Salmon J.J., Warren M.S., Winckelmans G.S., Fast Parallel Tree Codes For Gravitational And Fluid Dynamical N-Body Problems, lnt J Supercomputing Apps. 8: (2), pp. 129-142, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Grid communication costs. The AppLeS project has used similar calculations to determine how many and which available compute or data server nodes should be assigned to a simple adaptive iterative Jacobi application [3] a gene sequence comparison code [24] a magnetohydrodynamics application [22], an adaptive parallel tomography image reconstruction application [23] and adaptive data server selection in the SARA application [25] For each of these applications, a linear optimization model is formulated to compute the work assigned to each node per candidate system configuration and ....

Salmon J.J., Warren M.S., Winckelmans G.S., Fast Parallel Tree Codes For Gravitational And Fluid Dynamical N-Body Problems, lnt J Supercomputing Apps. 8: (2), pp. 129-142, 1994.

....2. SPACE FILLING CURVES Space filling curves provide an inexpensive way to map an interval to a three dimensional domain. In the last decade, these curves have found many applications, including multidimensional data mining, the solution of N body problems and parallel domain decomposition [7,3,5,8]. Two common space filling curves (henceforth SFC) are the Peano Hilbert and Morton orderings. Given our use of a Cartesian, multilevel mesh, either of these orderings can be easily generated, providing a linear ordering for each cell in the mesh. There are natural extensions for meshes with ....

J.K. Salmon and M.S. Warren and G.S. Winckelmans. Fast parallel tree codes for gravitational and fluid dynamical N-body problems. Intl. J. Supercomp. Appl. 8(2), 1994.

....grids is often based on a linear representation of the grid hierarchy in the form of a spacefilling curve. Several researchers have demonstrated the successful application of techniques based on space filling curves to N body simulations, graph partitioning, and other graph related problems [1,9,14,17,20 22,24,27,28]. These curves are available in several forms, with the ultimate choice depending on the actual application for which it is used. Figure 1 shows the two most popular space filling curves. Figure 1. Peano Hilbert (left) and Morton Z (right) space filling curves for a 8 Theta 8 structured mesh ....

J. Salmon, M. S. Warren and G. S. Winckelmans, `Fast parallel tree codes for gravitational and fluid dynamical N-body problems', Intl. J. of Supercomputer Appl., 8, (2), 129--142 (1994).

....is to avoid multiple requests of data from the same node by aggregating all such requests into a single network request followed by local sharing of data. This technique is used, for instance, in the gather scatter routines of the CMSSL, and have also been used by Liu [21] and Salmon et. al [28]. In many design and analysis problems for which MPPs are used, a great deal is known about data reference patterns. For arrays and other easily described data structures this global knowledge is exceedingly valuable, and the routing and scheduling of data can be made optimally for many common ....

John K. Salmon, Michael S. Warren, and Gregoire S. Winckelmans. Fast parallel tree codes for gravitational and fluid dynamical N--body problems. Int. J. of Supercomputer Applications and High Performance Computing, 8(2):129--142, Summer 1994.

....levels of the tree. In order to use the multipole expansions of the nodes, they must be precomputed. The expansion coefficients for a node can be recursively calculated from those of children nodes. The calculation cost of this part is O(N) For details of implementation, see [13] Salmon et al. [15] describes the implementation of the tree algorithm on distributed memory parallel computers. 2.2 Fast Multipole Method In the tree algorithm, the particles which generate the gravitational potential and the particles which feel the potential are not symmetric. The particles which generate ....

J. K. Salmon, G. S. Winckelmans, and M. S. Warren, Fast parallel treecodes for gravitational and fluid dynamical N-body problems. Intl. J. Supercomputer Appl. 8, 129 (1994).

....is, in turn used, in several applications 7 , is under development by John K. Salmon 8 of Caltech, Michael S. Warren 9 of Los Alamos, and David J. Edelsohn 10 of Syracuse University. The code itself and it s original application in gravitational N body simulations has been described in (Salmon, Winckelmans, and Warren 1994; Warren and Salmon 1993; Warren and Salmon 1994) 4.1.1 Details The application is currently written to the researchers own set of message passing primitives, e.g. asynchronous send, asynchronous receive, exchange, etc) These primitives are by design extremely simple. They 7 A description of ....

....John K. Salmon 8 of Caltech, Michael S. Warren 9 of Los Alamos, and David J. Edelsohn 10 of Syracuse University. The code itself and it s original application in gravitational N body simulations has been described in (Salmon, Winckelmans, and Warren 1994; Warren and Salmon 1993; Warren and Salmon 1994). 4.1.1 Details The application is currently written to the researchers own set of message passing primitives, e.g. asynchronous send, asynchronous receive, exchange, etc) These primitives are by design extremely simple. They 7 A description of an application solving potential flow problems ....

