Parallelizing the spectral transform method

Worley, Patrick H; Drake, John B.

doi:10.1002/cpe.4330040402

Cited by 16 publications

(5 citation statements)

References 21 publications

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“…Figure 2.2 depicts the core computational butterfly dataflow associated with a Cooley-Tukey radix-2 FFT used in many models [9], [10], [32]. In Figure 2.2, data flow is from left to right, "•" indicates a data value, "⊕" indicates addition, and ">" indicates multiplication.…”

Section: Fourier Transform As Indicated Inmentioning

confidence: 99%

“…Published performance results for the spectral transform focus on various climate and weather models on different architectures [1], [4], [5], [6], [7], [8], [9], [11], [12], [13], [16], [17], [19], [20], [21], [23], [26], [27], [28], [31], [32]. Such literature data are generally unsuitable for rigorous model performance comparisons because of the dissimilar factors from which the data were generated.…”

Section: Roy W Melton and Linda M Willsmentioning

confidence: 99%

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An Analysis of the Spectral Transform Operations in Climate and Weather Models

Melton¹,

Wills²

2008

SIAM J. Sci. Comput.

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The spectral transform method used in climate and weather models is known to be computationally intensive. Typically accounting for more than 90% of the execution time of a serial model, it is poised to benefit from computational parallelism. Since dimensionally global transforms impact parallel performance, it is important to establish the realizable parallel efficiency of the spectral transform. To this end, this paper quantitatively characterizes the parallel characteristics of the spectral transform within an atmospheric modeling context. It comprehensively characterizes and catalogs a baseline of operations required for the spectral transform. While previous investigations of the spectral transform method have offered highly idealized analyses that are abstract and simplified in terms of orders of computational magnitude, this research provides a detailed model of the computational complexity of the spectral transform, validated by empirical results. From this validated quantitative analysis, an operational closed-form expression characterizes spectral transform performance in terms of general processor parameters and atmospheric data dimensions. These generalized statements of the computational requirements for the spectral transform can serve as a basis for exploiting parallelism. Introduction.Given initial conditions that represent meteorological field values of the atmosphere at some point in time, climate and weather models predict future climate and weather based on numerical solutions of a set of time-dependent partial differential equations [24]. These models typically employ one of two solution methods: grid-point or spectral [25]. While most local and regional models are grid-point, most global models are spectral [3].The computational demands of current models tax even the most powerful computers available. As models evolve to reflect a more comprehensive understanding of atmospheric processes, these models require even more computations. The high costs of both model development and computing resources drive concerns about the feasibility of a desired solution for a given model on a particular hardware platform. The efficient, scalable mapping of climate and weather models to high-performance, massively parallel multiprocessor systems depends on characterizing the degree of parallelism inherent in the models. Even though data parallel computation is intrinsic to the modeled atmospheric processes, parallel characteristics (e.g., limitations, interactions, etc.) of the facilitating spectral transform have not been understood. This paper takes a first step toward addressing these concerns for spectral models by quantifying the number and types of operations required for the spectral transform.

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Section: Fourier Transform As Indicated Inmentioning

confidence: 99%

Section: Roy W Melton and Linda M Willsmentioning

confidence: 99%

An Analysis of the Spectral Transform Operations in Climate and Weather Models

Melton¹,

Wills²

2008

SIAM J. Sci. Comput.

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“…We and colleagues at Argonne and Oak Ridge national laboratories have developed a parallel . transform approach based on parallel FFT and quadrature algorithms [14,32,35]; this work has been incorporated in a parallel implementation [7,8] of the National Center for Atmospheric Research (NCAR)'s Community Climate Model (CCM2) [19]. Other researchers have examined a transpose approach, in which communication requirements are encapsulated in a matrix transpose operation.…”

Section: Introductionmentioning

confidence: 99%

Parallel Algorithms for the Spectral Transform Method

Foster¹,

Worley²

1997

SIAM J. Sci. Comput.

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The spectral transform method is a standard numerical technique for solving partial differentiM equations on a sphere and is widely used in atmospheric circulation models. Recent research has identified several promising algorithms for implementing this method on massively parallel computers; however, no detailed comparison of the different algorithms has previously been attempted. In this paper, we describe these different parallel algorithms and report on computational experiments that we have conducted to evaluate their efficiency on parallel computers. The experiments used a testbed code that solves the nonLinear shallow water equations on a sphere; considerable care was taken to ensure that the experiments provide a [air comparison of the different algorithms and that the " results are relevant to global models. We focus on hypercube-and mesh-connected multicomputers with cut-through routing, such as the Intel iPSC/860, DELTA, and Paragon, and the nCUBE/2, but also indicate how the results extend to other parallel computer architectures. The results of this study are relevant not only to the spectral transform method but also to multidimensional FFTs and other parallel transforms.

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“…J. Hack at NCAR. The 324 parallel version was implemented as part of the Department of Energy CHAMMP initiative [2], and has been described in detail in [14] and [17].…”

Section: Sswmsbmentioning

confidence: 99%

“…The parallel implementation of SSWMSB is based on a uniform data decomposition, and we would expect a phase analysis to be a reasonable approach. Additionally, this code goes to great lengths to maximize the overlap of communication and computation [17], and thus would appear to require a phase analysis or something at least as sophisticated.…”

Section: Introductionmentioning

confidence: 99%

Phase modeling of a parallel scientific code

Worley

Proceedings Scalable High Performance Computing Conference SHPCC-92.

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This paper describes a performance model f o r a parallel program that solves the nonlinear shallow water equations using the spectral tranform method. The model is generated via a phase analysis, and consists of a sequence of simple models whose sum describes the performance of the entire code. This use of a sequence of simple models increases the range of validity of the model as the problem and machines parameters scale.

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Parallelizing the spectral transform method

Cited by 16 publications

References 21 publications

An Analysis of the Spectral Transform Operations in Climate and Weather Models

An Analysis of the Spectral Transform Operations in Climate and Weather Models

Parallel Algorithms for the Spectral Transform Method

Phase modeling of a parallel scientific code

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