A fast algorithm for particle simulations
Journal of Computational Physics
Computer simulation of liquids
Computer simulation of liquids
Fast potential theory. II: Layer potentials and discrete sums
Journal of Computational Physics
Fast Fourier transforms for nonequispaced data
SIAM Journal on Scientific Computing
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
Journal of Computational Physics
Locally-corrected spectral methods and overdetermined elliptic systems
Journal of Computational Physics
A fast multipole method for the three-dimensional Stokes equations
Journal of Computational Physics
Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces
Journal of Computational Physics
A geometric nonuniform fast Fourier transform
Journal of Computational Physics
Spectral accuracy in fast Ewald-based methods for particle simulations
Journal of Computational Physics
A regularization method for the numerical solution of periodic Stokes flow
Journal of Computational Physics
A fast numerical method for computing doubly-periodic regularized Stokes flow in 3D
Journal of Computational Physics
Hi-index | 31.46 |
A spectrally accurate method for the fast evaluation of N-particle sums of the periodic Stokeslet is presented. Two different decomposition methods, leading to one sum in real space and one in reciprocal space, are considered. An FFT based method is applied to the reciprocal part of the sum, invoking the equivalence of multiplications in reciprocal space to convolutions in real space, thus using convolutions with a Gaussian function to place the point sources on a grid. Due to the spectral accuracy of the method, the grid size needed is low and also in practice, for a fixed domain size, independent of N. The leading cost, which is linear in N, arises from the to-grid and from-grid operations. Combining this FFT based method for the reciprocal sum with the direct evaluation of the real space sum, a spectrally accurate algorithm with a total complexity of O(NlogN) is obtained. This has been shown numerically as the system is scaled up at constant density.