Memory efficient adaptive mesh generation and implementation of multigrid algorithms using Sierpinski curves

Abstract

We will present an approach to numerical simulation on recursively structured adaptive discretisation grids. The respective grid generation process is based on recursive bisection of triangles along marked edges. The resulting refinement tree is sequentialised according to a Sierpinski space-filling curve, which leads to both minimal memory requirements and inherently cache-efficient processing schemes. The locality properties induced by the space-filling curve are even retained throughout adaptive refinement of the grid. We demonstrate the efficiency of the approach by implementing a multilevel-preconditioned conjugate gradient solver for a simple, yet adaptive, test problem: solving Poisson's equation on a re-entrant corner problem. (2008) 'Memory efficient adaptive mesh generation and implementation of multigrid algorithms using Sierpinski curves', Int. His research interests include hardware-aware algorithms in scientific computing based on space-filling curves. Stefanie Schraufstetter received a Degree in Mathematics at TUM in 2006; her degree thesis was part of the work presented in this paper. She is now working on her PhD at SCCS/TUM on the topic of efficient numerical algorithms for PDE. Csaba A. Vigh received a Degree in CSE at TUM in 2007. He holds a PhD scholarship within the International Graduate School of Science and Engineering at TUM, and is part of the research training group Hardware-aware simulation and computing.

DOI: 10.1504/IJCSE.2008.021108

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