Fast directional algorithms for the Helmholtz kernel

@article{Engquist2010FastDA,
  title={Fast directional algorithms for the Helmholtz kernel},
  author={Bj{\"o}rn Engquist and Lexing Ying},
  journal={J. Computational Applied Mathematics},
  year={2010},
  volume={234},
  pages={1851-1859}
}
This paper presents a new directional multilevel algorithm for solving N-body or N-point problems with highly oscillatory kernels. We address the problem by first proving that the interaction between a ball of radius r and a well-separated region has an approximate low rank representation, as long as the well-separated region belongs to a cone with a spanning angle of O(1/r) and is at a distance which is at least O(r2) away from the ball. Based on this representation, our algorithm organizes… CONTINUE READING
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