Truncation error analysis of multipole expansion

Shinichiro Ohnuki, Weng Cho Chew

Research output: Contribution to journalArticle

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 - Dec 1 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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