Salmon, J. K., G. S. Winckelmans, and M. S. Warren (1994). Fast parallel treecodes for gravitational and fluid dynamical N-body problems. J. Supercomputer Appl. 8. (to appear) available as ftp/nbody/ijsa.ps.Z@sampson.ccsf.caltech.edu.

....mentioned above have been developed. Salmon [27] implemented the Barnes Hut algorithm on the NCUBE and Intel iPSC, Warren and Salmon [34] reported experiments on the 512 node Intel Touchstone Delta, and later developed hashed implementations of a global tree structure which they report in [35, 18]. They have used their codes for astrophysical simulations and also for vortex dynamics. This paper builds on our CM 5 implementation [25] of the Barnes Hut algorithm for astrophysical simulations and contrasts our approach and conclusions with the aforementioned efforts. This abstract is ....

....3 g(jx Gamma p j) 2) where the filament ordering has to be considered in the computation of the central difference Delta p Delta p = 1 2 ( p 1 Gamma p Gamma1 ) 3) This is a characteristic of the filament approach in 3D vortex methods. In contrast with the vortex arrow approach [18, 23], updating the strength of the vortex elements in the filament method does not require the evaluation of the velocity gradient, which involves the computation of another integral over all of the particles. Also, filaments with form of closed curves, satisfy the divergence free condition of the ....

[Article contains additional citation context not shown here]

M. Warren J. Salmon and G. Winckelmans. Fast parallel tree codes for gravitational and fluid dynamical N-body problems. Intl. J. Supercomputer Applications, 8.2, 1994.

....efficient load balancing strategies for the enormous amount of data. The particle move in space due to the acceleration imposed by the interaction forces. This means, that a re balancing or a dynamic load balancing is needed for parallel computing, which can be done by space filling curves [31, 28, 22]. A slightly different situation can be found in adaptive discretizations of partial differential equations. Now a grid consisting of n nodes and elements or volumes has to be distributed to a parallel computer. The nodes and elements can be found at arbitrary positions (completely unstructured ....

J. K. Salmon, M. S. Warren, and G. Winckelmans, Fast parallel tree codes for gravitational and fluid dynamical n-body problems, International Journal of Supercomputer Applications, 8.

....is the core radius . The ordering of the grid points in the filaments is only important when computing the differentials d Delta j = 1 2 ( j 1 Gamma j Gamma1 ) 3) This is a characteristic of the filament approach in 3D vortex methods. In contrast with the vortex arrow algorithm [15, 22], updating the strength of the vortex elements in the filament method does not require the evaluation of the velocity gradient, which involves the computation of an additional integral over all of the particles. Also, filaments with form of closed curves, satisfy the divergence free condition of ....

....1, 1996, pp. 197 211 V.M. Fernandez et al. Filament Surgery and Temporal Grid Adaptivity Extensions . 200 where b = max j p Gamma 0 j is the size of the cluster and d = jx Gamma 0 j is the distance to the cluster. More precise estimates are also available by Salmon and Warren [22] and more recently by Winckelmans et al. 25] for the vortex dynamics problem. To reduce the computational complexity in the sums in Eq. 10, we use [6] the hierarchical method by Barnes and Hut [4] for gravitational fields. To organize a hierarchy of clusters, we first compute an oct tree ....

Salmon, J.K., Warren, M.S. and Winckelmans, G.S., "Fast Parallel Tree Codes for Gravitational and Fluid Dynamical N-Body Problems," Int'l. Supercomputer Appl., 8.2, 1994.

....assigned to different processors. Each processor will run a simulation with the complete set of channels and the computation of noise will require that all processors cooperate exchanging transmitter power values. Fortunately, there has been extensive research on parallelization of N body methods [34, 43, 66, 70, 62, 61, 69] and we expect to draw from this pool of knowledge, if necessary. Our first step towards a parallel implementation will be the development of a sequential simulator. This program should be used as a basis of comparison for performance analysis of its parallel counterpart (speedup) and also as an ....

John K. Salmon, Gr'egoire S. Winckelmans, and Michael S. Warren. Fast parallel treecodes for gravitational and fluid dynamical N-body problems. Intl. J. Supercomputer Appl., 8, 1994. (to appear).

