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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04/2009 - 02/13/2009
Canuto, Claudio; Gervasio, Paola; Quarteroni, Alfio
Finite-Element Preconditioning of G-NI Spectral Methods | Abstract | | Several old and new finite-element preconditioners for nodal-based spectral
discretizations of − Laplacian(u) = f in the domain Omega = (−1, 1)^d, (d = 2 or 3),
with Dirichlet or Neumann boundary conditions, are considered and compared in terms of both condition number and computational efficiency. The
computational domain covers the case of classical single-domain spectral approximations (see [5]), as well as that of more general spectral-element
methods in which the preconditioners are expressed in terms of local (upon every element) algebraic solvers. The primal spectral approximation is based on the Galerkin approach with Numerical Integration (G-NI) at the
Legendre-Gauss-Lobatto (LGL) nodes in the domain. The preconditioning matrices rely on either P1 or Q1 or Q1,NI (i.e., with Numerical Integration)
finite elements on meshes whose vertices coincide with the LGL nodes used for the spectral approximation. The analysis highlights certain preconditioners, that yield the solution at an overall cost proportional to Nd+1, where N denotes the polynomial degree in each direction.
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03/2009 - 01/19/2009
D'Elia, M.; Dede', L.; Quarteroni, A.
Reduced Basis Method for Parametrized Differential Algebraic Equations | Abstract | | Parametrized systems of Differential Algebraic Equations (DAEs) stand at the base of several mathematical models in Microelectronics, Computational Fluid Dynamics and other Engineering fields. Since the dimension of these systems can be huge, high computational costs could occur, so efficient numerical methods are
needed in order to contain the computational cost of the simulations. In this field, Model Order Reduction (MOR) methods represent a valid and efficient approach.
In particular, in this work we propose to use Reduced Basis (RB) methods for the solution of parametrized systems of DAEs. Our starting point is the formulation of the RB method for parametrized Partial Differential Equations (PDEs) and the one for non-parametrized DAEs. We describe how to obtain a projection of the
solution of the original problem onto a parameter dependent reduced subspace and we provide an a priori estimate for the approximation error. Numerical tests on problems of interest for electronic circuit design highlight the effectiveness of the proposed method. Comparison is made with the parametrized Proper Orthogonal
Decomposition (POD) method, which is a typical MOR method. |
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02/2009 - 01/16/2009
Bonaventura, Luca; Biotto, Cristian; Decoene, Astrid; Mari, Lorenzo; Miglio, Edie
A couple ecological-hydrodynamic model for the spatial distribution of sessile aquatic species in thermally forced basins | Abstract | | The life cycle of several sessile or highly sedentary aquatic species is characterized
by a pelagic stage, during which propagules are dispersed by the water flow. As a consequence, hydrodynamics plays a crucial role in redistributing offspring, thus deeply influencing the spatiotemporal dynamics of such species. In this work, we describe an integrated modeling framework that allows the coupling of a minimal – yet biologically well founded – ecological model for population dynamics at the local scale to an efficient numerical model of three dimensional |
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01/2009 - 01/15/2009
Miglio, Edie; Sgarra, Carlo;
A Finite Element Framework for Option Pricing with the Bates Model | Abstract | | In the present paper we present a finite element approach for option pricing in the framework of a well-known stochastic volatility model with
jumps, the Bates model. In this model the asset log-returns are assumed to follow a jump-diffusion model where the jump component consists of a Lévy process of compound Poisson type, while the volatility behavior is described by a stochastic differential equation of CIR type, with a meanreverting drift term and a diffusion component correlated with that of the
log-returns. Like in all the Lévy models, the option pricing problem can be formulated in terms of an integro-differential equation: for the Bates model the unknown F(S, V, t) (the option price) of the pricing equation depends on three independent variables and the differential operator part turns out to be of parabolic kind, while the nonlocal integral operator is calculated with respect to the Lévy measure of the jumps. In this paper we will present a variational formulation of the problem suitable for a finite element approach. The numerical results obtained for european options will be compared with those obtained with different methods. |
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28/2008 - 12/10/2008
D'Angelo, Carlo; Quarteroni, Alfio
On the coupling of 1D and 3D diffusion-reaction equations. Applications to tissue perfusion problems | Abstract | | In this paper we consider the coupling between two
diffusion-reaction problems, one taking place in a three-dimensional
domain, the other in a one-dimensional subdomain.
This coupled problem is the simplest model of fluid flow in a
three-dimensional porous medium featuring fractures that can be
described by one-dimensional manifolds. In particular this model
can provide the basis for a multiscale analysis of blood flow
through tissues, in which the capillary network is represented as a
porous matrix, while the major blood vessels are described by thin
tubular structures embedded into it: in this case, the model allows
the computation of the 3D and 1D blood pressures respectively in the
tissue and in the vessels.
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27/2008 - 11/25/2008
Quarteroni, Alfio
Mathematical Models in Science and Engineering
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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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