  We show how to solve time-harmonic wave scattering problems on unbounded
domains without truncation. The technique, first developed in numerical
relativity for time-domain wave equations, maps the unbounded domain to a
bounded domain and scales out the known oscillatory decay towards infinity. We
design a null infinity layer that corresponds to the infinite exterior domain
and restricts the transformations to an annular domain. The method does not
require the local Green function. Therefore we can use it to solve Helmholtz
equations with variable coefficients and certain nonlinear source terms. The
method's main advantages are the exact treatment of the local boundary and
access to radiative fields at infinity. The freedom in the transformations
allows us to choose parameters adapted to high-frequency wave propagation in
the exterior domain. We demonstrate the efficiency of the technique in one- and
two-dimensional numerical examples.
