Paul N. Swarztrauber

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This paper describes the \fractional Fourier transform", which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e 2 , the fractional Fourier transform is based on fractional roots of unity e 2 i , where is arbitrary.(More)
Several multiprocessor FFTs are developed in this paper for both vector multiprocessors with shared memory and the hypercube. Two FFTs for vector multiprocessors are given that compute an ordered transform and have a stride of one except for a single "link" step. Since multiple FFTs provide additional options for both vectorization and distribution we show(More)
The purpose of this paper is to describe technical note, NCAR TN/IA-109, which is intended to provide scientists with a package of computer programs which make use of current methods for solving elliptic partial differential equations. Computer models of geophysical processes often require the numerical solution of elliptic partial differential equations.(More)
The adaptation of the Cooley-Tukey. the Pease and the Stockham FFT's to vector computers is discussed. Each of these algorithms computes the same result namely, the discrete Fourier transform. They differ only in the way that intermediate computations are stored. Yet it is this difference that makes one or the other more appropriate depending on the(More)
Computer models of geophysical processes often require the numerical solution of elliptic partial differential equations. This is particularly true for models that make use of stream functions, velocity potentials, or vorticity equations and for models that compute the pressure of an incompressible fluid. The numerical solution of elliptic equations can be(More)
The fast Fourier transform (FFT) is often used to compute numerical approximations to continuous Fourier and Laplace transforms. However, a straightforward application of the FFT to these problems often requires a large FFT to be performed, even though most of the input data to this FFT may be zero and only a small fraction of the output data may be of(More)
We examine design alternatives for ordered FFT algorithms on massively parallel hypercube multiprocessors such as the Connection Machine. Particular emphasis is placed on reducing communication which is known to dominate the overall computing time. To this end we combine the order and computational phases of the FFT and also use sequence to processor maps(More)
The purpose of this paper is to describe technical note, NCAR TN/IA-109, which is intended to provide scientists with a package of computer programs which make use of current methods for solving elliptic partial differential equations. Computer models of geophysical processes often require the numerical solution of elliptic partial differential equations.(More)