Optimizing Two-Level Preconditionings for the Conjugate Gradient Method
LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers
An optimal order multilevel preconditioner with respect to problem and discretization parameters
Scientific computing and applications
Multilevel preconditioning of rotated bilinear non-conforming FEM problems
Computers & Mathematics with Applications
Large-Scale Scientific Computing
Multilevel preconditioning of 2D Rannacher-Turek FE problems: additive and multiplicative methods
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Robust AMLI methods for parabolic Crouzeix-Raviart FEM systems
Journal of Computational and Applied Mathematics
Milestones in the development of iterative solution methods
Journal on Image and Video Processing - Special issue on iterative signal processing in communications
Finite-element based sparse approximate inverses for block-factorized preconditioners
Advances in Computational Mathematics
Aggregation-based multilevel preconditioning of non-conforming FEM elasticity problems
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
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In this paper a recently proposed additive version of the algebraic multilevel iteration method for iterative solution of elliptic boundary value problems is studied. The method constructs a nearly optimal order parameter-free preconditioner, which is robust with respect to anisotropy and discontinuity of the problem coefficients. It uses a new strategy for approximating the blocks corresponding to "new" basis functions on each discretization level. To cope with the difficulties arising from the anisotropy, the problem on the coarsest mesh is solved using a bordering technique with a special choice of bordering vectors. The aim is to find a parameter-free "black-box" robust solver.The results are derived in the framework of a hierarchical basis, linear finite element discretization of an elliptic problem on arbitrary triangular meshes, and a hierarchical basis, bilinear finite element discretization on Cartesian meshes.A comparison of the method with some other iterative solution techniques is presented. Robustness and high efficiency of the proposed algorithm are demonstrated on several model-type problems.