6 papers
Local Multilevel Preconditioned Jacobi-Davidson Method for Elliptic Eigenvalue Problems on Adaptive Meshes
Jianing Guo, Qigang Liang, Xuejun Xu
In this work, we propose an efficient adaptive multilevel preconditioned Jacobi-Davidson (PJD) method for eigenvalue problems with singularity. Our multilevel method utilizes a loc…
A Two-Level Additive Schwarz Method for Computing Interior Multiple and Clustered Eigenvalues of Symmetric Elliptic Operators
Qigang Liang, Xuejun Xu
In this paper, we propose an efficient two-level additive Schwarz method for solving large-scale eigenvalue problems arising from the finite element discretization of symmetric ell…
Adaptive Multilevel Methods for the Maxwell Eigenvalue Problem
Qigang Liang, Xuejun Xu, Qingquan Zhang
In this paper, we propose an adaptive multilevel preconditioned Helmholtz-Jacobi-Davidson (PHJD) method for the Maxwell eigenvalue problem with singularities. The key idea in this…
Pointwise A Posteriori Error Estimators for Multiple and Clustered Eigenvalue Computations
Zhenglei Li, Qigang Liang, Xuejun Xu
In this work, we propose an a pointwise a posteriori error estimator for conforming finite element approximations of eigenfunctions corresponding to multiple and clustered eigenval…
Pointwise A Posteriori Error Estimators for Elliptic Eigenvalue Problems
Zhenglei Li, Qigang Liang, Xuejun Xu
In this work, we propose and analyze a pointwise a posteriori error estimator for simple eigenvalues of elliptic eigenvalue problems with adaptive finite element methods (AFEMs). W…
Computing Both Upper and Lower Eigenvalue Bounds by HDG Methods
Qigang Liang, Xuejun Xu, Liuyao Yuan
In this paper, we observe an interesting phenomenon for a hybridizable discontinuous Galerkin (HDG) method for eigenvalue problems. Specifically, using the same finite element meth…