R.W. Hockney, S.P. Goel, and J.W. Eastwood, "Quiet HighResolution Computer Models of a Plasma", Journal of Computational Physics, 14, 148, (1974).  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... (ie we need to resolve inter particle distances) but the number of particles contributing to these interactions is too large for the particleparticle approach One answer is to use a combination of PP and PM called particleparticle particle mesh(P 3 M) This was invented by Hockney et al.[2][3]. The basic idea is straightforward. Use PP to capture the near neighbor interactions out to some cutoff distance r c , chosen to include a sufficiently small number of particles that PP is still tractable. Then use PM to calculate 44 Figure 14: An example of the decomposition of the total 1=r ....

R.W. Hockney, S.P. Goel, and J.W. Eastwood, "Quiet HighResolution Computer Models of a Plasma", Journal of Computational Physics, 14, 148, (1974).

....balancing, 4) an option for using double precision for force computation. We shall discuss two of the most time consuming computational kernels in SOTON PAR: movout, which performs geometric hashing, and force, which performs the force evaluations. 2.1. Geometric Hashing The link cell method [4] is commonly used to speed up MD force calculations by minimizing the number of neighboring atoms that must be checked for possible interaction (based on a cut off distance of r c , beyond which particle interaction is assumed to be negligible) At each time step, all the atoms are hashed into ....

.... mapping.h data isfirst TRUE ; #ifdef USESYMMETRY copy sequence 4 1, 3 2, then 5 3 based on the ordering: 2] 1, 3] 4, 5] data nclist 4,1, 3,2, 5,3 ; #else copy sequence 4 1, 5 2, 6 3, then 7 4, 8 5, 9 6 based on the ordering: 1, 2, 3] [ 4, 5, 6] [ 7, 8, 9] data nclist 4,1, 5,2, 6,3, 7,4, 8,5, 9,6 ; #endif USESYMMETRY = start execution = #dir r noconcur #ifdef USEPROFILE call profstart( forcecol ) #endif spaceok = 1 = nbinx) nbinx = maxbinx) ASSERT(spaceok, forcecol: invalid nbinx , ....

R. W. Hockney, S. P. Goel, and J. W. Eastwood, Quiet highresolution computer models of a plasma, J. Comp. Phys, 14 (1974), pp. 148-- 158.

....were still necessary. Performance profiling had clearly established the contact checks as the primary computational bottleneck. The all against all particle distance check, though simple, scales computationally as O( making it impractical for large problems. By using a link cell type method [11][12] to create a neighbors list [13] the contact check was reduced to an O(N) operation, dramatically reducing the computational requirement. This method divides the physical space of the simulation into a regular grid of cells. A particle s owning cell can be determined with one pass through ....

R. W. Hockney, S. P. Goel, and J. W. Eastwood, "Quiet High-resolution Computer Models of a Plasma," J. Comp. Phys., 1974, 14:148-158.

....density) of the particular simulation. The advantage of the neighbor list is that once it is built, examining it for possible interactions is much faster than checking all atoms in the system. The second technique commonly used for speeding up MD calculations is known as the link cell method [32]. At every timestep, all the atoms are binned into 3 D cells of side length d where d = r c or slightly larger. This reduces the task of finding neighbors of a given atom to checking in 27 bins the bin the atom is in and the 26 surrounding ones. Since binning the atoms only requires O(N ) ....

R. W. Hockney, S. P. Goel, and J. W. Eastwood. Quiet high--resolution computer models of a plasma. J. Comp. Phys., 14:148--158, 1974.

....more processors than atoms. Recall from Section 2 that the original code checks all atoms to determine the interactions to be calculated. In this section we consider an optimized code for which the number of computations are reduced using techniques such as neighbor lists [21] and link cell method [12]. The neighbor list technique consists of maintaining a list of nearby atoms for each atom. This list is examined for possible interactions instead of checking all atoms in the system. The list is used for a few time steps to calculate force interactions and then it is rebuilt. With the link cell ....

Hockney, R. W., Goel, S. P. and J. W. Eastwood, "Quiet High-Resolution Computer Models of a Plasma," J. Comp. Phys., 14:148-158, 1974.

....2 that the benchmark application checks all pairs of atoms to determine the pairs within the cutoff radius. In this section we consider an optimization to this application whereby the number of distance calculation is reduced by using techniques such as neighbor lists [16] and the link cell method [8]. The neighborlist technique consists of maintaining a list of nearby atoms for each atom. This list is examined for possible interactions instead of checking all atoms in the system; the list is rebuilt every few time steps. With the link cell method, during each time step the atoms are binned ....

Hockney, R. W., S. P. Goel, and J. W. Eastwood, "Quiet High-Resolution Computer Models of a Plasma," J. Comp. Phys., 14:148--158, 1974.

....precision for force computations. Two of the most time consuming computational kernels in SOTON PAR are movout, which performs geometric hashing, and force, which performs the force and potential evaluations. 2. 1 Geometric Hashing Like SOTON PAR, our shared memory code uses the link cell method [8] to speed up MD force calculations. At each time step, all the atoms are hashed into three dimensional bins or cells of side length at least the cut off distance (r c ) The link cell method is memory efficient, requiring only O(N 3 b ) storage for the 3 D bins, 9 real vectors of length N (x; ....

R. W. Hockney, S. P. Goel, and J. W. Eastwood, "Quiet high-resolution computer models of a plasma", J. Comp. Phys, vol. 14, pp. 148-- 158, 1974.

....processors than atoms. Recall from Section 2 that the original code checks all atoms to determine the interactions to be calculated. In this section we consider an optimized code for which the number of computations is reduced by using techniques such as neighbor lists [18] and link cell method [9]. The neighbor list technique consists of maintaining a list of nearby atoms for each atom. This list is examined for possible interactions instead of checking all atoms in the system; the list is rebuilt every few time steps. With the link cell method, during each time step the atoms are binned ....

Hockney, R. W., S. P. Goel, and J. W. Eastwood, "Quiet High-Resolution Computer Models of a Plasma," J. Comp. Phys., 14:148-158, 1974.

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