论文标题
对称椭圆特征值问题的牛顿 - 距离法的收敛分析
Convergence analysis of the Newton-Schur method for the symmetric elliptic eigenvalue problem
论文作者
论文摘要
在本文中，我们考虑了希尔伯特空间中的牛顿 - 途径方法，并获得二次收敛。对于由标准有限元方法和非重叠域分解方法离散的对称椭圆特征问题，我们使用Steklov-Poincaré操作员将域$ω$上的特征性问题减少到非线性特征eigenear eigenear eigenvalue subproblem in $γ$，该$γ$，该$γ$ sub ins indominies ain borgaries ain borgaries ain borgaries ain borgaries ain bornainies。我们证明，牛顿 - 扫描方法的收敛速率为$ε_{n} \ leq ch^{2}（1+ \ ln（h/h））^{2} {2}ε^{2} $，其中常数$ c $在其中，其中$ c $独立于$ h $ h $ h $ h $ h $ h $和$ h $和$ h $ y和$ h $ and $和$ h $ and $ a}一步。数值实验证实了我们的理论分析。
In this paper, we consider the Newton-Schur method in Hilbert space and obtain quadratic convergence. For the symmetric elliptic eigenvalue problem discretized by the standard finite element method and non-overlapping domain decomposition method, we use the Steklov-Poincaré operator to reduce the eigenvalue problem on the domain $Ω$ into the nonlinear eigenvalue subproblem on $Γ$, which is the union of subdomain boundaries. We prove that the convergence rate for the Newton-Schur method is $ε_{N}\leq CH^{2}(1+\ln(H/h))^{2}ε^{2}$, where the constant $C$ is independent of the fine mesh size $h$ and coarse mesh size $H$, and $ε_{N}$ and $ε$ are errors after and before one iteration step respectively. Numerical experiments confirm our theoretical analysis.
