Efficient query processing on unstructured tetrahedral meshes

Modern scientific applications such as fluid dynamics and earthquake modeling heavily depend on massive volumes of data produced by computer simulations. Such applications require new data management capabilities in order to scale to terabyte-scale data volumes. The most common way to discretize the application domain is to decompose it into pyramids, forming an unstructured tetrahedral mesh. Modern simulations generate meshes of high resolution and precision, to be queried by a visualization or analysis tool. Tetrahedral meshes are extremely flexible and therefore vital to accurately model complex geometries, but also are difficult to index. To reduce query execution time, applications either use only subsets of the data or rely on different (less flexible) structures, thereby trading accuracy for speed.This paper presents efficient indexing techniques for common spatial (point and range) on tetrahedral meshes. Because the prevailing multidimensional indexing techniques attempt to approximate the tetrahedra using simpler shapes (primarily rectangles) the query performance deteriorates significantly as a function of the mesh's geometric complexity. We develop Directed Local Search (DLS), an efficient indexing algorithm based on mesh topology information that is practically insensitive to the geometric properties of meshes. We show how DLS can be easily and efficiently implemented within modern DBMS without requiring new exotic index structures and complex preprocessing. Finally, we present a new data layout approach for tetrahedral mesh datasets that provides better performance for scientific applications.compared to the traditional space filling curves. In our PostgreSQL implementation DLS reduces the number of disk page accesses by 26% to 4x, and improves the overall query execution time by 25% to 4.