2024-03-29T07:58:25Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00022906
2023-01-16T04:12:35Z
320:321:322
Periodic band structure calculation by the Sakurai–Sugiura method with a fast direct solver for the boundary element method with the fast multipole representation
Isakari, Hiroshi
67407
Takahashi, Toru
67408
Matsumoto, Toshiro
67409
Photonic/Phononic band structure
Periodic problem
Sakurai–Sugiura method
Non-linear eigenvalue problem
Fast direct solver for boundary element method
Fast multipole method
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.
journal article
Elsevier
2016-07
application/pdf
Engineering Analysis with Boundary Elements
68
42
53
http://dx.doi.org/10.1016/j.enganabound.2016.03.018
http://hdl.handle.net/2237/25084
0955-7997
https://nagoya.repo.nii.ac.jp/record/22906/files/main.pdf
eng
https://doi.org/10.1016/j.enganabound.2016.03.018
© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/