Fictitious domain methods for the numerical solution of three-dimensional acoustic scattering problems

Efficient iterative methods for the numerical solution of three-dimensional acoustic scattering problems are considered. The underlying exterior bound ary value problem is approximated by truncating the unbounded domain and by imposing a non-reflecting boundary condition on the artificial boundary. T he finite element discretization of the approximate boundary value problem is performed using locally fitted meshes, and algebraic fictitious domain m ethods with separable preconditioners are applied to the solution of the re sultant mesh equations. These methods are based on imbedding the original d omain into a larger one with a simple geometry (for example, a sphere or a parallelepiped). The iterative solution method is realized in a low-dimensi onal subspace, and partial solution methods are applied to the linear syste ms with the preconditioner. The results of numerical experiments demonstrat e the efficiency and accuracy of the approach.