Incomplete block factorization preconditioning for indefinite elliptic problems

The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficie nt matrix is block tridiagonal and symmetric indefinite. Such a linear syst em can be solved efficiently by a conjugate residual method, particularly w hen combined with a good preconditioner. We show that specific incomplete b lock factorization exists for the indefinite matrix if the mesh size is rea sonably small, and that this factorization can serve as an efficient precon ditioner. Some efforts are made to estimate the eigenvalues of the precondi tioned matrix. Numerical results are also given.