An Effective Semi-analytic Algorithm for Solving Helmholtz Equation in 1-D
An efficient and accurate algorithm for solving Helmholtz equation in 1-D is presented in this paper. The key point of this work is to derive the analytic form for the convolution of the Green’s function and a complex exponential function with a finite support domain. A linear subtraction skill is introduced to improve the sampling efficiency. Therefore, the convolution of any function with the Green’s function is given in a semi-analytic form, which can be computed in a fast way with the help of FFT or NUFFT.