A kernel-independent adaptive fast multipole algorithm in two and three dimensions

@article{Ying2004AKA,
  title={A kernel-independent adaptive fast multipole algorithm in two and three dimensions},
  author={Lexing Ying and George Biros and Denis Zorin},
  journal={Journal of Computational Physics},
  year={2004},
  volume={196},
  pages={591-626}
}
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References

SHOWING 1-10 OF 46 REFERENCES
An Improved Fast Multipole Algorithm for Potential Fields on the Line
TLDR
A new version of the fast multipole method for the evaluation of potential fields on the line is introduced, based on generalized Gaussian quadratures, which is roughly twice as fast as previously published algorithms.
A fast, high-order algorithm for the solution of surface scattering problems: basic implementation, tests, and applications
TLDR
The present algorithm can evaluate accurately in a personal computer scattering from bodies of acoustical sizes of several hundreds and exhibits super-algebraic convergence; it can be applied to smooth and nonsmooth scatterers, and it does not suffer from accuracy breakdowns of any kind.
A Generalized Fast Multipole Method for Nonoscillatory Kernels
TLDR
This work presents a modification of the fast multipole method (FMM) in two dimensions that approximates appropriately chosen parts of the kernel with "tensor products" of Legendre expansions and uses the singular value decomposition (SVD) to compress the resulting representations.
A new version of the fast multipole method for screened Coulomb interactions in three dimensions
TLDR
A new version of the fast multipole method (FMM) for screened Coulomb interactions in three dimensions relies on an expansion in evanescent plane waves, with which the amount of work can be reduced to 40p2 + 6p3 operations per box.
An Implementation of the Fast Multipole Method without Multipoles
TLDR
An implementation is presented of the fast multipole method, which uses approximations based on Poisson’s formula, and results are given that show the importance of good level selection.
Fast Fourier Transform Accelerated Fast Multipole Algorithm
TLDR
A new block decomposition of the multipole expansion data that provides numerical stability and efficient computation in the Fourier domain using the fast Fourier transform (FFT) is described.
Preconditioned, Adaptive, Multipole-Accelerated Iterative Methods for Three-Dimensional First-Kind Integral Equations of Potential Theory
This paper presents a preconditioned, Krylov-subspace iterative algorithm, where a modified multipole algorithm with a novel adaptation scheme is used to compute the iterates for solving dense matrix
Grid-Multipole Calculations
TLDR
New high-order, momentum conserving methods for spreading charge to and interpolating potential from the mesh allow efficient grid-based algorithms to be used in high- order accurate n-body particle codes such as the fast multipole algorithm of Greengard and Rokhlin.
A precorrected-FFT method for electrostatic analysis of complicated 3-D structures
TLDR
A new algorithm for accelerating the potential calculation which occurs in the inner loop of iterative algorithms for solving electromagnetic boundary integral equations, which can be superior to the fast multipole based schemes by more than an order of magnitude.
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