Large scale scientific computing models, requiring iterative algebraic solvers,
are needed to simulate high-frequency wave propagation.
This is because large degrees of freedom are needed to avoid the
celebrated Helmholtz computer model pollution effects.
Using low-order finite difference or finite element methods (FDM/FEM),
such issues have been well investigated for low and medium frequency
models (typically at most 
wavelengths per diameter of the wave
propagation domain).
Standard FDM/FEM based discretizations of the time-harmonic Helmholtz
wave propagation model lead to sign-indefinite systems with eigenvalues
in the left half of the complex plane.
Hence standard iterative methods (such as GMRES/BiCGstab) perform poorly,
and additional techniques such as multigrid (MG) or decomposition of the
domain are required for efficient and practical simulation of
high-frequency FDM/FEM Helmholtz models.
In this work, we investigate the use of multiple additive Schwarz type
domain decomposition (DD) approximations to efficiently simulate
high-frequency wave propagation with high-order FEM.
We compare our DD based results with those obtained using a standard
geometric MG approach for over 
wavelength models.