A Two-level Filtered Subspace Iterative Method for Generalized Hermitian Interior Eigenvalue Problems
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.
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BibTeX
@misc{li2026twolevel,
title = {{A Two-level Filtered Subspace Iterative Method for Generalized Hermitian Interior Eigenvalue Problems}},
author = {Qi Li and Shi Shu and Xiaofei Xu and Juan Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03804},
eprint = {2610.03804},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03804},
}
RIS
TY - UNPB
TI - A Two-level Filtered Subspace Iterative Method for Generalized Hermitian Interior Eigenvalue Problems
AU - Qi Li
AU - Shi Shu
AU - Xiaofei Xu
AU - Juan Zhang
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.03804
UR - https://arxiv.org/abs/2610.03804
AB - 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.
ER -