Catálogo de publicaciones - libros

We consider a mathematical model which describes the frictional contact between a viscoelastic body and an obstacle, the so-called foundation. The process is quasistatic and the behavior of the material is modeled with a constitutive law with memory. The contact is bilateral and the friction is modeled with Tresca’s law. The existence of a unique weak solution to the model was proved in [15]. Here we describe a fully discrete scheme for the problem, implement it in a computer code and provide numerical results in the study of a two-dimensional test problem.

The aim of this work is to present several numerical strategies to adapt efficiently the numerical algorithm published in [2] for the calculus of the deformation of an aluminium slab during a semicontinuous casting.

The main subject of this paper is the detailed description of an algorithm solving elastoplastic deformations. Our concern is a one time-step problem, for which the minimization of a convex but non-smooth functional is required. We propose a minimization algorithm based on the reduction of the functional to a quadratic functional in the displacement and the plastic strain increment omitting a certain nonlinear dependency. The algorithm also allows for an easy extension to higher order finite elements. A numerical example in 2D reports on first results for uniform h- and p- mesh refinements.

We consider the coupling of local discontinuous Galerkin (LDG) and boundary element methods (BEM) for a class of nonlinear exterior transmission boundary value problems in the plane. We introduce suitable numerical fluxes in order to obtain the LDG formulation, and additional unknowns to couple it with the BEM formulation. Finally, we show that the rates of convergence are optimal with respect to the mesh size.

An efficient method to solve time harmonic Maxwell’s equations in exterior domain for high frequencies is obtained by using the integral formulation of Després combined with a coupling method based on the Microlocal Discretization method (MD) and the Multi-Level Fast Multipole Method (MLFMM) [1]. In this paper, we consider curved finite elements of higher order in the MLFMM and in the MD/MLFMM methods. Moreover, we give some improvements of the MD/FMM method.

In this work we propose and analyse numerical methods for Helmholtz transmission problems in two and three dimensions. The methods we analyse use combined single and double layer potentials to represent the interior and exterior solution of the transmission problem. The corresponding boundary integral system includes weakly singular and hypersingular boundary integral operators on the interface. Its invertibility is equivalent to the unique solvability of the transmission problem, since the use of the above mentioned potentials does not introduce spurious eigenmodes in the formulation. We give necessary and sufficient conditions for the convergence of general Petrov-Galerkin schemes for solving the resulting system, providing some concrete methods for the two dimensional case. Some numerical experiments are shown.

We study in this paper a time-dependent eddy current problem posed in the whole space. We propose a weak formulation that can be rewritten as a well-posed saddle point problem when the constraint satisfied by the magnetic field in the dielectric medium is handled by means of a Lagrange multiplier. Furthermore, we provide a BEM—FEM formulation of the problem that leads to a semi-discrete Galerkin scheme based on Nedelec’s and Raviart-Thomas finite elements. Finally, we analyze the asymptotic behavior of the error in terms of the mesh size parameter.

This work is focused on a steady coupled model for pressure and temperature computations in lubricated journal bearing devices, including the thermal exchange with the environment through the bush and the shaft. The thermohydrodynamic problem is decoupled through a fixed point procedure. In this way, a finite element method for the hydrodynamic Reynolds equation with a cavitation model of Elrod-Adams is applied. Then, the energy equation in the lubricating film is solved by a second-order cell-vertex volume method and the heat equation on the bush by using a P1 collocation boundary element method while the very simple model considered for the shaft is straightforwardly integrated. Finally, some remarks are made about the extension of the present algorithm to the corresponding transient problem.

We present two different one-dimensional models for transport of solutes in soils. We numerically solve the mathematical problems arising from these models using stabilization techniques, maintaining a low computational cost guaranteing the stability of the schemes for any regimen to assure a right parameter adjustment. The numerical experiments are based on real data from laboratory experiments.

We encounter many problems, within which we try to model the groundwater flow in the disrupted rock massifs using numerical models. So-called “standard approaches” such as replacement by porous medium or double-porosity models of discrete stochastic fracture networks appear to have constraints and limitations, which make them unsuitable for the large-scale long-time hydrogeological calculations. This article presents the mathematical formulation of model based on a new approach to the modelling of groundwater flow, which combines the two above-mentioned approaches. The approach considers three substantial types of objects within a structure of modelled massif important for the groundwater flow - small stochastic fractures, large deterministic fractures and lines of intersection of the large fractures. The systems of stochastic fractures are represented by blocks of porous medium with suitably set hydraulic conductivity. The large fractures are represented as polygons placed in 3D space and their intersections are represented by lines. Thus flow in 3D porous medium, flow in 2D and 1D fracture systems, and communication among these three systems are modelled together.