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

作者：Yang, Ai-Li^*; Song, Lun-Ji; Wu, Yu-Jiang

来源：Mathematical and Computer Modelling, 2013, 57(3-4): 512-524.

DOI：10.1016/j.mcm.2012.06.031

• Condition number
• Block incremental unknowns
• Preconditioning
• Anisotropic problem
• Diagonal preconditioner

Condition number of the block incremental unknowns (BIU) matrix associated to anisotropic operator epsilon partial derivative(2)/partial derivative x(2) + partial derivative(2)/partial derivative y(2) with 0 < epsilon << 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) + epsilon 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 number of the BIU matrix is further reduced to O(1 + 4 epsilon pi(-2)h(-2)), which means that the condition number is optimal if epsilon = O(h(2)). Numerical experiments are performed to different examples and parameters, numerical results verify our theoretical analysis.

• 出版日期2013-2
• 单位兰州大学