  A new hybridizable discontinuous Galerkin method, named the CHDG method, is
proposed for solving time-harmonic scalar wave propagation problems. This
method relies on a standard discontinuous Galerkin scheme with upwind numerical
fluxes and high-order polynomial bases. Auxiliary unknowns corresponding to
characteristic variables are defined at the interface between the elements, and
the physical fields are eliminated to obtain a reduced system. The reduced
system can be written as a fixed-point problem that can be solved with
stationary iterative schemes. Numerical results with 2D benchmarks are
presented to study the performance of the approach. Compared to the standard
HDG approach, the properties of the reduced system are improved with CHDG,
which is more suited for iterative solution procedures. The condition number of
the reduced system is smaller with CHDG than with the standard HDG method.
Iterative solution procedures with CGNR or GMRES required smaller numbers of
iterations with CHDG.
