Distributing Fast Fourier Transform Algorithms for Grid Computing

An abstract machine based approach to distributing the Fast Fourier Transform (FFT) on a queue of N=2 L complex values across a network of N/2 virtual machines is presented. The strategy involves three stages, in general, (a) constructing the FFT virtual machine (FFT_VM) as a set of communicating virtual machine compute nodes, (b) instantiation of the FFT_VM on a physical “grid” of networked computers, and (c) execution of the FFT data queue. The fundamental computational unit of the FFT_VM is a virtual machine called FFT_VM_Butterfly which reflects a specialised computation and communication unit referred to as the Butterfly algorithm, a core component of the FFT algorithms typified as Cooley-Tukey. This approach affords opportunity to prove the correctness of the software design in various contexts of application based only on rigorous logical analysis and also demonstrates flexibility and adaptability to metacomputing design and construction and use of dynamic execution environments such as computational grids.

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