David, Filippo; Micheletti, Stefano; Perotto, Simona
Model adaptation enriched with an anisotropic mesh spacing for advection-diffusion-reaction systems | Abstract | | We propose a procedure aiming at reducing the computational cost involved
in the numerical approximation of (possibly nonlinear) advectiondiffusion-
reaction systems. The idea is to suitably combine a model with a
mesh adaptive procedure. In particular we first derive, separately, a model
error estimator and an anisotropic estimator for the discretization error,
suited for driving a model and a mesh adaptivity algorithm, respectively.
These two strategies are then properly combined, allowing for a merged
model-mesh control. The whole procedure is finally assessed on some numerical
test cases, essentially inspired by ecological and environmental application |
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19/2008 - 09/03/2008
Badia, Santiago; Nobile, Fabio; Vergara, Christian
Robin-Robin preconditioned Krylov methods for fluid-structure interaction problems | Abstract | | In this work we propose a Robin-Robin preconditioner combined
with Krylov iterations for the solution of the interface system
arising in fluid-structure interaction (FSI) problems. It can be
seen as a partitioned FSI procedure and in this respect it
generalizes the ideas introduced in [{ sl Badia, Nobile and Vergara,
J. Comput. Phys. { bf{227}} (2008) 7027 --7051]}.
We analyze the convergence of GMRES iterations with the Robin-Robin
preconditioner on a model problem and compare its efficiency with some
existing algorithms. The method is shown to be very efficient for many
challenging fluid-structure interaction problems, such as those
characterized by a large added-mass effect or by enclosed fluids. In
particular, the possibility to solve balloon-type problems without any
special treatment makes this algorithm very appealing compared to the
computationally intensive existing approaches |
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