DOMAIN DECOMPOSITION INTERFACE PRECONDITIONERS FOR 4TH-ORDER ELLIPTIC PROBLEMS

We present preconditioners for the interface system arising from solving fourth-order elliptic equations with domain decomposition methods. These preconditioners are derived from a Fourier analysis of the interface operator. We show that the condition number of the interface Schur complement is of order O(h-3), where h is the grid size. Precise estimates concerning the decay properties of the elements of the Schur complement are also obtained. Relationships between interface preconditioners for second-order problems and fourth-order problems are established. Analytical as well as numerical results are given to assess the performance of these preconditioners.