کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1136613 | 1489137 | 2013 | 13 صفحه PDF | دانلود رایگان |

Condition number of the block incremental unknowns (BIU) matrix associated to anisotropic operator ε∂2/∂x2+∂2/∂y2ε∂2/∂x2+∂2/∂y2 with 0<ε≪10<ε≪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+εh−2)c⋅(h−1+εh−2) instead of O(h−2)O(h−2) with usual nodal unknowns where hh 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+4επ−2h−2)O(1+4επ−2h−2), which means that the condition number is optimal if ε=O(h2)ε=O(h2). Numerical experiments are performed to different examples and parameters, numerical results verify our theoretical analysis.
Journal: Mathematical and Computer Modelling - Volume 57, Issues 3–4, February 2013, Pages 512–524