On the integration of highly oscillatory functions: Algorithms based on critical points and semi-periodic zones in scalar diffraction Original Research Article

Two methods for the computation of the diffraction integrals appearing in the scalar approximation of the theory of diffraction of electromagnetic waves are developed. The methods are tuned since they avoid the oscillations of the integral kernel by dividing the integration domain in semi-periodic zones. A further optimization is applied by taking advantage of the fact that the semi-periodic zones that contain a critical point have the main contribution to the result.