A method of local corrections for computing the velocity field due to a distribution of vortex blobs
Journal of Computational Physics
A fast algorithm for particle simulations
Journal of Computational Physics
The fast Fourier transform and its applications
The fast Fourier transform and its applications
Computer simulation using particles
Computer simulation using particles
Journal of Computational Chemistry
SIAM Journal on Scientific Computing
Journal of Computational Chemistry
Multipole translation theory for the three-dimensional Laplace and Helmholtz equations
SIAM Journal on Scientific Computing
Fast Fourier Transform Accelerated Fast Multipole Algorithm
SIAM Journal on Scientific Computing
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
Journal of Computational Physics
A precorrected-FFT method for electrostatic analysis of complicated 3-D structures
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A fast algorithm for modeling multiple bubbles dynamics
Journal of Computational Physics
"New-version-fast-multipole-method" accelerated electrostatic calculations in biomolecular systems
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
In this paper, we present a fast algorithm for rapid calculation of the potential fields in three dimensions. This method arises from an observation that potential evaluation using the multipole to local expansion translation operator can be expressed as a series discrete convolutions of the multipole moments with their associated spherical harmonics functions. The high efficiency of the algorithm is primarily due to the use of FFT algorithms to evaluate the numerous discrete convolutions. We refer to it as the Fast Fourier Transform on Multipoles (FFTM) method. It is demonstrated that FFTM is all accurate method. It is significantly more accurate than FMM for a given order of expansion. It is also shown that the algorithm has computational complexity of O(Na), where a ranges from 1.0 to 1.3.