  Numerical resolution of exterior Helmholtz problems requires some approach to
domain truncation. As an alternative to approximate nonreflecting boundary
conditions and invocation of the Dirichlet-to-Neumann map, we introduce a new,
nonlocal boundary condition. This condition is exact and requires the
evaluation of layer potentials involving the free space Green's function.
However, it seems to work in general unstructured geometry, and Galerkin finite
element discretization leads to convergence under the usual mesh constraints
imposed by G{\aa}rding-type inequalities. The nonlocal boundary conditions are
readily approximated by fast multipole methods, and the resulting linear system
can be preconditioned by the purely local operator involving transmission
boundary conditions.
