FICTITIOUS DOMAIN METHODS FOR THE NUMERICAL-SOLUTION OF 2-DIMENSIONALSCATTERING PROBLEMS

Fictitious domain methods for the numerical solution of two-dimensiona l scattering problems are considered, The original exterior boundary v alue problem is approximated by truncating the unbounded domain and by imposing a nonreflecting boundary condition on the artificial boundar y. First-order, second-order, and exact nonreflecting boundary conditi ons are tested on rectangular and circular boundaries. The finite elem ent discretizations of the corresponding approximate boundary value pr oblems are performed using locally fitted meshes, and the discrete equ ations are solved with fictitious domain methods. A special finite ele ment method using nonmatching meshes is considered. This method uses t he macro-hybrid formulation based on domain decomposition to couple po lar and cartesian coordinate systems, A special preconditioner based o n fictitious domains is introduced for the arising algebraic saddle-po int system such that the subspace of constraints becomes invariant wit h respect to the preconditioned iterative procedure. The performance o f the new method is compared to the fictitious domain methods both wit h respect to accuracy and computational cost. (C) 1998 Academic Press.