Periodic band structure calculation by the Sakurai-Sugiura method with a fast direct solver for the boundary element method with the fast multipole representation

Hiroshi Isakari, Toru Takahashi, Toshiro Matsumoto

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In this paper, we present a numerical method for periodic band structure calculation, which is associated with eigenvalue problems for periodic problems, using the boundary element method (BEM). In the BEM, the eigenvalue problems are converted into non-linear eigenvalue problems, which are not tractable with conventional eigensolvers. In the present study, to solve non-linear eigenvalue problems, the block Sakurai-Sugiura (SS) method, which can convert non-linear eigenvalue problems into generalised eigenvalue problems, is utilised. A fast direct solver for the BEM with a fast multipole representation is employed in the algorithm of the block SS method since algebraic equations need to be solved for multiple right-hand sides in the block SS method. We conduct several numerical experiments related to phononic structures to confirm the validity and efficiency of the proposed method. We confirm that the proposed method can calculate the band structure of the phononic structures, and the computational time with the proposed method is less than that with a conventional FEM-based eigensolvers with triangular linear elements even for relatively small problems.

Original languageEnglish
Pages (from-to)42-53
Number of pages12
JournalEngineering Analysis with Boundary Elements
Volume68
DOIs
Publication statusPublished - 2016 Jul 1
Externally publishedYes

Keywords

  • Fast direct solver for boundary element method
  • Fast multipole method
  • Non-linear eigenvalue problem
  • Periodic problem
  • Photonic/Phononic band structure
  • Sakurai-Sugiura method

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Computational Mathematics
  • Applied Mathematics

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