Catálogo de publicaciones - libros

In this paper, we reformulate global optimization problems in terms of boundary value problems. This allows us to introduce a new class of optimization algorithms. Indeed, many optimization methods, including non-deterministic ones, can be seen as discretizations of initial value problems for differential equations or systems of differential equations. Two algorithms included in this new class are applied and compared with a genetic algorithm for the design of multichannel optical filters.

Topology optimization searches for an optimal distribution of material and void without any restrictions on the structure of the design geometry. Shape optimization tunes the shape of the geometry, while the topology is fixed. In the paper we propose a sequential coupling so that a coarsely optimized topology is the initial guess for the following shape optimization. We aim at making this algorithm fast by using the adjoint sensitivity analysis to the Newton-method for the governing nonlinear state equation and a multigrid approach for the shape optimization. A finite element discretization method is employed. Numerical results are given for a 2-dimensional optimal design of a direct electric current electromagnet.

During the last decade, topology optimization has become an important branch in engineering sciences, e.g., to save material or to optimize the heat distribution inside a structure. The modelling of a certain class of such problems (e.g. vibration analysis) leads to the optimization of suitable functions defined on the set of all eigenvalues of the corresponding differential operator. The resulting optimization problems are typically nonsmooth and require adequate nonsmooth optimization techniques. In this article an approach for the treatment of a typical class of eigenvalue optimization problems based on a nonsmooth bundle method is considered, and a mathematical framework for its analysis is developed.

In the present work a numerical approach for the optimization of stirrer configurations is presented. The methodology is based on a parametrized grid generator, a flow solver, and a mathematical optimization tool, which are integrated into an automated procedure. The grid generator allows the parametrized generation of block-structured grids for the stirrer geometries. The flow solver is based on the discretization of the incompressible Navier-Stokes equations by means of a fully conservative finite-volume method for block-structured, boundary-fitted grids. As optimization tool the two approaches DFO and CONDOR are considered, which are implementations of trust region based derivative-free methods using multivariate polynomial interpolation. Both are designed to minimize smooth functions whose evaluations are considered expensive and whose derivatives are not available or not desirable to approximate. An exemplary application for a standard stirrer configuration illustrates the functionality and the properties of the proposed methods also involving a comparison of the two optimization algorithms.

Common methods of controlling river pollution include establishing water pollution monitoring stations located along the length of the river. The point where each station is located () is of crucial importance and, obviously, depends on the reasons for the sample. Collecting data about pollution at selected points along the river is not the only objective; must also be extrapolated to know the characteristics of the pollution in the entire river. In this work we will deal with the optimal location of sampling points. A mathematical formulation for this problem as well as an efficient algorithm to solve it will be given. Finally, in last sections, we will present numerical results obtained by using this algorithm when applied to a realistic situation in the last sections of a river.

A finite element method for the Kirchhoff plate bending problem is presented. This method has the twofold advantage of allowing low order polynomials and of holding convergence properties which does not deteriorate in the presence of free boundary conditions. Optimal a-priori and a-posteriori error estimates are shown without proof. Finally, some numerical tests are presented.

We summarize the main results obtained in [6]. For the MITC plate elements [2, 4] it is shown that the deflection has a superconvergence property. This is used in a local postprocessing method for obtaining an improved approximation for the deflection. The theoretical results are checked by various numerical computations.

We propose a finite difference space semi-discretization of the stabilized Bernoulli-Euler plate equation in a square. The scheme studied yields a uniform exponential decay rate with respect to the mesh size.

An -uniform second-order numerical method for singularly perturbed reaction-diffusion problems is proposed in this article. The difference scheme is based on cubic spline and classical finite difference scheme, which is applied on layer resolving Shishkin meshes. Uniform stability and uniform convergence of the scheme in the maximum norm are studied. A numerical example is presented to support the theoretical results.

We study the dynamic frictional contact of a viscoelastic beam with a deformable obstacle. The left end of the beam is rigidly attached and the horizontal movement of the right one is constrained because of the presence of a deformable obstacle. The effect of the friction is included in the vertical motion of the free end, by using Tresca’s law or Coulomb’s law.We recall an existence and uniqueness result. Then, by using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives, a numerical scheme is proposed. Error estimates are derived on the approximative solutions. Finally, some numerical results are shown.