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Derivation and efficient implementation of the fast multipole method
Abstract
The fast multipole method (FMM) of Greengard evaluates Coulomb interactions of point charges with computational requirements that increase linearly with the number of particles. In this work, the central transformations of the FMM are obtained in a very compact manner from simple algebraic manipulations of two addition theorems. The intermediate multipole and Taylor expansions are defined differently from previous work to yield simplified and more efficient transformations. Error estimates are obtained due to the effect of multipole truncation and the use of the multipole to Taylor transformation operator. Efficient implementation of the FMM for potential and forces is discussed, and calculations are presented that probe the accuracy and performance of the method.
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Cites
Computer Simulation of Liquids
Allen, M. P., & Tildesley, D. J. (2017) · doi:10.1093/oso/9780198803195.001.0001 · Cited by 20,945
Cited by
te Velde, G., Bickelhaupt, F. M., Baerends, E. J., Fonseca Guerra, C., van Gisbergen, S. J. A., Snijders, J. G., & Ziegler, T. (2001) · Journal of Computational Chemistry · doi:10.1002/jcc.1056 · Cited by 10,152
Time-dependent density functional theory for molecules in liquid solutions
Cossi, M., & Barone, V. (2001) · The Journal of Chemical Physics · doi:10.1063/1.1394921 · Cited by 2,081
Martyna, G. J., & Tuckerman, M. E. (1999) · The Journal of Chemical Physics · doi:10.1063/1.477923 · Cited by 687
Iyengar, S. S., Schlegel, H. B., Millam, J. M., A. Voth, G., Scuseria, G. E., & Frisch, M. J. (2001) · The Journal of Chemical Physics · doi:10.1063/1.1416876 · Cited by 451
Achieving Linear Scaling for the Electronic Quantum Coulomb Problem
Strain, M. C., Scuseria, G. E., & Frisch, M. J. (1996) · Science · doi:10.1126/science.271.5245.51 · Cited by 444
Metadata
- Authors
- White, C. A., & Head-Gordon, M.
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 1994-10-15
- Volume
- 101
- Issue
- 8
- Pages
- 6593-6605
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W2089733287
- Cited by
- 301
- References
- 1
- FWCI
- 7.08
- Type
- journal article
- Language
- en
- Open access
- closed
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- White, C. A., & Head-Gordon, M. (1994). Derivation and efficient implementation of the fast multipole method. The Journal of Chemical Physics. https://doi.org/10.1063/1.468354
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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