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 1148 prodotti
-
16/2009 - 20/05/2009
Aletti, Giacomo; May, Caterina; Secchi, Piercesare
A functional equation whose unknown is P ([0, 1]) valued | Abstract | | We study a functional equation whose unknown maps a euclidean space into the space of probability distributions on [0,1].
We prove existence and uniqueness of its solution under suitable regularity and boundary conditions and we characterize solutions that are diffuse on [0,1]. A canonical solution is obtained by means
of a Randomly Reinforced Urn with different reinforcement distributions having equal means. |
-
15/2009 - 07/05/2009
Perotto, Simona; Ern, Alexandre; Veneziani, Alessandro
Hierarchical local model reduction for elliptic problems I: a domain decomposition approach | Abstract | | Some engineering applications, for instance related to fluid dynamics in pipe or channel networks, feature a dominant spatial direction along which the most relevant dynamics develop. Nevertheless, local features of the problem depending on the other directions, that we call transverse, can be locally relevant to the whole problem. We propose in the context of ellip-
tic problems such as advection–diffusion–reaction equations, a hierarchical model reduction approach in which a coarse model featuring only the dominant direction dynamics is enriched locally by a fine model that accounts for the transverse variables via an appropriate modal expansion. We introduce a domain decomposition approach allowing us to employ a different
number of modal functions in different parts of the domain according to the local complexity of the problem at hand. The methodology is investigated numerically on several test cases. |
-
14/2009 - 08/04/2009
Beirao da Veiga, Lourenco; Verani, Marco
A posteriori boundary control for FEM approximation of elliptic eigenvalue problems | Abstract | | We derive new a posteriori error estimates for the nite element solution of an elliptic eigenvalue problem, which take into account also the e ects of the polygonal approximation of the domain. This suggests local error indicators that can be used to drive a procedure handling the mesh re nement together with the approximation of the domain. |
-
13/2009 - 07/04/2009
Miglio, Edie; Villa, Andrea
A mathematical derivation of compaction and basin models | Abstract | | In this paper we develop a theoretical and numerical model for the simulation of both the structural evolution and pore pressure evolution of a sedimentary basin. We use the volume averaging technique in order to get a complete macroscopical physical model and we introduce two different formulations of it. The relations with existing compaction and basin scale models are discussed. Then we introduce a temporal time-splitting scheme and study the existence and uniqueness of the solution of the semi discrete problem. We show the robustness of our scheme in a couple of one dimensional cases with smooth and non-smooth variations of the physical coefficients.
_____________
¤ENI - Steam3D
1 |
-
12/2009 - 06/04/2009
Badia, Santiago; Quaini, Annalisa; Quarteroni, Alfio
Coupling Biot and Navier-Stokes equations for modeling fluid-poroelastic media intercation | Abstract | | The interaction between a fluid and a poroelastic structure is a complex problem that couples the Navier-Stokes equations with the Biot system.
The finite element approximation of this problem is involved due to the fact that both subproblems are indefinite. In this work, we first design
residual-based stabilization techniques for the Biot system, motivated by the variational multiscale approach. Then, we state the monolithic Navier-Stokes/Biot system with the appropriate transmission conditions at the
interface. For the solution of the coupled system, we adopt both monolithic solvers and heterogeneous domain decomposition strategies. Different domain decomposition methods are considered and their convergence is analyzed for a simplified problem. We compare the efficiency of all the methods on a test problem that exhibits a large added-mass effect, as it
happens in hemodynamics applications. |
-
11/2009 - 05/04/2009
Formaggia, Luca; Villa, Andrea
Implicit tracking for multi-fluid simulations | Abstract | | In this work a new coupled level set - volume tracking method is introduced. To advance the solution in time, a MUSCL-type method combined
to a new °ux limiter is used. It is shown that our discrete method has many interesting properties that make it suitable for problems where the tracking of a large number of regions is needed. A dedicated reconstruction
algorithm for the level set reinizialization is also provided. We show some numerical tests demonstrating its effectiveness for multi-°uid problems. |
-
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. |
-
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).
|
|
