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OpenCL Based Parallel Algorithm for RBF-PUM Interpolation

Journal of Scientific Computing volume 74, pages 267–289 (2018)Cite this article

Abstract

We present a parallel algorithm for multivariate Radial Basis Function Partition of Unity Method (RBF-PUM) interpolation. The concurrent nature of the RBF-PUM enables designing parallel algorithms for dealing with a large number of scattered data-points in high space dimensions. To efficiently exploit this concurrency, our algorithm makes use of shared-memory parallel processors through the OpenCL standard. This efficiency is achieved by a parallel space partitioning strategy with linear computational time complexity with respect to the input and evaluation points. The speed of our approach allows for computationally more intensive construction of the interpolant. In fact, the RBF-PUM can be coupled with a cross-validation technique that searches for optimal values of the shape parameters associated with each local RBF interpolant, thus reducing the global interpolation error. The numerical experiments support our claims by illustrating the interpolation errors and the running times of our algorithm.

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Acknowledgements

The first author acknowledges financial support from the GNCS-INdAM and sincerely thanks professor Kai Hormann for the invitation to visit the USI in Lugano. This work was supported by the SNF under Project Number 200020_156178. The method presented in this paper is implemented within the MOONoLith software library. We sincerely thank the two anonymous referees for helping us significantly improve our paper. Finally, we are grateful to the Swiss national supercomputing centre for providing us with the computational resources and the OpenCL SDK on their system for the scaling experiments.

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Authors and Affiliations

  1. Department of Mathematics “G. Peano”, University of Torino, via Carlo Alberto 10, 10123, Torino, Italy

    Roberto Cavoretto

  2. Faculty of Informatics, Università della Svizzera italiana, via Giuseppe Buffi 13, 6904, Lugano, Switzerland

    Teseo Schneider & Patrick Zulian

Authors
  1. Roberto Cavoretto
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  2. Teseo Schneider
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  3. Patrick Zulian
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Correspondence to Teseo Schneider.

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Cavoretto, R., Schneider, T. & Zulian, P. OpenCL Based Parallel Algorithm for RBF-PUM Interpolation. J Sci Comput 74, 267–289 (2018). https://doi.org/10.1007/s10915-017-0431-x

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  • DOI: https://doi.org/10.1007/s10915-017-0431-x

Keywords

  • Mesh-free approximation
  • Partition of unity methods
  • Radial basis functions
  • Scattered data interpolation
  • Parallel algorithms
  • Opencl

Mathematics Subject Classification

  • 65D05
  • 65D15
  • 65Y05
  • 65Y20
  • 68W10