Medical systems usually consider linear propagation of ultrasound, an approximation of reality. However, numerous studies have attempted to accurately simulate the nonlinear pressure wave distortion and to evaluate the contribution of harmonic frequencies. In such simulations, the computation time is very large, except for the method based on the angular spectrum scheme where the derivative order is reduced using the Fourier transform. However, the harmonic computation is usually limited to the second harmonic because of quasi-linear approximation. In this paper, a slowly varying envelope approximation (SVEA) is used in the Fourier domain to compute the entire nonlinear distortion induced, including high harmonics and nonlinear mixing frequencies. The simulation by SVEA is evaluated by comparison with other simulation tools. The obtained deviation and difference remain low enough to fully validate such an approximation. Moreover, the simulator is implemented on a GPU to obtain a very fast tool, where the full nonlinear distorted 3-D + t field is computed in less than 10 s.