Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6928683 | Journal of Computational Physics | 2018 | 15 Pages |
Abstract
We consider computing the k-th eigenvalue and its corresponding eigenvector of a generalized Hermitian eigenvalue problem of nÃn large sparse matrices. In electronic structure calculations, several properties of materials, such as those of optoelectronic device materials, are governed by the eigenpair with a material-specific index k. We present a three-stage algorithm for computing the k-th eigenpair with validation of its index. In the first stage of the algorithm, we propose an efficient way of finding an interval containing the k-th eigenvalue (1âªkâªn) with a non-standard application of the Lanczos method. In the second stage, spectral bisection for large-scale problems is realized using a sparse direct linear solver to narrow down the interval of the k-th eigenvalue. In the third stage, we switch to a modified shift-and-invert Lanczos method to reduce bisection iterations and compute the k-th eigenpair with validation. Numerical results with problem sizes up to 1.5 million are reported, and the results demonstrate the accuracy and efficiency of the three-stage algorithm.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Dongjin Lee, Takeo Hoshi, Tomohiro Sogabe, Yuto Miyatake, Shao-Liang Zhang,