Parallel implementation and scalability analysis of 3D Fast Fourier Transform using 2D domain decomposition

“…Ayala's 2D Domain Decomposition Ayala and Wang [11] built upon the work of Dmitruk et al As with the other libraries, a 2D Pencil Decomposition is used. Due to the target application of Direct Numerical Simulation, the last transpose is not necessary in Ayala's method.…”

Section: D Domain Decomposition: "Slabs"mentioning

confidence: 99%

“…For example, a transpose along the x and y axes will only require communication between processors in the same xy plane to communicate. Equation 3 presents a performance model taken from Ayala and Wang's paper [11].…”

Section: D Domain Decomposition: "Slabs"mentioning

confidence: 99%

“…These previous approaches [8][9][10][11] have resulted in very detailed performance models that include many factors such as computation time, communication time, the presence of overlapping or pipelining, the location of the memory and so on.…”

Section: Introductionmentioning

confidence: 99%

“…The difficulties of building performance models are so great that when one is correctly found it is published in a recognized venue (e.g. Dimitruk published his model in the Parallel Computing Journal [8] and Ayala's model [11] is currently under review in the same journal).…”

Section: Introductionmentioning

confidence: 99%

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Abstract. This paper presents a comprehensive story of the development of simpler performance models for distributed implementations of the Fast Fourier Transform in 3 Dimensions (FFT3D). We start by providing an overview of several implementations and their performance models. Then, we present arguments to support the use of a simple power function instead of the full performance models proposed by other publications. We argue that our model can be obtained for a particular problem size with minimal experimentation while other models require significant tuning to determine their constants. Our advocacy for simpler performance models is inspired by the difficulties found when estimating the performance of FFT3D programs. Correctly estimating how well large-scale programs (such as FFT3D) will work is one of the most challenging problems faced by scientists. The significant effort devoted to this problem has resulted in the appearance of numerous works on performance modeling. The results produced by an exhaustive performance modeling study may predict the performance of a program with a reasonably good accuracy. However, those studies may become unusable because their aim for accuracy can make them so difficult and cumbersome to use that direct experimentation with the program may be preferable, defeating their original purpose. We propose an alternative approach in this paper that does not require a full, accurate, performance model. Our approach mitigates the problem of existing performance models, each one of the parameters and constants in the model has to be carefully measured and tuned, a process that is intrinsically harder than direct experimentation with the program at hand. Instead, we were able to simplify our approach by (1) building performance models that target particular applications in their normal operating conditions and (2) using simpler models that still produce good approximations for the particular case of a program's normal operating environment. We have conducted experiments using the Bluefire Supercomputer at the National Center for Atmospheric Research (NCAR), showing that our simplified model can predict the performance of a particular implementation with a high degree of accuracy and very little effort when the program is used in its intended operating range. Finally, although our performance model does not cover extreme cases, we show that its simple approximation under the normal operating conditions of FFT3D is able to provide solid, useful approximations.

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The transplantation technology of communication intensive applications on heterogeneous clusters

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Compared with traditional clusters, heterogeneous clusters cherish the high performance to price ratio. However, compared with the rapid development of hardware technology, the current software technology is still lagging behind. This article introduces a parallel programming model to describe the multidimensional structure, arrangement, and communication modes of the data, threads, and fast Fourier transform. This model provides a new mechanism for transplantation between different types of heterogeneous systems. Using direct methods of turbulence simulation as an example, this article discusses the new software technologies of the parallel software theory, methods of program design, algorithm design, and system software support and provides experience for application transplantation on these heterogeneous systems.

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Parallel implementation and scalability analysis of 3D Fast Fourier Transform using 2D domain decomposition

Cited by 55 publications

References 23 publications

Non-Uniform FFT and Its Applications in Particle Simulations

Non-Uniform FFT and Its Applications in Particle Simulations

Demystifying Performance Predictions of Distributed FFT3D Implementations

The transplantation technology of communication intensive applications on heterogeneous clusters

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