....comparable to the time integration error and discretization error. Using a generic design, we have implemented a variety of modules to solve problems in galactic dynamics [8] and cosmology [9] as well as fluiddynamical problems using smoothed particle hydrodynamics [10] a vortex particle method [11] and boundary integral methods [12] 3.1 The Hashed Oct Tree Library Our parallel N body code has been evolving for over a decade on many platforms. We began with an Intel ipsc 860, Ncube machines, and the Caltech JPL Mark III [13, 8] This original version of the code was abandoned after it won ....

J. K. Salmon, M. S. Warren, and G. S. Winckelmans, "Fast parallel treecodes for gravitational and fluid dynamical N-body problems," Intl. J. Supercomputer Appl., vol. 8, pp. 129--142, 1994.

....of a galaxy cluster. 20 cross product. Just as with the gravitational case, it is possible to approximate the summation with an expression involving the multipole moments of the vorticity distribution. A more detailed description of the application of our treecode to this problem may be found in [25]. We carried out a series of timings for a problem representing the evolution of an initially spherical vorticity distribution. Figure 10 shows the initial positions of vortex particles representing a surface vorticity: 3 8 sin( e : 34) 1 0 1 1 0 1 y 1 0 1 3 2 1 0 y ....

J. K. Salmon, M. S. Warren, and G. S. Winckelmans, "Fast parallel treecodes for gravitational and fluid dynamical N-body problems," Intl. J. Supercomputer Appl., vol. 8, pp. 129--142, 1994.

....tasks are relegated to a few user defined functions. Using this generic design we have implemented a variety of modules to solve problems in galactic dynamics [6] and cosmology [13] as well as fluid dynamical problems using smoothed particle hydrodynamics [10] a vortex particle method [5] and a panel method [11, 12] Further applications in the areas of molecular dynamics, chemistry, electromagnetic scattering and generation of correlated and constrained random fields are under development. Treecodes present interesting problems for parallelization because they are highly ....

J. K. Salmon, M. S. Warren, and G. S. Winckelmans, Fast parallel treecodes for gravitational and fluid dynamical N-body problems, Intl. J. Supercomputer Appl., 8 (1994), pp. 129--142.

....of the true divergence free vorticity field in long time computations. 1 Introduction A fast oct tree code, originally developed for three dimensional N body gravitational problems [26 28, 32 34] has been modified into (1) a fast N vortex code for viscous and inviscid vortex flow computations [29] using the regularized vortex particle method ( vortex element method, VEM) 19, 20, 25, 36 40] combined with the particle strength exchange scheme for viscous diffusion [4, 21] and (2) a fast N panel code for solving boundary integral equations in potential flow aerodynamics [41] using the ....

....) 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 desired levels of accuracy. In our implementations of the VEM (with smoothing of compact support) 35, 42] and of the BEM [29, 41, 42], multipole expansions of order p = 2 are used (i.e. monopole dipole quadrupole) Particular attention is given to ensuring that the error introduced by the use of multipole expansion approximations remains below a desired level for all evaluations. A runtime parameter, e tol , determines the ....

[Article contains additional citation context not shown here]

Salmon, J.K., Warren, M.S. and Winckelmans, G.S., "Fast Parallel Tree Codes for Gravitational and Fluid Dynamical N-Body Problems," Int. J. Supercomputer Appl., 8 (2), pp. 129--142, 1994.

No context found.

J. K. Salmon, M. S. Warren, and G. S. Winckelmans, "Fast Parallel Treecodes for Gravitational and Fluid Dynamical N-Body Problems," Intl. J. Supercomputer Appl., 8, 29-142, 1994.

....to the time integration error and discretization error. Using a generic design, we have implemented a variety of modules to solve problems in galactic dynamics [26] and cosmology [27] as well as fluid dynamical problems using smoothed particle hydrodynamics [28] a vortex particle method [29] and boundary integral methods [30] Solving each of these problems with different varieties of special purpose hardware, such as GRAPE [31] is clearly intractable. The Hashed Oct Tree Library Our parallel N body code has been evolving for several years, and on many platforms. We began with an ....

J. K. Salmon, M. S. Warren, and G. S. Winckelmans. Fast parallel treecodes for gravitational and fluid dynamical N-body problems. Intl. J. Supercomputer Appl., 8:129-142, 1994. (PostScript)

No context found.

J.. K. Salmon, M. S. Warren, and G. S. Winckelmans. Fast parallel tree codes for gravitational and fluid dynamical N-body problems. Int. J. Supercomputer Appl., 8(2):129--142, 1994.

No context found.

J.. K. Salmon, M. S. Warren, and G. S. Winckelmans. Fast parallel tree codes for gravitational and fluid dynamical N-body problems. Int. J. Supercomputer Appl., 8(2):129--142, 1994.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC