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Sparse Grids and Applications - Munich 2012 pp 195–219Cite as

Efficient Regular Sparse Grid Hierarchization by a Dynamic Memory Layout

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 97))

Abstract

We consider a new hierarchization algorithm for sparse grids of high dimension and low level. The algorithm is inspired by the theory of memory efficient algorithms. It is based on a cache-friendly layout of a compact data storage, and the idea of rearranging the data for the different phases of the algorithm. The core steps of the algorithm can be phrased as multiplying the input vector with two sparse matrices. A generalized counting makes it possible to create (or apply) the matrices in constant time per row. The algorithm is implemented as a proof of concept and first experiments show that it performs well in comparison with the previous implementation SG++, in particular for the case of high dimensions and low level.

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Acknowledgements

I am grateful to Dirk Pflüger for introducing me to the topic and providing me with the SG++ source code. For many fruitful discussions I want to thank Gerrit Buse, Dirk Pflüger and Hans Bungartz. Special thanks go to Philipp Hupp for many helpful comments and discussions to improve the presentation.

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Authors and Affiliations

  1. ETH Zürich, Universitätstrasse 6, 8092, Zürich, Switzerland

    Riko Jacob

Authors
  1. Riko Jacob
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Correspondence to Riko Jacob .

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Editors and Affiliations

  1. Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

    Jochen Garcke

  2. Institute for Parallel and Distributed Systems, Universität Stuttgart, Stuttgart, Germany

    Dirk Pflüger

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© 2014 Springer International Publishing Switzerland

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Jacob, R. (2014). Efficient Regular Sparse Grid Hierarchization by a Dynamic Memory Layout. In: Garcke, J., Pflüger, D. (eds) Sparse Grids and Applications - Munich 2012. Lecture Notes in Computational Science and Engineering, vol 97. Springer, Cham. https://doi.org/10.1007/978-3-319-04537-5_8

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