J. A. Board, Jr., J. W. Causey, J. F. Leathrum, Jr., A. Windemuth, K. Schulten, Accelerated molecular dynamics simulation with the parallel fast multipole algorithm, Chem. Phys. Lett. 198 (1992) 89--94.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....near and far field stages of the FMM, works well on shared memory machines, but less efficiently on distributed memory systems. Nonetheless, these ideas inspired the first parallel FMM for MD simulation of macromolecules, developed and demonstrated by the Duke University group in the early 1990s [5]. A recent, optimized implementation by Dachsel [6] has achieved machine accuracy potential summation for up to 10 charges on an IBM p690 SMP cluster. At first sight, the hierarchical data structure of BH tree codes would seem to rule out parallelism altogether, but it was soon realised that ....

J. A. Board Jr., J. W. Causey, J. F. Leathrum Jr., A. Windemuth, and K. Schulten, Accelerated molecular dynamics simulation with the parallel fast multipole algorithm, Chem. Phys. Lett. 198, 89--94 (1992).

.... is sufficiently far apart is computed by a Taylor (local) expansion utilizing the multi pole expansion of the distant sub cell (local expansion) Then the contributions are passed from parent cells to the children sub cells (downward pass) FMM has been implemented for different MD applications [11, 48, 73] and is especially suited for parallelization [93, 95, 96, 123] However, optimized FMM codes tend to be rather elaborate. More importantly, they do not conserve energy during MD simulations unless enforcing unusual high accuracy, e.g. 12th order multi poles [10, 128] Typically, the ....

John A. Board, Jr., J. W. Causey, James F. Leathrum, Jr., Andreas Windemuth, and Klaus Schulten. Accelerated molecular dynamics simulation 61 with the parallel fast multipole algorithm. Chem. Phys. Lett., 198:89--94, 1992.

....of systems. Hockney and Eastwood [28] discuss applications in plasma physics, device physics, astrophysics and material science. Our code has allowed us to make significant progress in the study of galaxy dynamics [22] and cosmology [23] In addition, we note applications in molecular dynamics [29], computational fluid dynamics [30, 31] and partial differential equations relevant to biology [32] Fast multipole methods have been used to address two dimensional problems in potential flows [33] and electromagnetic scattering [34] Much chemistry is done with small N , and these may not ....

J. A. Board, J. W. Causey, J. F. Leathrum, A. Windemuth, and K. Schulten, "Accelerated molecular dynamics simulation with the parallel fast multipole algorithm," Chem. Phys. Let., vol. 198, p. 89, 1992.

....data. The cost of dynamic schemes is loss of locality, which translates in increased overhead. Load balancing techniques have been extensively applied to N body simulations by using information about data (particles) distribution to guide the static assignment of data to processors [22] 24] 20][6][7] The assignment is recomputed after each time step as data changes over time. Some of these techniques include the orthogonal recursive bisection (ORB) and the Costzones methods [23] 22] Others use a hash function to build the hashed oct tree (HOT) which employs Morton order, a space filling ....

J. A. Board, J. Causey, J. F. Leathrum Jr. and others: "Accelerated Molecular Dynamic Simulations with the Parallel Fast Multipole Algorithm".- in: Chemical Physics Letters, 23-34, (1992)

....of these methods increases with the number of processors and problem size. For example, in N body simulations, load balancing techniques have been extensively applied by using information about data (i.e. particles) distribution to guide the static assignment of data to processors [36] 40] 33][9][10] The assignment is recomputed after each time step, because data changes over time. Some of these techniques use the orthogonal recursive bisection (ORB) or the Costzones methods [41] 35] 36] Some of the other techniques use a hash function to build the hashed oct tree (HOT) which employs ....

J. A. Board, J. Causey, J. F. Leathrum Jr., et al, Accelerated Molecular Dynamic Simulations with the Parallel Fast Multi- pole Algorithm, Chemical Physics Letters 198 (1992) 23--34.

....cells. the lowest level, leaf boxes contain bodies, and at higher levels, they contain the summary effects of the bodies in their rooted subtree. The calculation of forces on each body during a time step is, for the most part, independent. Thus, N body algorithms are amenable to parallel execution [18, 25, 29, 5, 6]; however, parallel implementations of N body simulations pose load balancing problems due to the irregularity of the distribution of bodies and, to a lesser extent, the different processing requirements of bodies in the interior and of those near the boundary of the space [30, 26, 15] The ....

J. A. Board, J. W. Causey, J. F. Leathrum, A. Windemuth and K. Schulten, Accelerated Molecular Dynamic Simulations with the Parallel Fast Multipole Algorithm, Chem. Phys. Let. 198, 1992.

