论文标题
双参数操作员预处理
Bi-Parametric Operator Preconditioning
论文作者
论文摘要
我们扩展了操作员预处理框架[R. Hiptmair，计算。数学。使用应用。 52（2006），pp。〜699--706] to petrov-galerkin方法，同时考虑到数值近似值时的变异形式及其预处理的参数依赖性扰动。通过考虑原始形式及其预处理的不同扰动参数，我们的BI-参数抽象设置可导致健壮和受控方案。对于希尔伯特的空间，当使用低临界度进行预处理或等效地，具有高度压缩的近似值时，我们为迭代求解器（例如$ h $独立的收敛边界）得出详尽的线性和超级线性收敛估计。
We extend the operator preconditioning framework [R. Hiptmair, Comput. Math. with Appl. 52 (2006), pp.~699--706] to Petrov-Galerkin methods while accounting for parameter-dependent perturbations of both variational forms and their preconditioners, as occurs when performing numerical approximations. By considering different perturbation parameters for the original form and its preconditioner, our bi-parametric abstract setting leads to robust and controlled schemes. For Hilbert spaces, we derive exhaustive linear and super-linear convergence estimates for iterative solvers, such as $h$-independent convergence bounds, when preconditioning with low-accuracy or, equivalently, with highly compressed approximations.
