Resumen
We present new third- and fifth-order Godunov-type central schemes for approximating solutions of the Hamilton-Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme that is based on a genuinely two-dimensional central weighted ENO reconstruction, and another scheme that is based on a simpler dimension-by-dimension reconstruction. The simpler dimension-by-dimension variant is then extended to a multidimensional fifth-order scheme. Our numerical examples in one, two, and three space dimensions verify the expected order of accuracy of the schemes.

Resumen
The article focuses on the virtual exploration of gigabyte data sets in real time. Where megabyte data sets were once considered large, data sets from individual simulations in the 300GB range are now found. But understanding the data resulting from high-end computations is a significant endeavor. Mathematician and pioneer computer scientist, Richard W. Hamming, pointed out that the purpose of computing is insight, not numbers. Analyzing large amounts of data presents a number of technical challenges. Simply getting all the data for analysis stresses even high-end hardware, it can take an hour to load a 100GB data set into memory. Loading the data little by little results in long times for a single pass through the data. Scientific visualization, or the use of computer graphics to represent data in ways that supports understanding, has played an increasingly important role in the analysis of large data sets. At NASA Ames Research Center's Numerical Aerospace Simulation Division, researchers are developing visualization systems for understanding very large data sets. INSET: Feature Extraction for Computational Fluid Dynamics.