Fourier analysis of frequency filtering decomposition preconditioners

In this paper, frequency filtering decomposition (FFD) preconditioner is analyzed by the approach of Fourier analysis. The condition number estimation of a preconditioned 2-D model problem is presented. Analysis reveals that condition number of the preconditioned matrix grows like O(h-1)O(h-1), with h   be the mesh size. By using the framework of FFD, a stabilized frequency filtering decomposition (SFFD) method is proposed and analyzed by Fourier method. Results show that SFFD preconditioner is superior to FFD preconditioner in the sense that κ(MSFFD-1A)⩽κ(MFFD-1A). Numerical tests are performed to illustrate the theoretical results and the superiority of SFFD preconditioner.