A Fast Algorithm for the Convolution of Functions with Compact Support Using Fourier Extensions

Journal Article · Thu Dec 21 00:00:00 EST 2017 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/17M1114764· OSTI ID:1427516

Xu, Kuan ^[1]; Austin, Anthony P. ^[2]; Wei, Ke ^[3]

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1. Univ. of Kent, Canterbury (United Kingdom). School of Mathematics, Statistics, and Actuarial Science
2. Argonne National Lab. (ANL), Argonne, IL (United States). Mathematics and Computer Science Division
3. Univ. of California, Davis, CA (United States). Dept. of Mathematics

In this paper, we present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result. Finally, the complexity of the algorithm is O(N(log N)²), where N is the number of degrees of freedom used in each of the Fourier extensions.

• Research Organization: Argonne National Lab. (ANL), Argonne, IL (United States); Univ. of California, Davis, CA (United States); Univ. of Kent, Canterbury (United Kingdom)
• Sponsoring Organization: USDOE Office of Science (SC); National Science Foundation (NSF); Royal Society (United Kingdom)
• Grant/Contract Number: AC02-06CH11357; RG160236; DTRA-DMS 1322393
• OSTI ID: 1427516
• Journal Information: SIAM Journal on Scientific Computing, Vol. 39, Issue 6; ISSN 1064-8275
• Publisher: SIAM
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
convolution
fast Fourier transform
Fourier extension
Fredholm convolution integral
Toeplitz matrix
Volterra convolution integral