A Survey of Algebraic Multilevel Iteration (AMLI) Methods

Abstract

For the solution by preconditioned conjugate gradient methods of symmetric positive definite equations as arising in boundary value problems we consider preconditioning methods of AMLI type. Particular attention is devoted to providing methods of optimal order of computational complexity which in addition promise to be robust, i.e. with a convergence rate which is bounded above independently of size of discretization parameter h, jumps in problem coefficients, and shape of finite elements or, equivalently, anisotropy of problem coefficients. In addition, the computational cost per iteration step must have optimal order.