Algebraic preconditioning analysis of the multilevel block incremental unknowns method for anisotropic elliptic operators

@article{Yang2013AlgebraicPA,
  title={Algebraic preconditioning analysis of the multilevel block incremental unknowns method for anisotropic elliptic operators},
  author={Ai-Li Yang and Lunji Song and Yujiang Wu},
  journal={Math. Comput. Model.},
  year={2013},
  volume={57},
  pages={512-524}
}
Abstract Condition number of the block incremental unknowns (BIU) matrix associated to anisotropic operator e ∂ 2 / ∂ x 2 + ∂ 2 / ∂ y 2 with 0 e ≪ 1 is analyzed; more general second-order anisotropic elliptic operators are also considered. Theoretical analyses show that the condition number of the BIU matrix is bounded by c ⋅ ( h − 1 + e h − 2 ) instead of O ( h − 2 ) with usual nodal unknowns where h is the mesh size. In addition, we introduce a diagonal preconditioner such that the condition… Expand
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