A novel nonlocal potential solver based on nonuniform FFT for efficient simulation of the Davey−Stewartson equations

We propose an efficient and accurate solver for the nonlocal potential in the Davey−Stewartson equations using nonuniform FFT (NUFFT). A discontinuity in the Fourier transform of the nonlocal potential causes “accuracy locking” if the potential is solved by standard FFT with periodic boundary condit...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2017-07, Vol.51 (4), p.1527-1538
Main Authors: Mauser, Norbert J., Stimming, Hans Peter, Zhang, Yong
Format: Article
Language:English
Subjects:
35Q55
65M70
65T50
76B45
Accuracy
Boundary conditions
Davey–Stewartson equations
Discontinuity
Fast Fourier transformations
Fourier transforms
Low frequencies
Mathematics
Nonlocal potential solver
nonuniform FFT
Numerical Analysis
Polar coordinates
Quadratures
Solvers
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Summary:We propose an efficient and accurate solver for the nonlocal potential in the Davey−Stewartson equations using nonuniform FFT (NUFFT). A discontinuity in the Fourier transform of the nonlocal potential causes “accuracy locking” if the potential is solved by standard FFT with periodic boundary conditions on a truncated domain. Using the fact that the discontinuity disappears in polar coordinates, we reformulate the potential integral and split it into high and low frequency parts. The high frequency part can be approximated by the standard FFT method, while the low frequency part is evaluated with a high order Gauss quadrature accelerated by nonuniform FFT. The NUFFT solver has O(Nlog N) complexity, where N is the total number of discretization points, and achieves higher accuracy than standard FFT solver, which makes its use in simulations very attractive. Extensive numerical results show the efficiency and accuracy of the proposed new method.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2016071