  Modelling radar wave propagation in frequency domain is appealing in full
waveform inversion because it allows decreasing the non-linearity of the
problem, decreasing the dimension of the data space, better description of
attenuation, and handling efficiently multiple sources. Besides, performing
2.5D modelling is interesting when physical properties can be assumed invariant
in one horizontal dimension because it allows reducing drastically computation
requirements compared to the 3D case. In 2.5D, finite-difference methods can be
used to propagate the wave in two directions in space and a spatial Fourier
transform is performed in the third direction to get a full three dimensional
solution. With a simple central finite-difference implementation, second order
accuracy in space is obtained and up to twenty grid points per wavelength are
necessary to accurately simulate electromagnetic waves. Such a large number of
grid points will impact on the storage requirement associated with frequency
domain modelling. We propose a high accuracy algorithm to solve the frequency
domain electromagnetic wave equation by finite-differences in 2.5D. The
algorithm relies on a nine-point stencil to build weighted-averaging numerical
operators. The weights are chosen to minimize numerical dispersion and
anisotropy, which allows relaxing the requirements on grid cell size and thus
decreases computational costs by a factor of about 3.6 compared to the central
finite-difference method. This new algorithm reduces the numerical error
without increasing the numerical bandwidth of the matrix system to solve, and
can be easily transposed to 3D frequency domain modelling.
