Boundary infinite elements for the Helmholtz equation in exterior domains

A novel approach to the development of in nite element formulations for exterior problems of time-harmonic acoustics is presented. This approach is based on a functional which provides a general framework for domain- based computation of exterior problems. Special cases include non-re ecting boundary conditions (such as the DtN method). A prominent feature of this formulation is the lack of integration over the unbounded domain, simplifying the task of discretization. The original formulation is generalized to account for derivative dis- continuities across in nite element boundaries, typical of standard in nite element approximations. Continuity between nite elements and in nite elements is enforced weakly, precluding compatibility requirements. Var- ious in nite element approximations for two-dimensional con gurations with circular interfaces are presented. Implementation requirements are relatively simple. Numerical results demonstrate the good performance of this scheme.