发表机构
Xiangtan University（湘潭大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出TLFSI方法，结合两级与滤波子空间迭代，高效计算广义Hermitian内部特征值问题中指定区间内的所有特征对，理论分析与数值实验验证其有效性。
AI 中文摘要
我们提出了一种两级滤波子空间迭代（TLFSI）方法，用于计算自伴偏微分方程特征值问题在有限元离散化后，其特征值位于感兴趣区间$[a,b]$内的所有特征对。该方法将两级方法与现代滤波子空间迭代框架相结合。在本文中，我们以轮廓积分滤波为例。两级方法根据感兴趣特征值的谱位置构造粗空间，并从中获得目标不变子空间的近似。我们证明了近似子空间与目标子空间之间的距离仅取决于感兴趣谱区域与其余谱之间的间隔，以及粗网格尺寸$H$。在基准弹性问题上的数值实验证实了理论预测。
英文摘要
We propose a two-level filtered subspace iterative (TLFSI) method for computing all eigenpairs whose eigenvalues in the interval of interest $[a,b]$ after finite element discretization of self-adjoint PDE eigenvalue problems. The method combines a two-level approach with a modern filtered subspace iteration framework. In this paper, we use contour integral filtering as an example. The two-level method constructs a coarse space according to the spectral location of the eigenvalues of interest and obtains from it an approximation to the target invariant subspace. We prove that the distance between the approximate and target subspaces depends only on the separation between the spectral region of interest and the remainder of the spectrum, together with the coarse mesh size \(H\). Numerical experiments on benchmark elasticity problems confirm the theoretical predictions.
Comments24 pages, 2 figures
