scholarly journals A Generalized Grid-Based Fast Multipole Method for Integrating Helmholtz Kernels

2017 ◽  
Vol 13 (2) ◽  
pp. 654-665 ◽  
Author(s):  
Pauli Parkkinen ◽  
Sergio A. Losilla ◽  
Eelis Solala ◽  
Elias A. Toivanen ◽  
Wen-Hua Xu ◽  
...  
Keyword(s):  
Fast Multipole Method ◽  
Fast Multipole ◽  
Multipole Method ◽  
Grid Based

scholarly journals The grid-based fast multipole method – a massively parallel numerical scheme for calculating two-electron interaction energies

2015 ◽  
Vol 17 (47) ◽  
pp. 31480-31490 ◽  
Author(s):  
Elias A. Toivanen ◽  
Sergio A. Losilla ◽  
Dage Sundholm
Keyword(s):  
Numerical Scheme ◽  
Fast Multipole Method ◽  
Massively Parallel ◽  
Electron Interaction ◽  
Interaction Energies ◽  
Fast Multipole ◽  
Charge Densities ◽  
Multipole Method ◽  
Grid Based

A grid-based fast multipole method has been developed for calculating two-electron interaction energies for non-overlapping charge densities.

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

2011 ◽  
Vol 230 (15) ◽  
pp. 5807-5821 ◽  
Author(s):  
Bo Zhang ◽  
Jingfang Huang ◽  
Nikos P. Pitsianis ◽  
Xiaobai Sun
Keyword(s):  
Fourier Series ◽  
Fast Multipole Method ◽  
Fast Multipole ◽  
Multipole Method

The Fast Multipole Method in Canonical Ensemble Dynamics on Massively Parallel Computers

1992 ◽  
Vol 278 ◽  
Author(s):  
Steven R. Lustig ◽  
J.J. Cristy ◽  
D.A. Pensak
Keyword(s):  
Canonical Ensemble ◽  
Yukawa Potential ◽  
Direct Method ◽  
Fast Multipole Method ◽  
Parallel Computers ◽  
Massively Parallel ◽  
Fast Multipole ◽  
Massively Parallel Computers ◽  
Multipole Method ◽  
Execution Times

AbstractThe fast multipole method (FMM) is implemented in canonical ensemble particle simulations to compute non-bonded interactions efficiently with explicit error control. Multipole and local expansions have been derived to implement the FMM efficiently in Cartesian coordinates for soft-sphere (inverse power law), Lennard- Jones, Morse and Yukawa potential functions. Significant reductions in execution times have been achieved with respect to the direct method. For a given number, N, of particles the execution times of the direct method scale asO(N2). The FMM execution times scale asO(N) on sequential workstations and vector processors and asymptotically0(logN) on massively parallel computers. Connection Machine CM-2 and WAVETRACER-DTC parallel FMM implementations execute faster than the Cray-YMP vectorized FMM for ensemble sizes larger than 28k and 35k, respectively. For 256k particle ensembles the CM-2 parallel FMM is 12 times faster than the Cray-YMP vectorized direct method and 2.2 times faster than the vectorized FMM. For 256k particle ensembles the WAVETRACER-DTC parallel FMM is 33 times faster than the Cray-YMP vectorized direct method.

A new version of the Fast Multipole Method for the Laplace equation in three dimensions

Acta Numerica ◽  
1997 ◽  
Vol 6 ◽  
pp. 229-269 ◽  
Author(s):  
Leslie Greengard ◽  
Vladimir Rokhlin
Keyword(s):  
Laplace Equation ◽  
Fast Multipole Method ◽  
High Accuracy ◽  
Three Dimensions ◽  
Potential Fields ◽  
Diagonal Form ◽  
Fast Multipole ◽  
Reasonable Cost ◽  
Multipole Method ◽  
Translation Operators

We introduce a new version of the Fast Multipole Method for the evaluation of potential fields in three dimensions. It is based on a new diagonal form for translation operators and yields high accuracy at a reasonable cost.

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