Fast operations for a Gabor-frame-based integral equation with equidistant sampling

We consider the computation time of a three-dimensional Gabor-frame-based spatial–spectral integral equation solver for scattering from dielectric objects embedded in a multilayer medium. Based on the Gabor frame, a new set of basis functions is proposed, together with a set of equidistant Dirac-delta test functions. Using this construction, we approximate the operations of Fourier transformation and pointwise multiplication by a method that is significantly faster than the original method. A numerical example is included where the computation time is reduced by a factor of 15, while preserving accuracy