Fast Evaluation of Scattering Oscillatory Integrals Over Fan-Shaped Regions

Oscillatory integrals over fan-shaped regions widely exist in scattering analysis, and this paper proposes a new rapid calculation routine for them. In the routine, the concerned bivariate scattering oscillatory integral is reduced to the calculation of two univariate oscillatory integrals. One is calculated with the improved Levin quadrature method, and another is transformed to a non-oscillatory integral that can be stably and accurately calculated with the Gauss-Chebyshev integration rule. Numerical examples show that the newly proposed method has the merits of being very accurate and efficient.