Abstract: This paper puts forward a new method to solve the electromagnetic parabolic equation (EMPE) by taking the vertically-layered inhomogeneous characteristics of the atmospheric refractive index into account. First, the Fourier transform and the convolution theorem are employed, and the second-order partial differential equation, i.e., the EMPE, in the height space is transformed into first-order constant coefficient differential equations in the frequency space. Then, by use of the lower triangular characteristics of the coefficient matrix, the numerical solutions are designed. Through constructing analytical solutions to the EMPE, the feasibility of the new method is validated. Finally, the numerical solutions to the new method are compared with those of the commonly used split-step Fourier algorithm.

Key words: optimization, complementarity problems, recurrent neural network model, projective operator, global convergence