Name
Title | ||
|---|---|---|
Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations |
Abstract | ||
|---|---|---|
The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing a nonorthogonal basis for ab initio electronic structure calculations. We propose a hybrid preconditioning scheme to effectively combine global and locally accelerated preconditioners for rapid iterative diagonalization of such eigenvalue problems. In partition-of-unity finite-element (PUFE) pseudopotential density-functional calculations, employing a nonorthogonal basis, we show that the hybrid preconditioned block steepest descent method is a cost-effective eigensolver, outperforming current state-of-the-art global preconditioning schemes, and comparably efficient for the ill-conditioned generalized eigenvalue problems produced by PUFE as the locally optimal block preconditioned conjugate-gradient method for the well-conditioned standard eigenvalue problems produced by planewave methods. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.jcp.2013.07.020 | J. Comput. Physics |
Keywords | Field | DocType |
electronic structure calculation,hybrid preconditioned block steepest,well-conditioned standard eigenvalue problem,hybrid preconditioning scheme,conjugate-gradient method,large ill-conditioned generalized eigenvalue,descent method,ill-conditioned generalized eigenvalue problem,eigenvalue problem,nonorthogonal basis,iterative diagonalization,steepest descent method | Bottleneck,Quantum,Mathematical optimization,Electronic structure,Plane wave,Method of steepest descent,Ab initio,Eigenvalues and eigenvectors,Mathematics,Pseudopotential | Journal |
Volume | Issue | ISSN |
255 | C | 0021-9991 |
Citations | PageRank | References |
1 | 0.35 | 11 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yun-Feng Cai | 1 | 21 | 4.06 |
| Zhaojun Bai | 2 | 661 | 107.69 |
| John E. Pask | 3 | 22 | 3.42 |
| N. Sukumar | 4 | 1 | 1.70 |