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An adaptive grid method is applied to a PDE model from geo-hydrology. Due to the higher mixed-order derivative, non-monotone waves can appear which could represent similar structures as observed in laboratory experiments [5, 16, 18]. The effectiveness of the adaptive grid, which is based on a smoothed equidistribution principle, is shown compared to uniformgrid simulations. On a uniformgrid (numerical) oscillating non-monotone wavesmay appearwhich are not present in the adaptive grid.

Construction of invertible transformations using differential equations is an interesting and challenging mathematical problem with important applications. We briefly review the existing method by means of harmonic maps in 2D and propose a method of constructing differentiable, invertible transformations between domains in two and three dimensions. Preliminary numerical results demonstrate the effectiveness of the method.

The process of combustion for a nonlinear heat conducting medium with a nonlinear volume source is considered. Blow-up self-similar solutions which describe the evolution of radially nonsymmetric waves — with complex symmetry and spiral waves — are realized numerically. Their asymptotic behaviour is analysed and their metastability is established. To solve the self-similar nonlinear problem the continuous analog of the Newton method and the finite element method are used. The semidiscrete Galerkin finite element method and an explicit difference scheme are used to solve the nonlinear parabolic problem. Special adaptive grids, consistent with the structure of the self-similar solutions, are utilized.

The objective of Grid computing is to make processing power as accessible and easy to use as electricity and water. The last decade has seen an unprecedented growth in Grid infrastructures which nowadays enables large-scale deployment of applications in the scientific computation domain. One of the main challenges in realizing the full potential of Grids is making these systems dependable. In this paper we present FailRank, a novel framework for integrating and ranking information sources that characterize failures in a grid system. After the failing sites have been ranked, these can be eliminated from the job scheduling resource pool yielding in that way a more predictable, dependable and adaptive infrastructure. We also present the tools we developed towards evaluating the FailRank framework. In particular, we present the FailBase Repository which is a 38GB corpus of state information that characterizes the EGEE Grid for one month in 2007. Such a corpus paves the way for the community to systematically uncover new, previously unknown patterns and rules between the multitudes of parameters that can contribute to failures in a Grid environment. Additionally, we present an experimental evaluation study of the FailRank system over 30 days which shows that our framework identifies failures in 93% of the cases and can achieve this by only fetching 65% of the available information sources. We believe that our work constitutes another important step towards realizing adaptive Grid computing systems. © 2008 World Scientific Publishing Company. 18 3 371 390 Cited By :1