Algebraic multigrid preconditioner for elliptic problems with mixed type boundary conditions. I. Two-grid preconditioners

The present paper, consisting of two parts, is devoted to constructing algebraic multigrid preconditioners for stiffness matrices arising in finite element approximation of elliptic problems in rectangular domain. The Dirichlet condition is placed on one part of the boundary and third type condition on the rest of the boundary. In the first part of the paper a sequence of two-grid preconditioners is described on the base of which the multigrid preconditioner will be constructed.