Truncation error analysis of multipole expansion

Shinichiro Ohnuki, Weng Cho Chew

Research output: Contribution to journalArticlepeer-review

Abstract

The multilevel fast multipole algorithm is based on the multipole expansion, which has numerical error sources such as truncation of the addition theorem, numerical integration, and interpolation/anterpolation. Of these, we focus on the truncation error and discuss its control precisely. The conventional selection rule fails when the buffer size is small compared to the desired numerical accuracy. We propose a new approach and show that the truncation error can be controlled and predicted regardless of the number of buffer sizes.

Original languageEnglish (US)
Pages (from-to)1293-1306
Number of pages14
JournalSIAM Journal on Scientific Computing
Volume25
Issue number4
DOIs
StatePublished - 2003

Keywords

  • Error analysis
  • Fast multipole method
  • Multilevel fast multipole algorithm
  • Truncation error

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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