A Performance Comparison of Tree Data Structures for N-Body Simulation

Waltz, Jacob; Page, Gary L.; Milder, Seth D.; Wallin, John F.; Antunes, A.

doi:10.1006/jcph.2001.6943

Cited by 18 publications

(23 citation statements)

References 15 publications

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“…He concludes that a spatially balanced 6 k − d tree will provide performance superior to that of a BH tree. In contrast, Waltz et al (2002) compare a BH tree to a k − d tree in direct code to code tests but make the opposite conclusion that BH trees ordinarily provide superior performance to k − d trees.…”

Section: What Kind Of Tree Is the Best?mentioning

confidence: 98%

“…However, neither the Anderson (1999) nor the Waltz et al (2002) studies discuss the relative costs of traversal and evaluation in any detail and further, it is not clear that their results are generalizable. For example, few codes in common use implement the comparatively costly "priority queue" node opening strategy of Salmon & Warren (1994), as Waltz et al (2002) do. Also, Waltz et al (2002) make their comparisons to density balanced k − d trees, while 6 In Anderson's nomenclature, density balancing is defined by the criterion described in the last section, that nodes at each level contain equal numbers of particles.…”

Section: What Kind Of Tree Is the Best?mentioning

confidence: 99%

“…He finds that k − d tree traversals result in shorter lists, meaning that k − d trees are preferable. On the other hand, Waltz et al (2002) use the average number of nodes touched during a traversal as their primary metric. They find that several times more nodes are opened in binary trees than in oct-trees, meaning that oct-trees are preferable.…”

Section: What Kind Of Tree Is the Best?mentioning

confidence: 99%

“…For example, few codes in common use implement the comparatively costly "priority queue" node opening strategy of Salmon & Warren (1994), as Waltz et al (2002) do. Also, Waltz et al (2002) make their comparisons to density balanced k − d trees, while 6 In Anderson's nomenclature, density balancing is defined by the criterion described in the last section, that nodes at each level contain equal numbers of particles. In contrast, nodes in a spatially balanced k − d tree may have unequal particle counts, and instead divide space equally at each level, as is done in oct-trees.…”

Section: What Kind Of Tree Is the Best?mentioning

confidence: 99%

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Vine—a Numerical Code for Simulating Astrophysical Systems Using Particles. Ii. Implementation and Performance Characteristics

Nelson

Wetzstein

Naab

2009

ApJS

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We continue our presentation of VINE. In this paper, we begin with a description of relevant architectural properties of the serial and shared memory parallel computers on which VINE is intended to run, and describe their influences on the design of the code itself. We continue with a detailed description of a number of optimizations made to the layout of the particle data in memory and to our implementation of a binary tree used to access that data for use in gravitational force calculations and searches for smoothed particle hydrodynamics (SPH) neighbor particles. We describe the modifications to the code necessary to obtain forces efficiently from special purpose "GRAPE" hardware, the interfaces required to allow transparent substitution of those forces in the code instead of those obtained from the tree, and the modifications necessary to use both tree and GRAPE together as a fused GRAPE/ tree combination. We conclude with an extensive series of performance tests, which demonstrate that the code can be run efficiently and without modification in serial on small workstations or in parallel using the OpenMP compiler directives on large-scale, shared memory parallel machines. We analyze the effects of the code optimizations and estimate that they improve its overall performance by more than an order of magnitude over that obtained by many other tree codes. Scaled parallel performance of the gravity and SPH calculations, together the most costly components of most simulations, is nearly linear up to at least 120 processors on moderate sized test problems using the Origin 3000 architecture, and to the maximum machine sizes available to us on several other architectures. At similar accuracy, performance of VINE, used in GRAPE-tree mode, is approximately a factor 2 slower than that of VINE, used in host-only mode. Further optimizations of the GRAPE/host communications could improve the speed by as much as a factor of 3, but have not yet been implemented in VINE. Finally, we find that although parallel performance on small problems may reach a plateau beyond which more processors bring no additional speedup, performance never decreases, a factor important for running large simulations on many processors with individual time steps, where only a small fraction of the total particles require updates at any given moment.

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Section: What Kind Of Tree Is the Best?mentioning

confidence: 98%

Section: What Kind Of Tree Is the Best?mentioning

confidence: 99%

Section: What Kind Of Tree Is the Best?mentioning

confidence: 99%

Section: What Kind Of Tree Is the Best?mentioning

confidence: 99%

See 2 more Smart Citations

Vine—a Numerical Code for Simulating Astrophysical Systems Using Particles. Ii. Implementation and Performance Characteristics

Nelson

Wetzstein

Naab

2009

ApJS

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“…The first category is tree-like method, such as hierarchical tree [23], binary tree and Barnes-Hut tree [24] and the tree-code [25]. In the tree-code a cube of side l enclosing all particles is subdivided into eight cubic boxes with each of them further subdivided into eight children boxes.…”

Section: Introductionmentioning

confidence: 99%

Search algorithm, and simulation of elastodynamic crack propagation by modified smoothed particle hydrodynamics (MSPH) method

Batra

Zhang

2006

Comput Mech

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We first present a nonuniform box search algorithm with length of each side of the square box dependent on the local smoothing length, and show that it can save up to 70% CPU time as compared to the uniform box search algorithm. This is especially relevant for transient problems in which, if we enlarge the sides of boxes, we can apply the search algorithm fewer times during the solution process, and improve the computational efficiency of a numerical scheme. We illustrate the application of the search algorithm and the modified smoothed particle hydrodynamics (MSPH) method by studying the propagation of cracks in elastostatic and elastodynamic problems. The dynamic stress intensity factor computed with the MSPH method either from the stress field near the crack tip or from the J-integral agrees very well with that computed by using the finite element method. Three problems are analyzed. One of these involves a plate with a centrally located crack, and the other with three cracks on plates's horizontal centroidal axis. In each case the plate edges parallel to the crack are loaded in a direction perpendicular to the crack surface. It is found that, at low strain rates, the presence of other cracks will delay the propagation of the central crack. However, at high strain rates, the speed of propagation of the central crack is unaffected by the presence of the other two cracks. In the third problem dealing with the simulation of crack propagation in a functionally graded plate, the crack speed is found to be close to the experimental one.

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A Linearly Fourth Order Multirate Runge–Kutta Method with Error Control

Fok

2015

J Sci Comput

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A Performance Comparison of Tree Data Structures for N-Body Simulation

Cited by 18 publications

References 15 publications

Vine—a Numerical Code for Simulating Astrophysical Systems Using Particles. Ii. Implementation and Performance Characteristics

Vine—a Numerical Code for Simulating Astrophysical Systems Using Particles. Ii. Implementation and Performance Characteristics

Search algorithm, and simulation of elastodynamic crack propagation by modified smoothed particle hydrodynamics (MSPH) method

A Linearly Fourth Order Multirate Runge–Kutta Method with Error Control

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