TY - JOUR
T1 - A level-set-based topology optimisation for acoustic–elastic coupled problems with a fast BEM–FEM solver
AU - Isakari, Hiroshi
AU - Kondo, Toyohiro
AU - Takahashi, Toru
AU - Matsumoto, Toshiro
N1 - Funding Information:
This work was supported by JSPS Grant-in-Aid for Scientific Research (B) (Grant No. 16H04255 ) and JSPS Grant-in-Aid for Challenging Exploratory Research (Grant No. 15K13856 ).
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2017/3/1
Y1 - 2017/3/1
N2 - This paper presents a structural optimisation method in three-dimensional acoustic–elastic coupled problems. The proposed optimisation method finds an optimal allocation of elastic materials which reduces the sound level on some fixed observation points. In the process of the optimisation, configuration of the elastic materials is expressed with a level set function, and the distribution of the level set function is iteratively updated with the help of the topological derivative. The topological derivative is associated with state and adjoint variables which are the solutions of the acoustic–elastic coupled problems. In this paper, the acoustic–elastic coupled problems are solved by a BEM–FEM coupled solver, in which the fast multipole method (FMM) and a multi-frontal solver for sparse matrices are efficiently combined. Along with the detailed formulations for the topological derivative and the BEM–FEM coupled solver, we present some numerical examples of optimal designs of elastic sound scatterer to manipulate sound waves, from which we confirm the effectiveness of the present method.
AB - This paper presents a structural optimisation method in three-dimensional acoustic–elastic coupled problems. The proposed optimisation method finds an optimal allocation of elastic materials which reduces the sound level on some fixed observation points. In the process of the optimisation, configuration of the elastic materials is expressed with a level set function, and the distribution of the level set function is iteratively updated with the help of the topological derivative. The topological derivative is associated with state and adjoint variables which are the solutions of the acoustic–elastic coupled problems. In this paper, the acoustic–elastic coupled problems are solved by a BEM–FEM coupled solver, in which the fast multipole method (FMM) and a multi-frontal solver for sparse matrices are efficiently combined. Along with the detailed formulations for the topological derivative and the BEM–FEM coupled solver, we present some numerical examples of optimal designs of elastic sound scatterer to manipulate sound waves, from which we confirm the effectiveness of the present method.
KW - Acoustic–elastic coupled problem
KW - BEM–FEM coupled solver
KW - Level set method
KW - Topological derivative
KW - Topology optimisation
KW - Wave scattering
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U2 - 10.1016/j.cma.2016.11.006
DO - 10.1016/j.cma.2016.11.006
M3 - Article
AN - SCOPUS:85002820871
VL - 315
SP - 501
EP - 521
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0374-2830
ER -