Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Environmental Molecular Sciences Lab.
We present two efficient iterative algorithms for solving the linear response eigen- value problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into a product eigenvalue problem that is self-adjoint with respect to a K-inner product. This product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. However, the other component of the eigenvector can be easily recovered in a postprocessing procedure. Therefore, the algorithms we present here are more efficient than existing algorithms that try to approximate both components of the eigenvectors simultaneously. The efficiency of the new algorithms is demonstrated by numerical examples.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); Ministry of Education, Youth and Sports (Cambodia)
- DOE Contract Number:
- AC02-05CH11231; AC02-05CH1123; KC-030106062653; AC05-76RL1830
- OSTI ID:
- 1406765
- Report Number(s):
- PNNL-SA-114405; 48614; KC0301060
- Journal Information:
- Computer Physics Communications, Vol. 221, Issue C; ISSN 0010-4655
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
S
|
journal | January 2018 |
A FEAST Algorithm for the Linear Response Eigenvalue Problem
|
journal | August 2019 |
Similar Records
New algorithms for iterative matrix‐free eigensolvers in quantum chemistry
A parallel additive Schwarz preconditioned Jacobi-Davidson algorithm for polynomial eigenvalue problems in quantum dot simulation