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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 99 (1998), S. 197-206 
    ISSN: 1432-2234
    Keywords: Key words: Scalable algorithms ; Supercomputing ; Quantum mechanics ; Divide-and-conquer ; Large molecules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. We describe an efficient algorithm for carrying out a “divide-and-conquer” fit of a molecule's electronic density on massively parallel computers. Near linear speedups are achieved with up to 48 processors on a Cray T3E, and our results indicate that similar efficiencies could be attained on an even greater number of processors. To achieve optimum efficiency, the algorithm combines coarse and fine-grain parallelization and adapts itself to the existing ratio of processors to subsystems. The subsystems employed in our divide-and-conquer approach can also be made smaller or bigger, depending on the number of processors available. This allows us to further reduce the wallclock time and improve the method's overall efficiency. The strategies implemented in this paper can be extended to any other divide-and-conquer method used within an ab initio, density functional, or semi-empirical quantum mechanical program.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 69 (1998), S. 405-421 
    ISSN: 0020-7608
    Keywords: density functional theory ; exchange-correlation potentials ; grids ; linear scaling methods ; divide-and-conquer ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The conventional linear combination of Gaussian-type orbitals (LCGTO) density functional (DF) method fits the exchange-correlation (XC) potentials and energy density within an auxiliary basis. The benefits of this approach versus straightforward numerical quadrature of the XC terms will be discussed. However, the conventional fitting procedure scales cubically with system size and is therefore ill-suited for applications on very large systems. A divide-and-conquer (DAC) approach to the fits of the XC terms has been developed and implemented within the DeFT DF software package. This DAC procedure will be outlined, and the results and timings of benchmark 6-31G** calculations on extended glycine polypeptides will be presented. Other changes made to DeFT's XC subroutines, necessary to achieve near-linear scaling, will also be discussed. DeFT's grids have also been refined to achieve greater precision, and a scheme using fewer points for fitting procedures and more points for numerical integrations is presented. Through our preliminary efforts, we have achieved scalings in the XC modules no worse than N1.4 (N is the number of atoms) for peptides that range in size up to 83 atoms.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 405-421, 1998
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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