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000021977 1001_ $$0P:(DE-Juel1)144723$$aDi Napoli, E.$$b0$$uFZJ
000021977 1112_ $$cLondon, UK$$d2012-06-28
000021977 245__ $$aBlock iterative solvers for sequences of correlated dense eigenvalue problems
000021977 260__ $$c2012
000021977 29510 $$a7th International Conference on  Parallel Matrix Algorithms and Applications (PMAA 2012)
000021977 3367_ $$0PUB:(DE-HGF)6$$2PUB:(DE-HGF)$$aConference Presentation
000021977 3367_ $$033$$2EndNote$$aConference Paper
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000021977 500__ $$3Presentation on a conference
000021977 520__ $$aSimulations in Density Functional Theory are made of dozens of sequences, where each sequence groups together eigenproblems with increasing self-consistent cycle iteration index. In a recent study, it has been shown a high degree of correlation between successive eigenproblems of each sequence. In particular, by tracking the evolution over iterations of the angles between eigenvectors of successive eigenproblems, it was shown that eigenvectors are almost collinear after the first few iterations. This result suggests we could use eigenvectors, computed at a certain iteration, as approximate solutions for the problem at the successive one. The key element is to exploit the collinearity between vectors of adjacent problems in order to improve the performance of the eigensolver. In this study we provide numerical examples where opportunely selected block iterative eigensolvers benefit from the re-use of eigenvectors when applied to sequences of eigenproblems extracted from simulations of real-world materials. In our investigation we vary several parameters in order to address how the solvers behave under different conditions. In most cases our study shows that, when the solvers are fed approximated eigenvectors as opposed to random vectors, they obtain a substantial speed-up and could become a valid alternative to direct methods.
000021977 536__ $$0G:(DE-Juel1)FUEK411$$2G:(DE-HGF)$$aScientific Computing$$cP41$$x0
000021977 536__ $$0G:(DE-Juel1)SDLQM$$aSimulation and Data Laboratory Quantum Materials (SDLQM) (SDLQM)$$cSDLQM$$fSimulation and Data Laboratory Quantum Materials (SDLQM)$$x2
000021977 909CO $$ooai:juser.fz-juelich.de:21977$$pVDB
000021977 9131_ $$0G:(DE-Juel1)FUEK411$$1G:(DE-HGF)POF2-410$$2G:(DE-HGF)POF2-400$$bSchlüsseltechnologien$$kP41$$lSupercomputing$$vScientific Computing$$x0
000021977 9141_ $$y2012
000021977 9201_ $$0I:(DE-Juel1)JSC-20090406$$gJSC$$kJSC$$lJülich Supercomputing Centre$$x0
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