Fictitious Domain Methods for the Numerical Solution of Three - dimensionalAcoustic Scattering ProblemsE

EEcient iterative methods for the numerical solution of three-dimensional acoustic scattering problems are considered. The underlying exterior boundary value problem is approximated by truncating the unbounded domain and by imposing a non-reeecting boundary condition on the artiicial boundary. The nite element discretization of the approximate boundary value problem is performed using locally tted meshes, and algebraic ctitious domain methods with separable pre-conditioners are applied to the solution of the arising mesh equations. These methods are based on imbedding the original domain into a larger one with a simple geometry (for example, a sphere or a parallelepiped). The iterative solution method is realized in a low-dimensional subspace, and partial solution methods are applied to the linear systems with the preconditioner. Results of numerical experiments demonstrate the eeciency and accuracy of the approach.