Fictitious domain method for structural-acoustic coupling problem in unbounded region

We consider a numerical treatment of structural-acoustic coupling problem between a shell and two acoustic regions: one is a bounded inner region and the other is an unbounded outer region. The problem exhibits a formulation of the domain decomposition method with a generalized Lagrangian multiplier. The Lagrangian multiplier is the normal deformation of the shell which is coupled with the tangential deformation. The problem is approximated by using the finite element method. We apply the fictitious domain method with locally fitted mesh to discretize the inner and outer regions and to construct preconditioners for the resulting block matrix equation. The block matrix equation is solved in two algorithms with the Krylov subspace iteration: the Schur complement method and a direct method. The direct method performs very well in terms of iteration count and execution time.