Efficient Dealiased Convolutions without Padding

Algorithms are developed for calculating dealiased linear convolution sums without the expense of conventional zero-padding or phase-shift techniques. For one-dimensional in-place convolutions, the memory requirements are identical with the zero-padding technique, with the important distinction that...

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Bibliographic Details
Published inSIAM journal on scientific computing Vol. 33; no. 1; pp. 386 - 406
Main Authors Bowman, John C., Roberts, Malcolm
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Subjects
Algorithms
Arrays
Computation
Computer programs
Convolution
Decoupling
Exact sciences and technology
Fourier analysis
Fourier transforms
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Studies
zero padding
65R99
65T50
implicit padding
Fast Fourier transformation
Fourier analysis
Algorithm
in-place transform
Implementation
fast Fourier transform
dealiasing
2/3 padding rule
Computation time
Numerical analysis
Convolution
ternary convolution
One-dimensional calculations
Scientific computation
Pseudospectral method
Software
bit reversal
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ISSN1064-8275
1095-7197
DOI10.1137/100787933

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Summary:Algorithms are developed for calculating dealiased linear convolution sums without the expense of conventional zero-padding or phase-shift techniques. For one-dimensional in-place convolutions, the memory requirements are identical with the zero-padding technique, with the important distinction that the additional work memory need not be contiguous with the input data. This decoupling of data and work arrays dramatically reduces the memory and computation time required to evaluate higher-dimensional in-place convolutions. The technique also allows one to dealias the higher-order convolutions that arise from Fourier transforming cubic and higher powers. Implicitly dealiased convolutions can be built on top of state-of-the-art fast Fourier transform libraries: vectorized multidimensional implementations for the complex and centered Hermitian (pseudospectral) cases have been implemented in the open-source software FFTW++. [PUBLICATION ABSTRACT]
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ISSN:1064-8275
1095-7197
DOI:10.1137/100787933