A coupling algorithm based on the finite element method and the wideband fast multipole boundary element method (FEM/wideband FMBEM) is proposed for the simulation of fluid-structure interaction and structural acoustic sensitivity analysis using the direct differentiation method. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. The FEM/Wideband FMBEM algorithm makes it possible to predict the effects of arbitrarily shaped vibrating structures on the sound field numerically.

For thin structures immersed in water, a full interaction between the structural domain and the fluid domain needs to be taken into account. In this work, the finite element method (FEM) is used to model the structure parts, while the boundary element method (BEM) is applied to the exterior acoustic domain. A coupling algorithm based on FEM and the wideband fast multipole BEM (FEM/Wideband FMBEM) is used for the simulation of acoustic-structure interaction. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. Structural-acoustic design sensitivity analysis is performed based on the coupling formulation. The design variable can be chosen as the material parameters, structure and fluid parameters, such as the fluid density, structural density, Poisson's ratio, Young's modulus, structural shape size and so on. Furthermore, the impact of sound-absorbing material on the scattering problem for structures underwater is researched. The acoustic admittance of the soundabsorbing material has also been chosen as the design variable for the sensitivity analysis. Numerical example is presented to demonstrate the validity and efficiency of the proposed algorithm.