Resumo em Inglês:

We consider the optimal scheduling of hydropower plants in a hydrothermal interconnected system. This problem, of outmost importance for large-scale power systems with a high proportion of hydraulic generation, requires a detailed description of the so-called hydro unit production function. In our model, we relate the amount of generated hydropower to nonlinear tailrace levels; we also take into account hydraulic losses, turbine-generator efficiencies, as well as multiple 0-1 states associated with forbidden operation zones. Forbidden zones are crucial to avoid nasty phenomena such as mechanical vibrations in the turbine, cavitation, and low efficiency levels. The minimization of operating costs subject to such detailed constraints results in a large-scale mixed-integer nonlinear programming problem. By means of Lagrangian Relaxation, the original problem is split into a sequence of smaller and easy-to-solve subproblems, coordinated by a dual master program. In order to deal better with the combinatorial aspect introduced by the forbidden zones, we derive three different decomposition strategies, applicable to various configurations of hydro plants (with few or many units, which can be identical or different). We use a Sequential Quadratic Programming algorithm to solve nonlinear subproblems. We assess our approach on a real-life hydroelectric configuration extracted from the south sub region of the Brazilian hydrothermal power system.

Resumo em Inglês:

This paper considers the numerical simulation of incompressible viscous fluid flow in an infinite strip. A mixed spectral method is proposed using the Legendre approximation in one direction and the Legendre rational approximation in another direction. Numerical results demonstrate the efficiency of this approach. Some results on the mixed Legendre-Legendre rational approximation are established, from which the stability and convergence of proposed method follow.

Resumo em Inglês:

Let Pm(z) be a matrix polynomial of degree m whose coefficients At <FONT FACE=Symbol>Î</FONT> Cq×q satisfy a recurrence relation of the form: h kA0+ h k+1A1+...+ h k+m-1Am-1 = h k+m, k > 0, where h k = RZkL <FONT FACE=Symbol>Î</FONT> Cp×q, R <FONT FACE=Symbol>Î</FONT> Cp×n, Z = diag (z1,...,z n) with z i <FONT FACE=Symbol>¹</FONT> z j for i <FONT FACE=Symbol>¹</FONT> j, 0 < |z j| < 1, and L <FONT FACE=Symbol>Î</FONT> Cn×q. The coefficients are not uniquely determined from the recurrence relation but the polynomials are always guaranteed to have n fixed eigenpairs, {z j,l j}, where l j is the jth column of L*. In this paper, we show that the z j's are also the n eigenvalues of an n×n matrix C A; based on this result the sensitivity of the z j's is investigated and bounds for their condition numbers are provided. The main result is that the z j's become relatively insensitive to perturbations in C A provided that the polynomial degree is large enough, the number n is small, and the eigenvalues are close to the unit circle but not extremely close to each other. Numerical results corresponding to a matrix polynomial arising from an application in system theory show that low sensitivity is possible even if the spectrum presents clustered eigenvalues.

Resumo em Inglês:

We describe an algorithm that improves on the standard algorithm for computing the minimal distance of cyclic codes.

Resumo em Inglês:

Some computable schemes for descent methods without line search are proposed. Convergence properties are presented. Numerical experiments concerning large scale unconstrained minimization problems are reported.

Resumo em Inglês:

In this paper, we will be mainly concerned with a parallel algorithm (in time and space) which is used to solve the incompressible Navier-Stokes problem. This relies on two main ideas: (a) a splitting of the main differential operator which permits to consider independently the most important difficulties (nonlinearity and incompressibility) and (b) the approximation of the resulting stationary problems by a family of second-order one-dimensional linear systems. The same strategy can be applied to two-dimensional and three-dimensional problems and involves the same level of difficulty. It can be also useful for the solution of other more complicate systems like Boussinesq or turbulence models. The behavior of the method is illustrated with some numerical experiments.

Resumo em Inglês:

In this work, we are interested in obtaining existence, uniqueness of the solution and an approximate numerical solution for the model of linear thermoelasticity with moving boundary. We apply finite element method with finite difference for evolution in time to obtain an approximate numerical solution. Some numerical experiments were presented to show the moving boundary's effects for problems in linear thermoelasticity.

Resumo em Inglês:

In this paper, we consider a special class of nonlinear semi-definite programming problems that represents the fixed order H2/H<FONT FACE=Symbol>¥</FONT> synthesis problem. An augmented Lagrangian sequential quadratic programming method combined with a trust region globalization strategy is described, taking advantage of the problem structure and using inexact computations. Some numerical examples that illustrate the performance of the method are given.