Multiple expansions and pseudospectral cardinal functions: A new generalization of the fast fourier transform

Journal Article · Sat Oct 31 23:00:00 EST 1992 · Journal of Computational Physics; (United States)

DOI:https://doi.org/10.1016/0021-9991(92)90333-T· OSTI ID:7310580

Boyd, J P ^[1]

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1. Univ. of Michigan, Ann Arbor, MI (United States)

The polynomial or trigonometric interpolant of an arbitrary function f(x) may be presented as a critical function' series whose coefficients are the values of f(x) at the interpolation points. We show that the cardinal series is identical to the sum of the forces due to a set of N point charges (with appropriate force laws). It follows that the cardinal series can be summed via the fast multipole method (FMM) in O(Nlog[sub 2]N) operations, which is much cheaper than the O(N[sup 2]) cost of direct summation. The FMM is slower than the fast Fourier transform (FFT), so the latter should always be used where applicable. However, the multipole expansion succeeds where the FFT fails. In particular, the FMM can be used to evaluate Fourier and Chebyshev series on an irregular grid as is needed when adaptively regridding in a time integration. Also, the multipole expansion can be applied to basis sets for which the FFT is inapplicable even on the canonical grid including Legendre polynomials, Hermite and Laguerre functions, spherical harmonics, and zinc functions. 12 refs.

• OSTI ID: 7310580
• Journal Information: Journal of Computational Physics; (United States), Journal Name: Journal of Computational Physics; (United States) Vol. 103:1; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID FLOW
FOURIER TRANSFORMATION
INTEGRAL TRANSFORMATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION
TRANSFORMATIONS