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| Hauptseite > Publikationsdatenbank > Block iterative solvers for sequences of correlated dense eigenvalue problems |
| Hauptseite > Publikationsdatenbank > Block iterative solvers for sequences of correlated dense eigenvalue problems |
| Conference Presentation | PreJuSER-21977 |
2012
Abstract: Simulations in Density Functional Theory are made of dozens of sequences, where each sequence groups together eigenproblems with increasing self-consistent cycle iteration index. In a recent study, it has been shown a high degree of correlation between successive eigenproblems of each sequence. In particular, by tracking the evolution over iterations of the angles between eigenvectors of successive eigenproblems, it was shown that eigenvectors are almost collinear after the first few iterations. This result suggests we could use eigenvectors, computed at a certain iteration, as approximate solutions for the problem at the successive one. The key element is to exploit the collinearity between vectors of adjacent problems in order to improve the performance of the eigensolver. In this study we provide numerical examples where opportunely selected block iterative eigensolvers benefit from the re-use of eigenvectors when applied to sequences of eigenproblems extracted from simulations of real-world materials. In our investigation we vary several parameters in order to address how the solvers behave under different conditions. In most cases our study shows that, when the solvers are fed approximated eigenvectors as opposed to random vectors, they obtain a substantial speed-up and could become a valid alternative to direct methods.
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