## Abstract

Diagonal translation operators form the core of the dynamic multilevel fast multipole algorithm (MLFMA). An application of the MLFMA requires knowledge of these operators over a large number of samples. In fact, the cost of a naive evaluation is O(N^{3/2}), where N is the number of unknowns. More importantly, in a distributed memory computer, if the operators are precomputed and replicated in every processor, the memory requirements scale as O(Np), where p is the number of processors. In this paper, we construct fast polynomial representations of the diagonal operators which require O(√N) storage, and which can be computed in O(N log (1/q)) time, where q is the desired precision. We report some numerical results demonstrating the performance of the new representations.

Original language | English (US) |
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Pages (from-to) | 298-303 |

Number of pages | 6 |

Journal | Microwave and Optical Technology Letters |

Volume | 28 |

Issue number | 5 |

DOIs | |

State | Published - Mar 2001 |

## ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Electrical and Electronic Engineering