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 1151 products
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25/2007 - 12/10/2007
Micheletti, Stefano; Perotto, Simona
Space-Time Adaption for Advection-Diffusion-Reaction Problems on Anisotropic Meshes | Abstract | | We deal with the approximation of an unsteady advection-diffusion-
reaction problem by means of space-time finite elements, continuous affine
in space and piecewise constant in time. In particular, we are interested in
the advection-dominated framework. To face the trade-off between
computational cost and accuracy, we devise a space-time adaptive procedure
where both the time step and the spatial grid are adapted throughout the
simulation. Two are the key points involved: the derivation of an a
posteriori error estimator where the contributions of the spatial and of the
temporal discretization are split; a balance of these two contributions via a
proper adaptive scheme. The main novelty of the paper is the interest for
an anisotropic mesh adaption framework.
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24/2007 - 12/06/2007
Sangalli, Laura M.; Secchi, Piercesare; Vantini, Simone; Veneziani, Alessandro
A Case Study in Functional Data Analisys: Geometrical Features of the Internal Carotid Artery | Abstract | | This pilot study is a product of the AneuRisk Project, a
scientific program that aims at evaluating the role of vascular
geometry and hemodynamics in the pathogenesis of cerebral
aneurysms. By means of functional data analyses, we explore the
AneuRisk dataset to highlight the relations between the geometric
features of the internal carotid artery, expressed by its radius
profile and centerline curvature, and the aneurysm location. After
introducing a new similarity index for functional data, we
eliminate ancillary variability of vessel radius and curvature
profiles, through an iterative registration procedure. We then
reduce data dimension by means of functional principal components
analysis. Finally a quadratic discriminant analysis of functional
principal components scores allows to discriminate patients with
aneurysms in different districts. |
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23/2007 - 11/26/2007
Sangalli, Laura M.; Secchi, Piercesare; Vantini, Simone; Veneziani, Alessandro
Efficient estimation of 3-dimensional centerlines of inner carotid arteries and their curvature functions by free knot regression splines | Abstract | | This work stems from the need for accurate estimation of the
curvature function of an artery, that emerged within ANEURISK
Project, a research program that aims at investigating the role of
vascular morphology and hemodynamics on the pathogenesis of cerebral
aneurysms. We develop here a regression technique that exploits free
knot splines in a novel setting, to estimate 3-dimensional curves,
and their derivatives. We thoroughly compare this technique to a
classical regression method, local polynomial smoothing, showing
that 3-dimensional free knot regression splines yield more accurate
and efficient estimates.
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22/2007 - 11/20/2007
Roberts, Gareth O.; Sangalli, Laura M.
Latent diffusion models for event history analysis | Abstract | | We consider Bayesian hierarchical models for
event history analysis, where the event times are modeled through an underlying diffusion process, which determines the hazard rate. We show how these models can be efficiently treated by means of Markov
chain Monte Carlo techniques. |
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21/2007 - 11/06/2007
Massimi, Paolo; Quarteroni, Alfio; Saleri, Fausto; Scrofani, Giovanni
Modeling of Salt Tectonics | Abstract | | In this work a general framework for the simulation of sedimentary basins in presence of salt structures is addressed. Sediments and evaporites are modeled as non-Newtonian fluids and the thermal effects induced by the presence of salt are taken into account. The computational strategy is based on a Lagrangian methodology with intensive grid adaptivity, togheter with a kinematic modeling of faults and different kinds of boundary conditions representing sedimentation, erosion, basement evolution, lithospheric compression and extension. The proposed methodology is applied to simple test cases as well as to a geological reconstruction of industrial interest. |
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20/2007 - 11/05/2007
Burman, Erik; Quarteroni, Alfio; Stamm, Benjamin
Stabilization Strategies for High Order Methods for Transport Dominated Problems | Abstract | | Standard high order Galerkin methods, such as pure spectral or high order finite element methods, have
insufficient stability properties when applied to transport dominated problems. In this paper we review some stabilization
strategies for pure spectral methods and spectral multidomain approaches.
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19/2007 - 10/31/2007
Burman, Erik; Quarteroni, Alfio; Stamm, Benjamin
Interior Penalty Continuous and Discontinuous Finite Element Approximations of Hyperbolic Equations | Abstract | | In this paper we present the continuous and discontinuous Galerkin
methods in a unified setting for the numerical approximation of the transport
dominated advection-reaction equation. Both methods are stabilized by the
interior penalty method, more precisely by the jump of the gradient in the continuous
case whereas in the discontinuous case the stabilization of the jump of
the solution and optionally of its gradient is required to achieve optimal convergence.
We prove that the solution in the case of the continuous Galerkin
approach can be considered as a limit of the discontinuous one when the stabilization
parameter associated with the penalization of the solution jump tends
to infinity. As a consequence, the limit of the numerical flux of the discontinuous
method yields a numerical flux for the continuous method too. Numerical
results will highlight the theoretical results that are proven in this paper.
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18/2007 - 10/30/2007
Micheletti, Stefano; Perotto, Simona
Output functional control for nonlinear equations driven by anisotropic mesh adaption. The Navier-Stokes equations. | Abstract | | The contribution of this paper is twofold: firstly, a general
approach to the goal-oriented a posteriori analysis of nonlinear
partial differential equations is laid down, generalizing the standard
DWR method to Petrov-Galerkin formulations. This accounts for:
different approximations of the primal and dual problems;
nonhomogeneous Dirichlet boundary conditions, even
different on passing from the primal to the dual problem;
the error due to data approximation; the effect of stabilization
(e.g. for advective-dominated problems).
Secondly, moving from this framework, and employing anisotropic interpolation
error estimates, a sound anisotropic mesh adaption
procedure is devised for the numerical approximation of the
Navier-Stokes equations by continuous piecewise linear finite elements.
The resulting adaptive procedure is thoroughly addressed and
validated on some relevant test cases.
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