Load Balancing and Data Locality in Adaptive Hierarchical N-Body Methods: Barnes-Hut, Fast Multipole, and Radiosity

Singh, Jaswinder Pal; Holt, Chris; Totsuka, Takashi; Gupta, Anoop; Hennessy, John L.

doi:10.1006/jpdc.1995.1077

Cited by 177 publications

(131 citation statements)

References 22 publications

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“…The idea to parallelize the FMM is not new and there are publications that address some basic issues [9,19,20,21,24]. However these publications are mostly related to the development of more coarse-grained parallel algorithms.…”

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confidence: 99%

Fast multipole methods on graphics processors

Gumerov

Duraiswami

2008

Journal of Computational Physics

157

131

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The Fast Multipole Method allows the rapid evaluation of sums of radial basis functions centered at points distributed inside a computational domain at a large number of evaluation points to a specified accuracy . The method scales as O (N ) in both time and memory compared to the direct method with complexity O(N 2 ), which allows the solution of larger problems with given resources. Graphical processing units (GPU) are now increasingly viewed as data parallel compute coprocessors that can provide significant computational performance at low price. We describe acceleration of the FMM using the data parallel GPU architecture.The FMM has a complex hierarchical (adaptive) structure, which is not easily implemented on dataparallel processors. We described strategies for parallelization of all components of the FMM, develop a model to explain the performance of the algorithm on the GPU architecture; and determined optimal settings for the FMM on the GPU, which are different from those on usual CPUs. Some innovations in the FMM algorithm, including the use of modified stencils, real polynomial basis functions for the Laplace kernel, and decompositions of the translation operators, are also described.We obtained accelerations of the Laplace kernel FMM on a single NVIDIA GeForce 8800 GTX GPU in the range of 30-60 compared to a serial CPU FMM implementation. For a problem with a million sources, the summations involved are performed in approximately one second. This performance is equivalent to solving of the same problem at a 43 Teraflop rate if we use straightforward summation.

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mentioning

confidence: 99%

Fast multipole methods on graphics processors

Gumerov

Duraiswami

2008

Journal of Computational Physics

157

131

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“…Permutation RTRTs that SPF can represent include Cuthill-McKee [14], Reverse Cuthill-McKee [36], breadthfirst [2], Sloan [24], recursive coordinate bisection [70], consecutive packing [19], reordering based on graph partitioning [56,26], hybrid techniques based on graph partitioning and another heuristic within the partition [2,64], reordering based on space-filling curves [39], lexicographical grouping or sorting [15,19,24], and hyper-breadth-first [63]. The reordering algorithms that depend on a mapping of data indices to simulation space coordinate data (e.g., recursive coordinate bisection [70] and space-filling curves [39]) will require additional input be provided to the inspector, but this input can be expressed as an abstract relation.…”

Section: Data and Iteration Permutation Reorderingsmentioning

confidence: 99%

“…To overcome these problems, Run-Time Reordering Transformations (RTRTs) have been developed [14,15,56,51,2,19,40,24,28,58,39,26]. Typically, an RTRT is implemented using an inspector and an executor.…”

Section: Introductionmentioning

confidence: 99%

An approach for code generation in the Sparse Polyhedral Framework

et al. 2016

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Applications that manipulate sparse data structures contain memory reference patterns that are unknown at compile time due to indirect accesses such as A [B[i]]. To exploit parallelism and improve locality in such applications, prior work has developed a number of run-time reordering transformations (RTRTs). This paper presents the Sparse Polyhedral Framework (SPF) for specifying RTRTs and compositions thereof and algorithms for automatically generating efficient inspector and executor code to implement such transformations. Experimental results indicate that the performance of automatically generated inspectors and executors competes with the performance of hand-written ones in some cases.

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“…In practice, all the particles to be processed are put in a "queue" and each PE gets, every time, the first particle in the queue and evaluates its acceleration (see Singh et al 1995). The large amount of communications and remote accesses required by such an approach, heavily affects the absolute performances (because this DD is independent of the spatial configuration) making it inconvenient for practical use (see Capuzzo-Dolcetta & Miocchi 1998, 1999.…”

Section: The Performancementioning

confidence: 99%

An efficient parallel tree-code for the simulation of self-gravitating systems

Miocchi

Capuzzo-Dolcetta

2002

A&A

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Abstract. We describe a parallel version of our tree-code for the simulation of self-gravitating systems in Astrophysics. It is based on a dynamic and adaptive method for the domain decomposition, which exploits the hierarchical data arrangement used by the tree-code. It shows low computational costs for the parallelization overhead -less than 4% of the total CPU-time in the tests done -because the domain decomposition is performed "on the fly" during the tree-construction and the portion of the tree that is local to each processor "enriches" itself of remote data only when they are actually needed. The performance of an implementation of the parallel code on a Cray T3E is presented and discussed. They exhibit a very good behaviour of the speedup (=15 with 16 processors and 10 5 particles) and a rather low load unbalancing (<10% using up to 16 processors), achieving a high computation speed in the forces evaluation (>10 4 particles/sec with 8 processors).

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Load Balancing and Data Locality in Adaptive Hierarchical N-Body Methods: Barnes-Hut, Fast Multipole, and Radiosity

Cited by 177 publications

References 22 publications

Fast multipole methods on graphics processors

Fast multipole methods on graphics processors

An approach for code generation in the Sparse Polyhedral Framework

An efficient parallel tree-code for the simulation of self-gravitating systems

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