Simple procedure for multifrequency analysis

A study was conducted to propose a simple procedure for efficient multifrequency analysis (MFA). The procedure was based on constructing a single time-dependent problem which involved all the frequencies of interest, solving it, and extracting the desired Helmholtz solutions using fast Fourier transform (FFT). The main objective of the procedure was to show that efficient MFA analysis was performed by using only standard solution tools, such as a solver for the time-dependent wave equation and an FFT routine under certain conditions. The computational cost of the proposed procedure was compared with that of solving M separate Helmholtz problems. The framework of finite element (FE) discretization in space and finite difference discretization in time was considered in the proposed procedure.