....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 ....

J. A. Board, J. W. Causey, J. F. Leathrum, A. Windemuth, and K. Schulten. Accelerated molecular dynamics simulation with the parallel fast multipole algorithm. Chem. Phys. Let., 198:89, 1992.

....Our new algorithm will draw on techniques from the FMA, but applied novelly to create an online 2 nonparametric estimation algorithm. A brute force online algorithm contains a double 1 The fast multipole algorithm and modifications thereof for a wide variety of physics problems can be found in [2, 3, 5, 6, 8, 9, 12, 16, 17, 21, 23, 25]. 2 An online algorithm is defined as an algorithm operating in a simulated real time environment, where the input dataset grows with each new point seen (or grows in blocks) and recomputes the estimates by adding input points sequentially. z1 z2 z3 zn z Figure 1: Multipole expansion. A ....

J. A. Board, Jr., J. W. Causey, J. F. Leathrum, Jr., A. Windemuth, and K. Schulten. Accelerated molecular dynamics simulation with the parallel fast multipole algorithm. Chemical Physics Letters, 198:89--94, 1992.

....of the O(n 2 ) terms in the last sum in the potential of Table 1 need to be calculated. To make full use of the resulting sparsity (which varies from iteration to iteration) efficient data structures must be maintained; see, e.g. Schreiber et al. 281] More recently, fast multipole expansions [25, 120, 284] and variants [70, 91] of the Ewald method (Ewald [92] were used as an alternative to cut off methods, with a significant increase in quality York et al. 353, 354] An improvement of a divide and conquer method by Appel [8] for fast potential evaluation is discussed in Xue et al. 352] While ....

....potentials. One of the obvious difficulties is that because of the high dimension and the expensive evaluation of the potential, even local optimization is slow. For large molecules, this is the case even when the potential calculations are speeded up using fast multipole expansions [25, 120, 284] or potential cutoffs. The fastest optimization methods, the adopted basis Newton Raphson (ABNR) method and truncated Newton (TN) methods, employed, e.g. in CHARMM [33, 76] combine elements of Newton s method with reduced subspace techniques to reduce storage requirements and 26 A. NEUMAIER ....

J. A. Board, J. W. Causey, T. F. Leathrum Jr., A. Windemuth and K. Schulten, Accelerated molecular dynamics simulation with the parallel fast multipole algorithm, Chem. Phys. Lett. 198 (1992), pp. 89--94.

....evaluating one fixed size multipole expansion. BarnesHut algorithm performs instead a leaf to root tree traversal, for each particle, to compute the effects of the far field interactions. 2.1. 2 Parallel Implementations of the N body Algorithms N body algorithms are amenable to parallel execution [20, 43, 51, 11, 12]. In the Barnes Hut algorithm, experiences with uniprocessor implementations have shown that the time spent building the tree and traversing it to compute the center of mass and accelerations are negligible in comparison with the time spent computing accelerations. Thus, the tree is built from ....

....rather than spherical ones. Schmidt and Lee developed a vectorized version of the algorithm using Fortran for the Cray Y MP [43] 38 Leathrum and Board developed modified versions of the 3 d FMA for several multicomputers, both shared and disjoint address space, achieving good speedups [30, 11, 32]. Their codes are applicable to the N body problems in molecular dynamics and astrophysics. 2.3.1 Available Parallelism The FMA has several opportunities for exploiting parallelism. The data structure is a tree of multidimensional arrays of cells with regular communication patterns. The algorithm ....

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J.A. Board, J.W. Causey, J.F. Leathrum, A. Windemuth, and K. Schulten. Accelerated Molecular Dynamic Simulations with the Parallel Fast Multipole Algorithm. Chem. Phys. Let., 198, 1992.

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J. A. Board, Jr., J. W. Causey, J. F. Leathrum, Jr., A. Windemuth, K. Schulten, Accelerated molecular dynamics simulation with the parallel fast multipole algorithm, Chem. Phys. Lett. 198 (1992) 89--94.

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J. A. Board, J. W. Causey, J. F. Leathrum, A. Windemuth and K. Schulten, Accelerated Molecular Dynamic Simulations with the Parallel Fast Multipole Algorithm, Chem. Phys. Let. 198, 1992.

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J. A. Board, J. W. Causey, J. F. Leathrum, A. Windemuth, K. Schulten: "Accelerated molecular dynamics simulation with the parallel fast multipole algorithm". Chemical Physics Letters (2 Oct. 1992) vol. 198, no. 1--2, pp. 89--94

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