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| Home > Publications database > Parallel block Chebyshev subspace iteration algorithm optimized for sequences of correlated dense eigenproblems |
| Home > Publications database > Parallel block Chebyshev subspace iteration algorithm optimized for sequences of correlated dense eigenproblems |
| Conference Presentation (Other) | FZJ-2012-00907 |
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2012
Abstract: In many material science applications simulations are made of dozens of sequences, where each sequence groups together eigenproblems with increasing self-consistent cycle outer-iteration index. Successive eigenproblems in a sequence possess a high degree of correlation. In particular it has been demonstrated that eigenvectors of adjacent eigenproblems become progressively more collinear to each other as the outer-iteration index increases. This result suggests one could use eigenvectors, computed at a certain outer-iteration, as approximate solutions to improve the performance of the eigensolver at the next one. In order to opti- mally exploit the approximate solution, we developed a block iterative eigensolver augmented with a Chebyshev polynomial accelerator (BChFSI). Numerical tests show that, when the sequential version of the solver is fed approximate solutions instead of random vectors, it achieves up to a 5X speedup. Moreover the parallel shared memory implementation of the algorithm obtains a high level of efficiency up to 80 \% of the theoretical peak performance. Despite the eigenproblems in the sequence being relatively large and dense, the parallel BChFSI fed with ap- proximate solutions performs substantially better than the corresponding direct eigensolver, even for a significant portion of the sought-after spectrum
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