Abstract
The most efficient numerical methods for the solution of partial differential equations, multigrid methods on adaptively refined grids, imply several drawbacks from the point of view of memory-efficiency on high-performance computer architectures: First, we loose the trivial structure expressed by the simple i,j-indexing of grid points or cells. This effect is even worsened by the usage of hierarchical data and – if implemented in a naive way – leads to both increased storage requirements (neighbourhoodrelations possibly modified difference stencils) and a less efficient data access (worse locality of data and additional data dependencies), in addition. Our approach to overcome this quandary between numerical and hardware-efficiency relies on structured but still highly flexible adaptive grids, the so-called space-partitioning grids, cell-oriented operator evaluations, and the construction of very efficient data structures based on the concept of space-filling curves. The focus of this paper is in particular on the technical and algorithmical details concerning the interplay between data structures, space-partitioning grids and space-filling curves.
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Mehl, M. (2006). Cache-Optimal Data-Structures for Hierarchical Methods on Adaptively Refined Space-Partitioning Grids. In: Gerndt, M., Kranzlmüller, D. (eds) High Performance Computing and Communications. HPCC 2006. Lecture Notes in Computer Science, vol 4208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11847366_15
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DOI: https://doi.org/10.1007/11847366_15
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