Memory-Efficient Sierpinski-Order Traversals on Dynamically Adaptive, Recursively Structured Triangular Grids

  • Michael Bader
  • Kaveh Rahnema
  • Csaba Vigh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7134)


Adaptive mesh refinement and iterative traversals of unknowns on such adaptive grids are fundamental building blocks for PDE solvers. We discuss a respective integrated approach for grid refinement and processing of unknowns that is based on recursively structured triangular grids and space-filling element orders. In earlier work, the approach was demonstrated to be highly memory- and cache-efficient. In this paper, we analyse the cache efficiency of the traversal algorithms using the I/O model. Further, we discuss how the nested recursive traversal algorithms can be efficiently implemented. For that purpose, we compare the memory throughput of respective implementations with simple stream benchmarks, and study the dependence of memory throughput and floating point performance from the computational load per element.


adaptive mesh refinement cache oblivious algorithms space-filling curves memory-bound performance partial differential equations 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Michael Bader
    • 1
  • Kaveh Rahnema
    • 1
  • Csaba Vigh
    • 2
  1. 1.Institute of Parallel and Distributed SystemsUniversität StuttgartGermany
  2. 2.Department of InformaticsTechnische Universität MünchenGermany

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