Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Cache-Oblivious Spacetree Traversals

  • Michael BaderEmail author
  • Tobias Weinzierl
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_583-1

Years and Authors of Summarized Original Work






In scientific computing and related fields, mathematical functions are often approximated on meshes where each mesh cell contains a local approximation (e.g., using polynomials) of the represented quantity (density functions, physical quantities such as temperature or pressure, etc.). The grid cells may adaptively refine within areas of high interest or where the applied numerical algorithms demand improved resolution. The resolution even may dynamically change throughout the computation.

In this context, we consider tree-structuredadaptive meshes, i.e., meshes that result from a recursive subdivision of grid cells. They can be represented via trees – quadtrees or octrees being the most prominent examples. In typical problem settings, quantities are stored on entities (vertices, edges, faces, cells) of the grid. The computation of these variables is usually characterized by local interaction rules...


Space-filling curves Tree-structured grids Octree Quadtree Spacetree Grid traversals Cache-oblivious algorithms 
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Recommended Reading

  1. 1.
    Bader M (2013) Space-filling curves – an introduction with applications in scientific computing. Texts in computational science and engineering, vol 9. Springer, Heidelberg/New York http://link.springer.com/book/10.1007/978-3-642-31046-1/page/1
  2. 2.
    Bader M, Rahnema K, Vigh CA (2012) Memory-efficient Sierpinski-order traversals on dynamically adaptive, recursively structured triangular grids. In: Jonasson K (ed) Applied parallel and scientific computing – 10th international conference, PARA 2010. Lecture notes in computer science, vol 7134. Springer, Berlin/New York, pp 302–311Google Scholar
  3. 3.
    Burstedde C, Wilcox LC, Ghattas O (2011) p4est: scalable algorithms for parallel adaptive mesh refinement on forests of octrees. SIAM J Sci Comput 33(3):1103–1133zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Mitchell WF (2007) A refinement-tree based partitioning method for dynamic load balancing with adaptively refined grids. J Parallel Distrib Comput 67(4):417–429zbMATHCrossRefGoogle Scholar
  5. 5.
    Sagan H (1994) Space-filling curves. Universitext. Springer, New YorkzbMATHCrossRefGoogle Scholar
  6. 6.
    Weinzierl T (2009) A framework for parallel PDE solvers on multiscale adaptive Cartesian grids. Dissertation, Institut für Informatik, Technische Universität München, München, http://www.dr.hut-verlag.de/978-3-86853-146-6.html

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of InformaticsTechnische Universität MünchenGarchingGermany
  2. 2.School of Engineering and Computing SciencesDurham UniversityDurhamUK