变分不等式的二次插值多水平预处理共轭梯度法

Multilevel preconditioned CG-Iteration based on quadric interpolation for variational inequalities

讨论了由障碍问题所描述的一类变分不等式。在多水平预处理共轭梯度法的基础上,考虑在内迭代中采用二次插值算子,由此构造了一个新的多水平预条件子。证明了在新的预条件子作用下,线性辅助问题中的迭代矩阵的条件数仅为O(l2),远小于节点基下的迭代矩阵的条件数O(h-2)。

A kind of variational inequalities which describes obstacle problem is considered. Based on multilevel preconditioned cg-iteration, a new multilevel preconditioner is constructed in inner iteration by using quadric interpolation operator, and proof that under the action of the new preconditioner, the condition number of iterative matrix which come from linear auxiliary problem only is O（l^2） ,much less than the condition number O（h^-2） of iterative matrix which based on node basis.