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We show two algorithms for computing multidimensional Fast Fourier Transforms (FFTs) on a multiprocessor system with distributed memory when problem sizes are so large that the data do not fit in the memory of the entire system. Instead, data reside on a parallel disk system and are brought into memory in sections. We use the Parallel Disk Model for implementation and analysis.
The first method is a straightforward out-of-core variant of a well-known method for in-core, multidimensional FFTs. It performs 1-dimensional FFT computations on each dimension in turn. This method is easy to generalize to any number of dimensions, and it also readily permits the individual dimensions to be of any sizes that are integer powers of~2. The key step is an out-of-core transpose operation that places the data along each dimension into contiguous positions on the parallel disk system so that the data for the 1-dimensional FFTs are contiguous.
The second method is an adaptation of another well-known method for in-core, multidimensional FFTs. This method computes all dimensions simultaneously. It is more difficult to generalize to arbitrary radices and number of dimensions in this method than in the first method. Our present implementation is therefore limited to two dimensions of equal size, that are again integer powers of~2.
We present I/O complexity analyses for both methods as well as empirical results for a DEC~2100 server and an SGI Origin~2000, each of which has a parallel disk system. Our results indicate that the methods are comparable in speed in two-dimensions.
Undergraduate Honors Thesis. Advisor: Tom Cormen.
Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]
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Lauren M. Baptist, "Two Algorithms for Performing Multidimensional, Multiprocessor, Out-of-Core FFTs." Dartmouth Computer Science Technical Report PCS-TR99-350, June 1999.
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