02206706

j

02206706 Notay, Y. Robust parameter-free algebraic multilevel preconditioning. Numer. Linear Algebra Appl. 9, No. 6-7, 409-428 (2002). 2002 John Wiley \& Sons, Chichester EN iterative methods convergence preconditioning

doi:10.1002/nla.294

Summary: To precondition large sparse linear systems resulting from the discretization of second-order elliptic partial differential equations, many recent works focus on the so-called algebraic multilevel methods. These are based on a block incomplete factorization process applied to the system matrix partitioned in hierarchical form. They have been shown to be both robust and efficient in several circumstances, leading to iterative solution schemes of optimal order of computational complexity. Now, despite the procedure is essentially algebraic, previous works focus generally on a specific context and consider schemes that use classical grid hierarchies with characteristic mesh sizes $h,\, 2h,\, 4h,$ etc. Therefore, these methods require some extra information besides the matrix of the linear system and lack of robustness in some situations where semi-coarsening would be desirable. In the paper, we develop a general method that can be applied in a black box fashion to a wide class of problems, ranging from 2D model Poisson problems to 3D singularly perturbed convection-diffusion equations.