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 1238 prodotti
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10/2009 - 20/03/2009
Zunino, Paolo
Numerical approximation of incompressible flows with net flux defective boundary conditions by means of penalty techniques | Abstract | | We consider incompressible flow problems with defective boundary conditions prescribing only the net flux on some inflow and outflow sections of the boundary. As a pradigm for such problems, we simply refer to Stokes flow. After a brief review of the problem and of its well posedness, we discretize the corresponding variational formulation by means of finite elements and looking at the boundary conditions as constraints, we exploit a penalty method to account for them. We perform the analysis of the method in terms of consistency, boundedness and stability of the discrete bilinear form and we show that the application of the penalty method does not affect the optimal convergence properties of the finite element discretization.
Since the additional terms introduced to account for the defective boundary conditions are non local, we also analyze the spectral properties of the equivalent algebraic formulation and we exploit them to set up an efficient solution strategy. In contrast to alternative discretization methods based for instance on Lagrange multipliers accounting for the constraints on the boundary, the present scheme is particularly effective because it only mildly
affects the computational cost of the numerical approximation. Indeed, it does not require neither multipliers nor sub-iterations or additional adjoint problems with respect to the reference problem at hand. |
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09/2009 - 19/03/2009
Agostoni, Elio; Salsa, Sandro; Perego, Mauro; Veneziani, Alessandro
Mathematical and numerical Modeling of Focal Cerebral Ischemia | Abstract | | Cerebral focal ischemia is a local degeneration of brain tissue induced by a reduction of blood supply. We introduce a mathematical model that
includes the blood dynamics, represented by a
ow in a porous medium and ion dynamics (calcium and potassium), together with other variables (energy stores, tissue integrity, oxygen and glucose) representing the biochemical events consequent to the vessel occlusion. The accurate description of the coupling between fuid dynamics and Biochemics is one of the distinctive features of the present work. We present both 2D and 3D simulations.
Occurrence of peculiar ion dynamics, called spreading depression waves, formerly pointed out in the literature, is observed in 2D results. The role of some parameters of the problem in suppressing these waves is discussed.
We moreover simulate in 3D the e ects of a forced reperfusion of the occluded vessel ( brinolysis) and the consequent blood leakage (hemorrhagic
infarct).
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08/2009 - 16/03/2009
Antonietti, Paola F.; Houston, Paul
An hr-adaptive discontinuous Galerkin method for advection-diffusion problems | Abstract | | We propose an adaptive mesh refinement strategy based on exploiting a combination of a pre-processing mesh re-distribution algorithm employing a harmonic mapping technique, and standard (isotropic) mesh subdivision for discontinuous Galerkin approximations of advection-diffusion problems. Numerical experiments indicate that the resulting adaptive strategy can efficiently reduce the computed discretization error by clustering the nodes in the computational mesh where the analytical solution undergoes rapid variation.
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07/2009 - 16/02/2009
Perego, Mauro; Veneziani, Alessandro
An efficient generalization of the Rush-Larsen method for solving electro-physiology membrane equations | Abstract | | In this paper we address a second-order class of methods for solving ordinary differential systems coming from some problems in electro-physiology.
The set of methods generalizes to the second order a previous proposal by Rush and Larsen (1978). We prove that the methods are second-order
convergent and are in general more stable than the corresponding multistep methods. Moreover, they feature better positivity properties. We
present their time-adaptive formulation, which is well suited for our electrophysiology problems. In particular, numerical results are presented on the Monodomain model coupled to Luo-Rudy I ionic models for the propagation of the cardiac potential.
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06/2009 - 15/02/2009
Formaggia, Luca; Veneziani, Alessandro; Vergara, Christian
Numerical solution of flow rate boundary problems for an incompressible fluid in deformable domains | Abstract | | In this paper we consider the numerical solution of the interaction of an incompressible fluid and an elastic structure in a truncated computational domain. As well known, in this case there is the problem of prescribing realistic boundary data on the artificial sections, when only partial data are available. This problem has been investigated extensively for the rigid case. In this work we start considering the compliant case, by focusing on the flow rate conditions for the fluid. We propose three formulations of this problem, different algorithms for its numerical solution and carry out several 2D numerical simulations with the aim of comparing the performances of the different algorithms.
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05/2009 - 14/02/2009
Ieva, Francesca; Paganoni, Anna Maria
A case study on treatment times in patients with ST-Segment Elevation Myocardial Infarction | Abstract | | In this paper we conduct a statistical analysis of data coming from an observational case study about patients with ST-Segment Elevation Acute
Myocardial Infarction treated in one of the 23 hospitals of the Milano net-work for acute coronary syndromes and emergency services. The principal aim of this article is to identify from a statistical perspective the most important prognostic factors for in-hospital survival and reperfusion efficacy. We model the dependency between outcome variables and predictors
with Generalized Additive Models. These statistical analyses have demonstrated the clinical guess that an early pre-alarm of the Emergency Room is an essential step to improve the clinical treatment of patients. |
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04/2009 - 13/02/2009
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 - 19/01/2009
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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