Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1237 prodotti
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52/2012 - 06/12/2012
Perotto, S.
Hierarchical model (Hi-Mod) reduction in non-rectilinear domains | Abstract | | For the numerical solution of second-order elliptic problems featuring dynamics with a dominant direction
(e.g., drug dynamics in the circulatory system), we proposed a Hierarchical Model (HiMod) reduction procedure.
We actually perform a finite element discretization along the mainstream direction and a spectral modal approximation for the transverse dynamics.
The number of modes can locally vary along the centerline to properly fit the relevant transverse dynamics. In previous works we have considered the cases of rectilinear domains. Here we address the more general case of curved domains, where the direction of the dominant component of the solution is non-rectilinear. |
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51/2012 - 29/11/2012
Beck, J.; Nobile, F.; Tamellini, L.; Tempone, R.
A quasi-optimal sparse grids procedure for groundwater flows | Abstract | | In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work “On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods” to a Darcy problem where the permeability is modeled as a lognormal random field. We propose an explicit a-priori/a-posteriori procedure for the construction of such quasi-optimal grid and show its effectiveness on a numerical example. In this approach, the two main ingredients are an estimate of the decay of the Hermite coefficients of the solution and an efficient nested quadrature rule with respect to the Gaussian weight. |
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50/2012 - 28/11/2012
Carcano, S.; Bonaventura, L.; Neri, A.; Esposti Ongaro, T.
A second order accurate numerical model for multiphase underexpanded volcanic jets | Abstract | | An improved version of the PDAC (Pyroclastic Dispersal Analysis Code) numerical model for the simulation of multiphase volcanic flows is presented and validated for the simulation
of multiphase volcanic jets in supersonic regimes.
The present version of PDAC includes second-order time and space discretizations and fully multidimensional advection discretizations, in order to reduce numerical diffusion and
enhance the accuracy of the original model.
The resulting numerical model is tested against the problem of jet decompression in
both two and three dimensions. For homogeneous jets, numerical results show a good quantitative agreement
with experimental results on the laboratory scale in terms of Mach disk location. For multiphase jets, we consider monodisperse and polydisperse mixtures of particles
with different diameter. For fine particles, for which the pseudogas limit is valid,
the multiphase model correctly reproduces
predictions of the pseudogas model. For both fine and coarse particles, we
measure the importance of multiphase
effects with relation to the characteristic time scales of multiphase jets and we quantify how
particles affect the average jet dynamics in terms of pressure, mixture density, vertical velocity and temperature.
Furthermore, time
dependent vent conditions are introduced, in order to achieve numerical
simulation of eruption regimes characterized by transient jet behaviour. We show how in case of rapid change in vent conditions, volcanic jet structures do not evolve through a succession of steady state configurations and the transition between different flow
conditions can result in the collapse of the volcanic column. |
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49/2012 - 27/11/2012
Migliorati, G.; Nobile, F.; von Schwerin, E.; Tempone, R.
Approximation of Quantities of Interest in stochastic PDEs by the random discrete L2 projection on polynomial spaces | Abstract | | In this work we consider the random discrete L2 projection on polynomial spaces (hereafter RDP) for the approximation of scalar Quantities of Interest (QOIs) related to the solution of a Partial Differential Equation model with random input parameters. The RDP technique consists of randomly sampling the input parameters and computing the corresponding values of the QOI, as in a standard Monte Carlo approach. Then, the QOI is approximated as a multivariate polynomial
function of the input parameters by a discrete least squares approach.
We consider several examples including the Darcy equations with random permeability; the linear elasticity equations with random elastic coefficient; the Navier-Stokes equations in random geometries and with random fluid viscosity.
We show that the RDP technique is well suited for QOIs that depend smoothly on a moderate number of random parameters. Our numerical tests confirm the
theoretical findings in [14], which have shown that, in the case of a single random parameter uniformly distributed, the RDP technique is stable and optimally convergent if the number of sampling points scales quadratically with the dimension of the polynomial space. However, in the case of several random input parameters, numerical evidence shows that this condition could be relaxed and a linear scaling seems enough to achieve stable and optimal convergence, making the RDP technique very promising for high dimensional uncertainty quantification. |
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48/2012 - 26/11/2012
Ghiglietti, A.; Paganoni, A.M.
Statistical properties of two-color randomly reinforced urn design targeting fixed allocations | Abstract | | This paper deals with the statistical properties of a response adaptive design, described in terms of a two colors urn model, targeting prespecified asymptotic allocations. Results on the rate of convergence of number of patients assigned to each treatment are proved as well as on the asymptotic behavior of the urn composition. Suitable statistics are introduced and studied to test the hypothesis on treatment s differences. |
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47/2012 - 30/10/2012
Astorino, M.; Chouly, F.; Quarteroni, A.
Multiscale coupling of finite element and lattice Boltzmann methods for time dependent problems | Abstract | | In this work we propose a new numerical procedure for the simulation of time-dependent problems based on the coupling between the finite element method and the lattice Boltzmann method. The two methods are regarded as macroscale and mesoscale solvers, respectively. The procedure is based on the Parareal paradigm and allows for a truly multiscale coupling between two numerical methods having optimal efficiency at different space and time scales. The motivations behind this approach are manifold. Among others, we have that one technique may be more efficient, or physically more appropriate or less memory consuming than the other depending on the target of the simulation and/or on the sub-region of the computational
domain. The theoretical and numerical framework is presented for parabolic equations even though its potential applicability is much wider (e.g. Navier-Stokes equations). Various numerical examples on the heat equation will validate the proposed procedure and illustrate its multiple advantages.
Keywords: finite element method, lattice Boltzmann method, multiscale coupling, Parareal, parallel-in-time domain decomposition. |
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46/2012 - 26/10/2012
Dassi, F.; Perotto, S.; Formaggia, L.; Ruffo, P.
Efficient geometric reconstruction of complex geological structures | Abstract | | Complex geological structures pose a challenge to domain discretization. Indeed data are normally given as a set of intersecting surfaces, sometimes with incomplete data, from which one has to identify the computational domain to build a mesh suited for numerical simulations. In this paper we describe a set of tools which have been developed for this purpose. Specialized data structures have been developed to efficiently identify intersections of triangulated surfaces and to conformally include these intersections in the starting meshes, while improving the mesh quality. Then, an effective algorithm has been implemented to detect the different sub-regions forming the computational domain; this algorithm has been properly enhanced to take into account the specific characteristics involved in the simulation of geological basins. |
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45/2012 - 24/10/2012
Negri, F.; Rozza, G.; Manzoni, A.; Quarteroni, A.
Reduced basis method for parametrized elliptic optimal control problems | Abstract | | We propose a suitable model reduction paradigm -the certied reduced basis method (RB) - for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations (PDEs). In particular, we develop the methodology for parametrized quadratic optimization problems with elliptic equations as constraint. Firstly, we recast the optimal control problem in the framework of saddle-point problems in order to take advantage of the already developed RB theory for Stokes-type problems. Then, the usual ingredients of
the RB methodology are provided: a Galerkin projection onto a low-dimensional space of basis functions properly selected by an adaptive procedure; an affine parametric dependence enabling to perform competitive Offine-Online splitting in the computational procedure; an efficient and rigorous a posteriori error estimate on the state, control and adjoint variables as well as on the cost functional. Finally, the reduction scheme is applied to some numerical tests conrming the theoretical results and showing the efficiency of the proposed technique.
Keywords: reduced basis methods, parametrized optimal control problems, saddle-point problems, model order reduction, PDE-constrained optimization, a posteriori error estimate |
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