A Two-level Filtered Subspace Iterative Method for Generalized Hermitian Interior Eigenvalue Problems
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Li, Qi, Shu, Shi, Xu, Xiaofei, Zhang, Juan
Institution: Xiangtan University
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G2794467561
OpenAlex ID: W7220660468