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000150535 037__ $$aFZJ-2014-00589
000150535 1001_ $$0P:(DE-Juel1)144723$$aDi Napoli, Edoardo$$b0
000150535 1112_ $$aNumerical Analysis and Scientific Computation with Applications$$cCalais$$d2013-06-24 - 2013-06-26$$gNASCA13$$wFrance
000150535 245__ $$aPreconditioning Chebyshev subspace iteration applied to sequences of dense eigenproblems in ab initio simulations
000150535 260__ $$c2013
000150535 3367_ $$0PUB:(DE-HGF)6$$2PUB:(DE-HGF)$$aConference Presentation$$bconf$$mconf$$s1418826866_23273$$xInvited
000150535 3367_ $$033$$2EndNote$$aConference Paper
000150535 3367_ $$2DataCite$$aOther
000150535 3367_ $$2ORCID$$aLECTURE_SPEECH
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000150535 3367_ $$2BibTeX$$aINPROCEEDINGS
000150535 520__ $$aResearch in several branches of chemistry and materials science relies on large ab initio numerical simulations. The majority of these simulations are based on computational methods developed within the framework of Density Functional Theory (DFT) [1]. Among all the DFT-based methods the Full-potential Linearized Augmented Plane Wave (FLAPW) [2, 3] method constitutes the most precise computational framework to calculate ground state energy of periodic and crystalline materials. FLAPW provides the means to solve a high-dimensional quantum mechanical problem by representing it as a non-linear generalized eigenvalue problem which is solved self-consistently through a series of successive outer-iteration cycles. As a consequence each self-consistent simulation is made of dozens of sequences of dense generalized eigenproblems P : Ax = λBx. Each sequence, P1 , . . . Pi . . . PN , groups together eigenproblems with increasing outer-iteration index i. Successive eigenproblems in a FLAPW-generated 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 [4]. 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 maximally exploit the approximate solution, we developed a subspace iteration method augmented with an optimized Chebyshev polynomial accelerator together with an efficient locking mechanism (ChFSI). The resulting eigensolver was implemented in C language and parallelized for both shared and distributed architectures. Numerical tests show that, when the eigensolver is preconditioned with approximate solutions instead of random vectors, it achieves up to a 5X speedup. Moreover ChFSI takes great advantage of computational resources by obtaining levels of efficiency up to 80 % of the theoretical peak performance. In particular, by making better use of massively parallel architectures, the distributed memory version will allow the FLAPW method users to simulate larger physical systems than are currently accessible. Additionally, despite the eigenproblems in the sequence being relatively large and dense, the parallel ChFSI preconditioned with approximate solutions performs substantially better than the corresponding direct eigensolvers, even for a significant portion of the sought-after spectrum. [1] R. M. Dreizler, and E. K. U. Gross, Density Functional Theory (Springer-Verlag, 1990) [2] A. J. Freeman, H. Krakauer, M. Weinert, and E. Wimmer, Phys. Rev. B 24 (1981) 864. [3] A. J. Freeman, and H. J. F. Jansen, Phys. Rev. B 30 (1984) 561 [4] E. Di Napoli, S. Blu ̈gel, and P. Bientinesi, Comp. Phys. Comm. 183 (2012), pp. 1674- 1682, [arXiv:1108.2594]
000150535 536__ $$0G:(DE-HGF)POF2-411$$a411 - Computational Science and Mathematical Methods (POF2-411)$$cPOF2-411$$fPOF II$$x0
000150535 536__ $$0G:(DE-Juel1)SDLQM$$aSimulation and Data Laboratory Quantum Materials (SDLQM) (SDLQM)$$cSDLQM$$fSimulation and Data Laboratory Quantum Materials (SDLQM)$$x2
000150535 7001_ $$0P:(DE-HGF)0$$aBerljafa, Mario$$b1
000150535 773__ $$y2013
000150535 909CO $$ooai:juser.fz-juelich.de:150535$$pVDB
000150535 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)144723$$aForschungszentrum Jülich GmbH$$b0$$kFZJ
000150535 9131_ $$0G:(DE-HGF)POF2-411$$1G:(DE-HGF)POF2-410$$2G:(DE-HGF)POF2-400$$3G:(DE-HGF)POF2$$4G:(DE-HGF)POF$$aDE-HGF$$bSchlüsseltechnologien$$lSupercomputing$$vComputational Science and Mathematical Methods$$x0
000150535 9141_ $$y2013
000150535 9201_ $$0I:(DE-Juel1)JSC-20090406$$kJSC$$lJülich Supercomputing Center$$x0
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