A fast algorithm for particle simulations
Journal of Computational Physics
An implementation of the fast multipole method without multipoles
SIAM Journal on Scientific and Statistical Computing
Efficient algorithms for computing a strong rank-revealing QR factorization
SIAM Journal on Scientific Computing
Yet another fast multipole method without multipoles—pseudoparticle multipole method
Journal of Computational Physics
A multigrid tutorial: second edition
A multigrid tutorial: second edition
A Generalized Fast Multipole Method for Nonoscillatory Kernels
SIAM Journal on Scientific Computing
The rapid evaluation of potential fields in particle systems
The rapid evaluation of potential fields in particle systems
A kernel-independent adaptive fast multipole algorithm in two and three dimensions
Journal of Computational Physics
On the Compression of Low Rank Matrices
SIAM Journal on Scientific Computing
A wideband fast multipole method for the Helmholtz equation in three dimensions
Journal of Computational Physics
An Accelerated Kernel-Independent Fast Multipole Method in One Dimension
SIAM Journal on Scientific Computing
Fast and accurate numerical methods for solving elliptic difference equations defined on lattices
Journal of Computational Physics
Hi-index | 7.29 |
The Fast Multipole Method (FMM) provides a highly efficient computational tool for solving constant coefficient partial differential equations (e.g. the Poisson equation) on infinite domains. The solution to such an equation is given as the convolution between a fundamental solution and the given data function, and the FMM is used to rapidly evaluate the sum resulting upon discretization of the integral. This paper describes an analogous procedure for rapidly solving elliptic difference equations on infinite lattices. In particular, a fast summation technique for a discrete equivalent of the continuum fundamental solution is constructed. The asymptotic complexity of the proposed method is O(N"s"o"u"r"c"e), where N"s"o"u"r"c"e is the number of points subject to body loads. This is in contrast to FFT based methods which solve a lattice Poisson problem at a cost O(N"@WlogN"@W) independent of N"s"o"u"r"c"e, where @W is an artificial rectangular box containing the loaded points and N"@W is the number of lattice points in @W.