Block preconditioning and domain decomposition methods. II

AbstractDomain decomposition methods for the solution of partial differential equations are attractive on parallel processors, because each processor can work independently on a large subtask. The corresponding stiffness matrix takes a sparse block structure, for which preconditioned iterative methods can be used when solving linear systems with the stiffness matrix. For domains decomposed in strips we get a blocktridiagonal structure for which a new block LU preconditioner was presented in an earlier report [5] by the authors.An alternative method, and also the one more commonly used for substructuring methods, is based on approximation of the Schur complement matrix. This approximation is frequently done by various difference methods (see [6], [11], and [16]). In the present paper we examine methods based on algebraic approximation methods. This is similar to methods used by Chan [9]