FINITE-ELEMENT METHODS FOR THE HELMHOLTZ-EQUATION IN AN EXTERIOR DOMAIN - MODEL PROBLEMS

Finite element methods are presented for the reduced wave equation in unbounded domains. Model problems of radiation with inhomogeneous Neumann boundary conditions, including the effects of a moving acoustic medium, are examined for the entire range of propagation and decay. Exterior boundary conditions for the computational problem over a finite domain are derived from an exact relation between the solution and its derivatives on that boundary. Galerkin, Galerkin/least-squares and Galerkin/gradient least-squares finite element methods are evaluated by comparing errors pointwise and in integral norms. The Galerkin/least-squares method is shown to exhibit superior behavior for this class of problems.