Efficient Storage and Processing of Adaptive Triangular Grids Using Sierpinski Curves

Abstract

We present an algorithm to store and process fully adaptive computational grids requiring only a minimal amount of memory. The adaptive grid is specified by a recursive decomposition of triangular grid cells; the cells are stored and processed in an order that is given by Sierpinski’s space filling curve. A sophisticated system of stacks is used to ensure the efficient access to the unknowns. The resulting scheme makes it possible to process grids containing more than one hundred million cells on a common workstation, and is also inherently cache efficient.