A Domain Decomposition Technique for Two-dimensional Scattering Problems with Coated Obstacles

A special procedure for the numerical solution of two-dimensional obstacle scattering problems is considered. The original exterior problem is approximated by introducing a rectangular artiicial boundary and by imposing an absorbing boundary condition. The scatterer is assumed to have a dielectric coating of variable thickness. Finite element discretization is performed with a structured mesh, which is reened in the coating and locally tted to the boundaries. In the solution procedure, the problem is decomposed into two parts. For one part, a separable preconditioner is obtained by applying an algebraic ctitious domain method. The preconditioner for the whole problem is coupled from domain decomposition and ctitious domain preconditioners. The preconditioned GMRES method is applied in a low-dimensional subspace. The partial solution technique is used to solve a problem with the separable part of preconditioner on each iteration. The other part of the preconditioner is based on the LU decomposition.