Polygon clipping is a frequent operation in many fields, including computer graphics, CAD, and GIS. Thus, efficient and general polygon clipping algorithms are of great importance. Greiner and Hormann (1998) propose a simple and time-efficient algorithm that can clip arbitrary polygons, including concave and self-intersecting polygons with holes. However, the Greiner–Hormann algorithm does not properly handle degenerate intersection cases, without the undesirable need for perturbing vertices. We present an extension of the Greiner–Hormann polygon clipping algorithm that properly deals with such degenerate cases.@en

In this paper we introduce a numerical scheme which preserves the behavior of solutions to the Kolmogorov Equation as time tends to infinity. The method presented is based on a self-similar change of variables technique to transform the Kolmogorov Equation into a new form, such that the problem of designing structure preserving schemes, for the original equation, amounts to building a standard scheme for the transformed equation. This transformation also has the added benefit of allowing for an exact operator splitting scheme, whereas in the original form a standard operator splitting was only second-order. Finally, we verify the preservation of long time behavior through numerical simulations.@en

This chapter presents an overview of the evolution of computer architecture, giving special attention on those advances which have promoted the current hybrid systems. After that, we focus on the most extended programming strategies applied to hybrid computing. In fact, programming is one of the most important challenges for this kind of systems, as it requires a high knowledge of the hardware to achieve a good performance. Current hybrid systems are basically composed by three components, two processors (multicore and manycore) and an interconnection bus (PCIe), which connects both processors. Each of the components must be managed differently. After presenting the particular features of current hybrid systems, authors focus on introducing some approaches to exploit simultaneously each of the components. Finally, to clarify how to program in these platforms, two cases studies are presented and analyzed in deep. At the end of the chapter, authors outline the main insights behind hybrid computing and introduce upcoming advances in hybrid systems. @en

This paper presents a conforming finite element discretization of the streamfunction formulation of the one-layer stationary quasi-geostrophic equations, which are a commonly used model for the large scale wind-driven ocean circulation. Optimal error estimates for this finite element discretization with the Argyris element are derived. To the best of the authors’ knowledge, these represent the first optimal error estimates for the finite element discretization of the quasi-geostrophic equations. Numerical tests for the finite element discretization of the quasi-geostrophic equations and two of its standard simplifications (the linear Stommel model and the linear Stommel–Munk model) are carried out. By benchmarking the numerical results against those in the published literature, we conclude that our finite element discretization is accurate. Furthermore, the numerical results have the same convergence rates as those predicted by the theoretical error estimates.@en

In this paper we proposed a two-level finite element discretization of the nonlinear stationary quasi-geostrophic equations, which model the wind driven large scale ocean circulation. Optimal error estimates for the two-level finite element discretization were derived. Numerical experiments for the two-level algorithm with the Argyris finite element were also carried out. The numerical results verified the theoretical error estimates and showed that, for the appropriate scaling between the coarse and fine mesh sizes, the two-level algorithm significantly decreases the computational time of the standard one-level algorithm.@en