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| Hauptseite > Publikationsdatenbank > Correlations in sequences of generalized eigenproblems arising in Density Functional Theory > print |
| Hauptseite > Publikationsdatenbank > Correlations in sequences of generalized eigenproblems arising in Density Functional Theory > print |
| 001 | 21077 | ||
| 005 | 20221109161712.0 | ||
| 024 | 7 | _ | |2 DOI |a 10.1016/j.cpc.2012.03.006 |
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| 084 | _ | _ | |2 WoS |a Computer Science, Interdisciplinary Applications |
| 084 | _ | _ | |2 WoS |a Physics, Mathematical |
| 100 | 1 | _ | |0 P:(DE-Juel1)144723 |a Di Napoli, E. |b 0 |u FZJ |
| 245 | _ | _ | |a Correlations in sequences of generalized eigenproblems arising in Density Functional Theory |
| 260 | _ | _ | |a Amsterdam |b North Holland Publ. Co. |c 2012 |
| 300 | _ | _ | |a 1674 - 1682 |
| 336 | 7 | _ | |a Journal Article |0 PUB:(DE-HGF)16 |2 PUB:(DE-HGF) |
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| 440 | _ | 0 | |0 1439 |a Computer Physics Communications |v 183 |x 0010-4655 |y 8 |
| 500 | _ | _ | |a 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". |
| 520 | _ | _ | |a 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. |
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| 653 | 2 | 0 | |2 Author |a Density Functional Theory |
| 653 | 2 | 0 | |2 Author |a Sequence of generalized eigenproblems |
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| 653 | 2 | 0 | |2 Author |a Eigenproblem correlation |
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| 773 | _ | _ | |0 PERI:(DE-600)1466511-6 |a 10.1016/j.cpc.2012.03.006 |g Vol. 183, p. 1674 - 1682 |p 1674 - 1682 |q 183<1674 - 1682 |t Computer physics communications |v 183 |x 0010-4655 |y 2012 |
| 856 | 7 | _ | |u http://dx.doi.org/10.1016/j.cpc.2012.03.006 |
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