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 1275 products
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MOX 78 - 01/23/2006
Agoshkov, Valery; Gervasio, Paola; Quarteroni, Alfio
Optimal Control in Heterogeneous Domain Decomposition Methods for Advection-Diffusion Equations | Abstract | | New domain decomposition methods (DDM) based on optimal control approach are introduced for the coupling of first and second order equations on overlapping subdomains. Several cost functionals and control functions are proposed. Uniqueness and existence results are proved for the coupled problem, and the convergence of iterative processes is analyzed.
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MOX 77 - 01/16/2006
Quarteroni, Alfio
What mathematics can do for the simulation of blood circulation | Abstract | | In this paper we introduce some basic differential models for the description of blood flow in the circulatory system. We comment on their mathematical properties, their meaningfulness and their limitation to yield realistic and accurate numerical simulations, and their contribution for a better understanding of cardiovascular physio-pathology.
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MOX 76 - 01/13/2006
Formaggia, Luca; Micheletti, Stefano; Sacco, Riccardo; Veneziani, Alessandro
Mathematical modelling and numerical simulation of a glow-plug | Abstract | | In this work we derive a mathematical model that
describes the working of a glow-plug of the type used in Diesel engines
to preheat the air-diesel fuel mixture.
The proposed model consists of a time dependent one dimensional
partial differential equation which incorporates the electro-thermal
interaction between the electric current flowing in the plug and the
temperature.
It has been obtained by integrating the heat
equation on each section of the plug, assuming axial symmetry and using
thermal equilibrium relation in the radial direction. The problem is
highly non-linear because of the radiation boundary conditions and the
dependence on temperature of several parameters. In particular, heat
is generated by an electric resistance whose characteristic strongly
depends on temperature.
We have adopted a quasi-Newton treatment of the non-linear term and a
mixed finite element formulation for the linearized problem. Time
advancing has been carried out using a semi-implicit Euler scheme.
Several numerical simulations have been carried in order to assess the
validity of the model, whose predictions have been compared with
available experimental data.
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MOX 75 - 01/12/2006
Baudisch, J.; Bonaventura, Luca; Iske, A.; Miglio, Edie
Matrix valued Radial Basis Functions for local vector field reconstruction: applications to computational fluid dynamic models | Abstract | | Matrix valued radial basis functions
are applied to achieve accurate local vector field reconstructions of smooth vector fields from normal components assigned at the edges of a computational mesh. The theory underlying this reconstruction approach is reviewed and reformulated so as to allow for more straightforward application.
The accuracy of the locally reconstructed fields is assessed by appropriate numerical tests. Applications to numerical models for geophysical fluid dynamics problems show that such reconstruction techniques can usefully complement low order discretization approaches with important discrete conservation properties.
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MOX 74 - 12/14/2005
Aletti, G.; May, C.; Secchi, Piercesare
On the distribution of the limit proportion for a two-color, randomly reinforced urn with equal reinforcement distributions | Abstract | | We consider a two-color randomly reinforced urn with equal reinforcement distributions and we characterize the distribution of the urn s limit proportions as the unique continous solution of a functional equation involving unknown probability distributions on [0.1]. |
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MOX 73 - 12/13/2005
Caliò, Franca Miglio, Edie Moroni, G. Rasella, M.
Curve fairing using integral spline operators | Abstract | | In this paper a local automatic planar curve fairing algorithm based parametric B-spline class is presented. In particular we employ a particular class of spline characterized by a shape parameterer lambda: for this family of spline it has been shown (see [9]) that the value of the parameter affects the shape of the whole spline curve. We have exploited this last property locally in order to move a subset of the control points defining the given curve. In our approach the value of lambda is chosen in order
to minimize a functional related to the fairness of the curve and in particular we have considered a functional involving the second derivative of the curvature. The numerical test cases we have performed showed the effectiveness of algorithm both in academic and real-world situations.
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MOX 72 - 12/12/2005
Dogan, G.; Morin, P.; Nochetto, R.H., Verani, Marco
Finite Element Methods for Shape Optimization and Applications | Abstract | | We present a variational framework for shape optimization problems that establishes and clarifies explicit connections among the continuous formulation, its full discretization and the resulting linear algebraic systems.
Our approach hinges on the following essential features: shape differential calculus, a semi-implicit time discretization and a finite element method for space discretization. We use shape differential calculus to express variations
of bulk and surface energies with respect to domain changes. The semi-implicit time discretization allows us to track the domain boundary without an explicit parametrization, and has the exibility to choose different descent directions by varying the scalar product used for the computation of normal velocity. We propose a Schur complement approach to solve the resulting linear systems e_ciently. We discuss applications of this framework to image segmentation, optimal shape design for PDE, and surface diffusion, along with the choice of suitable scalar products in each case. We illustrate the method with several numerical experiments, some developing pinch-off and topological changes in finite time.
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MOX 71 - 11/24/2005
Babuska, I.; Nobile, Fabio; Tempone, Raul
A stochastic collocation method for elliptic partial differential equations with random input data | Abstract | | In this paper we propose and analyze a Stochastic-Collocation method to solve elliptic Partial Differential Equations with random coefficients and forcing terms (input data of the model). The input data are assumed to depend on a fi nite number of random variables. The method consists in a Galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space and naturally leads to the solution of uncoupled deterministic prob¬lems as in the Monte Carlo approach. It can be seen as a generalization of the Stochastic Galerkin method proposed in [Babuˇ ska -Tempone-Zouraris, SIAM J. Num. Anal. 42(2004)] and allows one to treat easily a wider range of situations, such as: input data that depend non-linearly on the random variables, diffusivity coefficients with unbounded second moments , random variables that are correlated or have unbounded support. We provide a rigorous convergence analysis and demonstrate exponential con¬vergence of the “probability error” with respect of the number of Gauss points in each direction in the probability space, under some regularity assumptions on the random input data. Numerical examples show the effectiveness of the method. |
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