Connection and comparison between frequency shift time integration and a spectral transformation preconditioner

The numerical study of exterior acoustics problems is usually carried out in the frequency domain. Finite element analyses often require the solution of large scale algebraic linear systems. For very large problems, sometimes the time domain is used. Implicit time integration requires linear system solves, but these are often far easier than those from the frequency domain. This paper shows a connection between a spectral transformation preconditioner and frequency shift time integration. This preconditioner is close to the shifted Laplace preconditioner. The preconditioned iterative method appears to be faster than time integration.