An efficient blocking M2L translation for low-frequency fast multipole method in three dimensions

Toru Takahashi, Yuta Shimba, Hiroshi Isakari, Toshiro Matsumoto

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We propose an efficient scheme to perform the multipole-to-local (M2L) translation in the three-dimensional low-frequency fast multipole method (LFFMM). Our strategy is to combine a group of matrix-vector products associated with M2L translation into a matrix-matrix product in order to diminish the memory traffic. For this purpose, we first developed a grouping method (termed as internal blocking) based on the congruent transformations (rotational and reflectional symmetries) of M2L-translators for each target box in the FMM hierarchy (adaptive octree). Next, we considered another method of grouping (termed as external blocking) that was able to handle M2L translations for multiple target boxes collectively by using the translational invariance of the M2L translation. By combining these internal and external blockings, the M2L translation can be performed efficiently whilst preservingthe numerical accuracy exactly. We assessed the proposed blocking scheme numerically and applied it to the boundary integral equation method to solve electromagnetic scattering problems for perfectly electrical conductor. From the numerical results, it was found that the proposed M2L scheme achieved a few times speedup compared to the non-blocking scheme.

Original languageEnglish
Pages (from-to)151-164
Number of pages14
JournalComputer Physics Communications
Publication statusPublished - 2016 May 1
Externally publishedYes


  • BLAS
  • Boundary element method
  • Cache/register blocking
  • Congruent transformation
  • Fast multipole method
  • Matrix-matrix product
  • Multipole-to-local translation
  • Numerical linear algebra

ASJC Scopus subject areas

  • Hardware and Architecture
  • Physics and Astronomy(all)


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