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The generalized geometric programming algorithm GOP has been found to be one of the better algorithms for optimizing algebraic functions subject to algebraic constraints. The paper discusses two problems with the GOP algorithm presented by Avriel et al. (1980). The first problem is that, because of the way that constraint tolerances are checked, the checks may pass even when a constraint is violated beyond the acceptable tolerance. This problem can affect an acceleration technique suggested for the algorithm. This paper presents two possible solutions to this problem. The second problem is the algorithm's weakness in handling equality constraints. This problem seems to especially affect the `Phase I' part of the algorithm, which finds a feasible solution from a random starting point. While extensions have been made to get around this limitation, no discussion on why the original algorithm has problems with equality constraints has been made. This paper discusses why the problems exist. [ABSTRACT FROM AUTHOR]

The adaptive variational multiscale method is an extension of the variational multiscale method where the fine-scale part of the solution is approximated by a sum of numerically computed solutions to localized subgrid problems. Furthermore, the crucial discretization parameters are chosen automatically by an adaptive algorithm based on a posteriori error estimates. This method has been developed for diffusion-dominated problems and applied to multiscale problems that arise in oil reservoir simulation. In this paper, we extend the method to convection–diffusion problems. We present a duality based a posteriori error representation formula and an adaptive algorithm that tunes the fine-scale mesh size and the patch sizes of the local problems. Numerical results show rapid convergence of the adaptive algorithm. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper is devoted to the analysis of two- or three-dimensional contact problems with Coulomb friction and large deformation. The classical approach is based on two minimum principles or two variational inequalities: the first for unilateral contact and the second for friction. A coupled approach using only one principle or one inequality is presented. This new approach allows us to extend the notion of normality law to dissipative behaviors with a non-associated flow rule, such as surface friction. Non-differentiable contact potentials are regularized by means of the augmented Lagrangian method. Using the C++ language, an object-oriented finite element database is created, which allows us to implement the contact and friction in an existing code in a very simple and neat way. Numerical examples are carried out in many difficult cases such as shock absorber and three-dimensional contact. The numerical results prove that this approach is robust and efficient concerning numerical stability. [ABSTRACT FROM AUTHOR]

Most commonly used second-order-accurate, dissipative time integration algorithms for structural dynamics possess a spurious root. For an algorithm to be accurate, it has been suggested that the spurious root must be small and ideally be zero in the low-frequency limit. In the paper we show that good accuracy can be achieved even lithe spurious root does not tend towards zero in the low-frequency limit. This permits more flexibility in the design of time integration algorithms. As an example, we present an algorithm that has greater accuracy than several other dissipative algorithms even though for all frequencies its spurious root is non-zero. We also show that the degraded performance of the Bazzi-ρ algorithm is not due to its non-zero spurious root. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for obtaining the inverse of a tridiagonal matrix numerically. The algorithm does not require diagonal dominance in the matrix and is also computationally efficient. [ABSTRACT FROM AUTHOR]