  The complex scaling/perfectly matched layer method is a widely spread
technique to simulate wave propagation problems in open domains. The method is
very popular, because its implementation is very easy and does not require the
knowledge of a fundamental solution. However, for anisotropic media the method
may yield an unphysical radiation condition and lead to erroneous and unstable
results. In this article we argue that a radial scaling (opposed to a cartesian
scaling) does not suffer from this drawback and produces the desired radiation
condition. This result is of great importance as it rehabilitates the
application of the complex scaling method for anisotropic media. To present
further details we consider the radial complex scaling method for scalar
anisotropic resonance problems. We prove that the associated operator is
Fredholm and show the convergence of approximations generated by simulateneous
domain truncation and finite element discretization. We present computational
studies to undergird our theoretical results.
