268 IGPM.pdf        December 2006
TITLE Notes on Adaptive Grids in 2D and 3D Part I: Navigating through Cell Hierarchies using Cell Identifiers
AUTHORS Alexander Voß
ABSTRACT In this paper we show how cells of different types from an adaptive grid in two or three spatial dimensions can be addressed by using so-called cell identifiers instead of memory consuming and error-prone pointer structures. Here we focus on horizontal and vertical grid navigation -- the backbone of multilevel PDE-solvers based on discretizations that only need element connectivity across faces. That means, we present very fast and effective methods to compute cell identifiers of parent, children and neighbor cells based on a given identifier as well as appropriate refinement strategies for cells of type triangles, rectangles, tetrahedrons, cubes and prisms.
KEYWORDS Data structure, adaptive grid, hybrid grid, cell enumeration strategy