Modified tangential frequency filtering decomposition and its fourier analysis

We present a modification of a tangential frequency filtering decomposition (TFFD) preconditioner [1]. The key idea is to add a “lumping term” ch whose influence can be determined by means of Fourier analysis [2, 3]. For the standard five-point stencil, we derive an optimal order q = 4 3 , and constant c = (2π) 4 3 . With the choice of optimal order of modification, the Fourier results show that the condition number of the preconditioned matrix is asymptotically O(h− 2 3 ), and the spectrum distribution of the preconditioned matrix can be predicted by the Fourier results. The performance of MTFFD preconditioner is compared with tangential frequency filtering (TFFD) preconditioner on a variety of large sparse matrices arising from the discretization of PDEs with discontinuous coefficients. The numerical results show that the MTFFD preconditioner is much more efficient than the TFFD preconditioner.