Hierarchical hybrid grids: data structures and core algorithms for multigrid.

For many scientific and engineering applications, it is often desirable to use unstructured grids to represent complex geometries. Unfortunately, the data structures required to represent discretizations on such grids typically result in extremely inefficient performance on current high-performance architectures. Here, we introduce a grid framework using patch-wise, regular refinement that retains the flexibility of unstructured grids, while achieving performance comparable to that seen with purely structured grids. This approach leads to a grid hierarchy suitable for use with geometric multigrid methods, thus combining asymptotically optimal algorithms with extremely efficient data structures to obtain a powerful technique for large scale simulations. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]