Optimised three-dimensional Fourier interpolation: An analysis of techniques and application to a linear-scaling density functional theory code
Optimised three-dimensional Fourier interpolation: An analysis of techniques and application to a linear-scaling density functional theory code
The Fourier interpolation of 3D data-sets is a performance critical operation in many fields, including certain forms of image processing and density functional theory (DFT) quantum chemistry codes based on plane wave basis sets, to which this paper is targeted. In this paper we describe three different algorithms for performing this operation built from standard discrete Fourier transform operations, and derive theoretical operation counts. The algorithms compared consist of the most straightforward implementation and two that exploit techniques such as phase-shifts and knowledge of zero padding to reduce computational cost. Through a library implementation (tintl) we explore the performance characteristics of these algorithms and the performance impact of different implementation choices on actual hardware. We present comparisons within the linear-scaling DFT code ONETEP where we replace the existing interpolation implementation with our library implementation configured to choose the most efficient algorithm. Within the ONETEP Fourier interpolation stages, we demonstrate speed-ups of over 1.55×.
8-19
Russell, Francis P.
17b438c0-54bc-44de-b893-0b800b298954
Wilkinson, Karl A.
8e2e967a-138c-4833-8526-908a1db8abee
Kelly, Paul H.J.
ad446fc7-9fe5-4965-8bd9-5fc4bdf067ee
Skylaris, Chris-Kriton
8f593d13-3ace-4558-ba08-04e48211af61
February 2015
Russell, Francis P.
17b438c0-54bc-44de-b893-0b800b298954
Wilkinson, Karl A.
8e2e967a-138c-4833-8526-908a1db8abee
Kelly, Paul H.J.
ad446fc7-9fe5-4965-8bd9-5fc4bdf067ee
Skylaris, Chris-Kriton
8f593d13-3ace-4558-ba08-04e48211af61
Russell, Francis P., Wilkinson, Karl A., Kelly, Paul H.J. and Skylaris, Chris-Kriton
(2015)
Optimised three-dimensional Fourier interpolation: An analysis of techniques and application to a linear-scaling density functional theory code.
Computer Physics Communications, 187, .
(doi:10.1016/j.cpc.2014.09.019).
Abstract
The Fourier interpolation of 3D data-sets is a performance critical operation in many fields, including certain forms of image processing and density functional theory (DFT) quantum chemistry codes based on plane wave basis sets, to which this paper is targeted. In this paper we describe three different algorithms for performing this operation built from standard discrete Fourier transform operations, and derive theoretical operation counts. The algorithms compared consist of the most straightforward implementation and two that exploit techniques such as phase-shifts and knowledge of zero padding to reduce computational cost. Through a library implementation (tintl) we explore the performance characteristics of these algorithms and the performance impact of different implementation choices on actual hardware. We present comparisons within the linear-scaling DFT code ONETEP where we replace the existing interpolation implementation with our library implementation configured to choose the most efficient algorithm. Within the ONETEP Fourier interpolation stages, we demonstrate speed-ups of over 1.55×.
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Accepted/In Press date: 29 September 2014
e-pub ahead of print date: 7 October 2014
Published date: February 2015
Organisations:
Computational Systems Chemistry
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Local EPrints ID: 396125
URI: http://eprints.soton.ac.uk/id/eprint/396125
ISSN: 0010-4655
PURE UUID: 7dcfeb02-f25f-4cdb-9621-61efd5afe2ab
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Date deposited: 02 Jun 2016 13:35
Last modified: 15 Mar 2024 03:26
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Author:
Francis P. Russell
Author:
Karl A. Wilkinson
Author:
Paul H.J. Kelly
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