Acceleration of LaBonte’s iteration by multigrid method

Hirano, Satoshi; Hayashi, N.

doi:10.1063/1.372767

Cited by 2 publications

(1 citation statement)

References 4 publications

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“…In 1973, a linear complexity was achieved by those methods (Brandt, 1972). Many applications in practice are demonstrated in many papers (Sagui and Darden, 2000;Poplau et al, 2004;Zaslavsky and Schlick, 1998;Bernholc et al, 1997;Fattebert and Bernholc, 2000;Hirano and Hayash, 2000;Skeel et al, 2002;Hackbusch, 2010;Trotenberg et al, 2001).…”

Section: Introductionmentioning

confidence: 99%

Multilevel Evaluation of Coulomb Lattice Sums of Charge Systems

Suwan¹,

Brandt²,

Ilyin³

2012

Journal of Mathematics and Statistics

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Problem statement: Due to the long range nature of interactions of the N-body systems, direct computation of the Coulomb potential energy involves O(N²) operations. To decrease such complexity, a simple Multilevel Summation method has been developed. Approach: In the frame of the Multilevel Summation method, the two-body interaction is decomposed into two parts: a local part and a smooth part. The local part vanishes beyond some cut-off distance; hence, its contribution to the potential energy is calculated in O(N) operations. In contrast to some common fast summation methods, the smooth part is calculated in real space on a sequence of grids with increasing meshsize in O(N) operations. Results: The method is tested on the calculation of the Madelung constants of ionic crystals in one, two and three dimensional cases. For a cut-off distance equals three times the meshsize of the ionic crystal, an error less than 0.01% is obtained. Conclusion: In computing the coulomb lattice sums of charge systems consisting of N bodies, the Multilevel Summation method decreases the complexity to O(N) operations

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