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@ARTICLE{DiNapoli:21077,
      author       = {Di Napoli, E. and Blügel, S. and Bientinesi, P.},
      title        = {{C}orrelations in sequences of generalized eigenproblems
                      arising in {D}ensity {F}unctional {T}heory},
      journal      = {Computer physics communications},
      volume       = {183},
      issn         = {0010-4655},
      address      = {Amsterdam},
      publisher    = {North Holland Publ. Co.},
      reportid     = {PreJuSER-21077},
      pages        = {1674 - 1682},
      year         = {2012},
      note         = {Article based on research supported by the Julich Aachen
                      Research Alliance (JARA-HPC) consortium, the Deutsche
                      Forschungsgemeinschaft (DFG), and the Volkswagen
                      Foundation.Financial support from the following institutions
                      is gratefully acknowledged: the JARA-HPC through the Midterm
                      Seed Funds 2009 grant, the Deutsche Forschungsgemeinschaft
                      (German Research Association) through grant GSC 111, and the
                      Volkswagen Foundation through the fellowship "Computational
                      Sciences".},
      abstract     = {Density Functional Theory (DFT) is one of the most used ab
                      initio theoretical frameworks in materials science. It
                      derives the ground state properties of a multi-atomic
                      ensemble directly from the computation of its one-particle
                      density n(r). In DFT-based simulations the solution is
                      calculated through a chain of successive self-consistent
                      cycles: in each cycle a series of coupled equations
                      (Kohn-Sham) translates to a large number of generalized
                      eigenvalue problems whose eigenpairs are the principal means
                      for expressing n(r). A simulation ends when n(r) has
                      converged to the solution within the required numerical
                      accuracy. This usually happens after several cycles,
                      resulting in a process calling for the solution of many
                      sequences of eigenproblems. In this paper, the authors
                      report evidence showing unexpected correlations between
                      adjacent eigenproblems within each sequence. By
                      investigating the numerical properties of the sequences of
                      generalized eigenproblems it is shown that the eigenvectors
                      undergo an "evolution" process. At the same time it is shown
                      that the Hamiltonian matrices exhibit a similar evolution
                      and manifest a specific pattern in the information they
                      carry. Correlation between eigenproblems within a sequence
                      is of capital importance: information extracted from the
                      simulation at one step of the sequence could be used to
                      compute the solution at the next step. Although they are not
                      explored in this work, the implications could be manifold:
                      from increasing the performance of material simulations, to
                      the development of an improved iterative solver, to
                      modifying the mathematical foundations of the DFT
                      computational paradigm in use, thus opening the way to the
                      investigation of new materials. (C) 2012 Elsevier B.V. All
                      rights reserved.},
      keywords     = {J (WoSType)},
      cin          = {IAS-1 / JARA-FIT / JARA-SIM / JSC / PGI-1},
      ddc          = {004},
      cid          = {I:(DE-Juel1)IAS-1-20090406 / $I:(DE-82)080009_20140620$ /
                      I:(DE-Juel1)VDB1045 / I:(DE-Juel1)JSC-20090406 /
                      I:(DE-Juel1)PGI-1-20110106},
      pnm          = {Scientific Computing (FUEK411) / Grundlagen für
                      zukünftige Informationstechnologien (FUEK412) / 411 -
                      Computational Science and Mathematical Methods (POF2-411) /
                      Simulation and Data Laboratory Quantum Materials (SDLQM)
                      (SDLQM)},
      pid          = {G:(DE-Juel1)FUEK411 / G:(DE-Juel1)FUEK412 /
                      G:(DE-HGF)POF2-411 / G:(DE-Juel1)SDLQM},
      shelfmark    = {Computer Science, Interdisciplinary Applications / Physics,
                      Mathematical},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000304384500014},
      doi          = {10.1016/j.cpc.2012.03.006},
      url          = {https://juser.fz-juelich.de/record/21077},
}