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Title: A Fourier-series-based kernel-independent fast multipole method

Abstract

We present in this paper a new kernel-independent fast multipole method (FMM), named as FKI-FMM, for pairwise particle interactions with translation-invariant kernel functions. FKI-FMM creates, using numerical techniques, sufficiently accurate and compressive representations of a given kernel function over multi-scale interaction regions in the form of a truncated Fourier series. It provides also economic operators for the multipole-to-multipole, multipole-to-local, and local-to-local translations that are typical and essential in the FMM algorithms. The multipole-to-local translation operator, in particular, is readily diagonal and does not dominate in arithmetic operations. FKI-FMM provides an alternative and competitive option, among other kernel-independent FMM algorithms, for an efficient application of the FMM, especially for applications where the kernel function consists of multi-physics and multi-scale components as those arising in recent studies of biological systems. We present the complexity analysis and demonstrate with experimental results the FKI-FMM performance in accuracy and efficiency.

Authors:
 [1];  [2];  [1];  [3];  [1]
  1. Department of Computer Science, Duke University, Durham, NC 27708 (United States)
  2. Department of Mathematics, University of North Carolina at Chapel Hill, CB 3250, Phillips Hall, Chapel Hill, NC 27599 (United States)
  3. (Greece)
Publication Date:
OSTI Identifier:
21592595
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 230; Journal Issue: 15; Other Information: DOI: 10.1016/j.jcp.2011.03.049; PII: S0021-9991(11)00210-5; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ACCURACY; ALGORITHMS; APPROXIMATIONS; EFFICIENCY; FOURIER TRANSFORMATION; GREEN FUNCTION; PARTICLE INTERACTIONS; PERFORMANCE; CALCULATION METHODS; FUNCTIONS; INTEGRAL TRANSFORMATIONS; INTERACTIONS; MATHEMATICAL LOGIC; TRANSFORMATIONS

Citation Formats

Zhang Bo, E-mail: zhangb@cs.duke.edu, Huang Jingfang, E-mail: huang@amath.unc.edu, Pitsianis, Nikos P., E-mail: nikos.pitsianis@eng.auth.gr, Department of Electrical and Computer Engineering, Aristotle University, Thessaloniki 54124, and Sun Xiaobai, E-mail: xiaobai@cs.duke.edu. A Fourier-series-based kernel-independent fast multipole method. United States: N. p., 2011. Web. doi:10.1016/j.jcp.2011.03.049.
Zhang Bo, E-mail: zhangb@cs.duke.edu, Huang Jingfang, E-mail: huang@amath.unc.edu, Pitsianis, Nikos P., E-mail: nikos.pitsianis@eng.auth.gr, Department of Electrical and Computer Engineering, Aristotle University, Thessaloniki 54124, & Sun Xiaobai, E-mail: xiaobai@cs.duke.edu. A Fourier-series-based kernel-independent fast multipole method. United States. https://doi.org/10.1016/j.jcp.2011.03.049
Zhang Bo, E-mail: zhangb@cs.duke.edu, Huang Jingfang, E-mail: huang@amath.unc.edu, Pitsianis, Nikos P., E-mail: nikos.pitsianis@eng.auth.gr, Department of Electrical and Computer Engineering, Aristotle University, Thessaloniki 54124, and Sun Xiaobai, E-mail: xiaobai@cs.duke.edu. 2011. "A Fourier-series-based kernel-independent fast multipole method". United States. https://doi.org/10.1016/j.jcp.2011.03.049.
@article{osti_21592595,
title = {A Fourier-series-based kernel-independent fast multipole method},
author = {Zhang Bo, E-mail: zhangb@cs.duke.edu and Huang Jingfang, E-mail: huang@amath.unc.edu and Pitsianis, Nikos P., E-mail: nikos.pitsianis@eng.auth.gr and Department of Electrical and Computer Engineering, Aristotle University, Thessaloniki 54124 and Sun Xiaobai, E-mail: xiaobai@cs.duke.edu},
abstractNote = {We present in this paper a new kernel-independent fast multipole method (FMM), named as FKI-FMM, for pairwise particle interactions with translation-invariant kernel functions. FKI-FMM creates, using numerical techniques, sufficiently accurate and compressive representations of a given kernel function over multi-scale interaction regions in the form of a truncated Fourier series. It provides also economic operators for the multipole-to-multipole, multipole-to-local, and local-to-local translations that are typical and essential in the FMM algorithms. The multipole-to-local translation operator, in particular, is readily diagonal and does not dominate in arithmetic operations. FKI-FMM provides an alternative and competitive option, among other kernel-independent FMM algorithms, for an efficient application of the FMM, especially for applications where the kernel function consists of multi-physics and multi-scale components as those arising in recent studies of biological systems. We present the complexity analysis and demonstrate with experimental results the FKI-FMM performance in accuracy and efficiency.},
doi = {10.1016/j.jcp.2011.03.049},
url = {https://www.osti.gov/biblio/21592595}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 15,
volume = 230,
place = {United States},
year = {2011},
month = {7}
}