  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.
