L. Greengard and V. Rokhlin. On the evaluation of electrostatic interactions in molecular modeling. Chem. Scr., 29A:139--144, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... of equidistributed particles reveals that the complexity for this case is only O(N ) while the algorithm of Barnes and Hut remains O(N log N ) Rokhlin [53] independently of Appel, introduced very similar ideas for the solution of integral equations of potential theory, which he and Greengard [28, 29, 9, 30] extended rigorously to what is now known as the Fast Multipole Method. In his dissertation Greengard describes the non adaptive Fast Multipole Method for two and three space dimensions and also presents the adaptive Fast Multipole Method in two space dimensions. Due to the applicability of ....

Leslie Greengard and V. Rokhlin. On the evaluation of electrostatic interactions in molecular modeling. Chemica Scripta, 29A:139--144, 1989.

....forces require only O(N) operations for N atoms. Efficient approximation algorithms for evaluating the non bonded forces among atoms have been introduced recently using diverse techniques. An approximation algorithm for evaluating the Coulombic forces has been considered by Greengard and Rokhlin [9] using multipole expansions. A related algorithm for computing simultaneously the Coulombic and short range forces (e.g. Lennard Jones potentials) has been introduced by Draghicescu in her thesis [8] Both of these techniques (as well as techniques that involve solving a Laplace equation for the ....

L. Greengard and V. Rokhlin, On the evaluation of electrostatic interactions in molecular modeling, Chemica Scripta 29A (1989), 139-144.

....prediction; even if P6=NP, protein structure prediction may be a tractable restricted form of PSP (x4.6) 35 Straightforward simulation requires computing O(N 2 ) pairwise interactions. Grid based neighbor lists (van Gunsteren et al. 1984) and multipole expansions (Greengard, 1987; Greengard and Rokhlin, 1989; Schmidt and Lee, 1991) may be employed to achieve near linear time performance, which of course would also satisfy the proviso. 36 If the guaranteed physical folding time T (N) is known, and the computational speed of the simulation S(N)F (N) can be determined, then the method for finding the ....

Greengard, L. and Rokhlin, V. (1989). On the evaluation of electrostatic interactions in molecular modeling. Chemica Scripta, 29A:139--144.

....and our approach Thus, the above problems (gravitation, VEM, BEM, etc. are all O(N 2 ) in complexity (per time step for gravitation and VEM, per iteration for BEM) for each of the N elements, find the derivatives of the field induced by all N elements. The use of fast tree codes, in 2D and 3D [2, 3, 5 10, 14, 16 18, 23, 24, 26 35, 41, 43], reduces the computing cost associated with all evaluations from O(N 2 ) to something much more tractable: O(N log N ) or O(N 1 ffl ) with ffl 1, or even O(N) depending on the complexity of the implementation. The big O notation can however be misleading for practical values of N and ....

Greengard, L. and Rokhlin, V., "On the Evaluation of Electrostatic Interactions in Molecular Modeling," Chemica Scripta, 29 A, pp. 139--144, 1989.

.... reveals that the complexity for this case is only O(N ) while the algorithm of Barnes and Hut remains O(N log N ) Rokhlin [Rok85] independently of Appel, introduced very similar ideas for the solution of integral equations of potential theory, which he and Greengard [Gre87, GR87, CGR88, GR89] extended rigorously to what is now known as the Fast Multipole Method. In his dissertation Greengard describes the non adaptive Fast Multipole Method for two and three space dimensions and also presents the adaptive Fast Multipole Method in two space dimensions. Due to the applicability of ....

Leslie Greengard and V. Rokhlin. On the evaluation of electrostatic interactions in molecular modeling. Chemica Scripta, 29A:139--144, 1989.

....the constants that are discarded by the asymptotic analysis. Large scale application of tree based approximation methods has (to our knowledge) only occurred in astrophysics, 41, 16, 40, 24] although preliminary work has been done ontwo dimensional [33, 31, 21, 19] and three dimensional systems [22, 39, 8, 15] from other disciplines. One roadblock to the widespread acceptance of tree codes is that they are inherently complex to program, especially for parallel machines. We report on an implementation of a tree code which is not specific to a particular problem domain. Although designed with ....

L. Greengard and V. I. Rokhlin. On the evaluation of electrostatic interactions in molecular modeling. Chemica Scripta, 29A:139--144, 1989.

.... reveals that the complexity for this case is only O(N ) while the algorithm of Barnes and Hut remains O(N log N ) Rokhlin [Rok85] independently of Appel, introduced very similar ideas for the solution of integral equations of potential theory, which he and Greengard [Gre87, GR87, CGR88, GR89] extended rigorously to what is now known as the Fast Multipole Method. In his dissertation Greengard describes the nonadaptive Fast Multipole Method for two and three space dimensions and also presents the adaptive Fast Multipole Method in two space dimensions. Due to the applicability of ....

Leslie Greengard and V. Rokhlin. On the evaluation of electrostatic interactions in molecular modeling. Chemica Scripta, 29A:139--144, 1989.

....can be achieved. By additionally using a hierarchy of local Taylor expansions for the evaluation of the electrostatic potential in the vicinity of a group of particles Greengard and Rokhlin have constructed the so called fast multipole method (FMM) that even scales with O(N) for large systems [34,35]. For MD simulations of biomolecules the FMM type grouping of charges, defined by a fixed and regular subdivision of space, requires multipole expansions of rather high order (more than 6 terms of the expansion) as to achieve sufficient numerical accuracy [34] If, instead, as shown in Figure 1, ....

.... scales with O(N) for large systems [34,35] For MD simulations of biomolecules the FMM type grouping of charges, defined by a fixed and regular subdivision of space, requires multipole expansions of rather high order (more than 6 terms of the expansion) as to achieve sufficient numerical accuracy [34]. If, instead, as shown in Figure 1, the charge grouping is adapted to specific structural and dynamical properties of the simulated biomolecules, the multipole expansions can be truncated at quite low orders, e.g. after the second order, while maintaining sufficient accuracy [36 38] In the ....

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L. Greengard and V. Rokhlin. On the evaluation of electrostatic interactions in molecular modeling. Chem. Scr., 29A:139--144, 1989.

....) operations, and the nonbonded forces, which are of O(N 2 ) complexity. Efficient approximation algorithms for evaluating the nonbonded forces among atoms have been introduced recently. An approximation algorithm for evaluating the Coulombic forces has been considered by Greengard and Rokhlin [12] using multipole expansions. A related algorithm for computing simultaneously the Coulombic and short range forces (e.g. Lennard Jones potentials) has been introduced by Draghicescu in her thesis [8] Both of these techniques, as well as techniques that involve solving a Laplace equation for the ....

L. Greengard and V. Rokhlin. On the evaluation of electrostatic interactions in molecular modeling. Chemica Scripta, 29A:139--144, 1989.

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L. Greengard and V. Rokhlin. On the evaluation of electrostatic interactions in molecular modeling. Chem. Scr., 29A:139--144, 1989.

No context found.

L. Greengard and V. Rokhlin, "On the evaluation of electrostatic interactions in molecular modeling," Chemica Scripta, 29a (1989), Sep:139-144.

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