Low frequency tangential filtering decomposition

For block‐tridiagonal systems of linear equations arising from the discretization of partial differential equations, a composite preconditioner is proposed and tested. It combines a classical ILU0 factorization for high frequencies with a tangential filtering preconditioner. The choice of the filtering vector is important: the test‐vector is the Ritz eigenvector corresponding to the approximate lowest eigenvalue, obtained after a limited number of iterations of a ILU0 preconditioned Krylov method. Numerical tests are carried out for this method. Copyright © 2006 John Wiley & Sons, Ltd.