Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/146051
Title: Fast fourier-like mapped Chebyshev spectral-Galerkin methods for PDEs with integral fractional Laplacian in unbounded domains
Authors: Sheng, Changtao
Shen, Jie
Tang, Tao
Wang, Li-Lian
Yuan, Huifang
Keywords: Science::Mathematics
Issue Date: 2020
Source: Sheng, C., Shen, J., Tang, T., Wang, L.-L., & Yuan, H. (2020). Fast fourier-like mapped Chebyshev spectral-Galerkin methods for PDEs with integral fractional Laplacian in unbounded domains. SIAM Journal on Numerical Analysis, 58(5), 2435-2464. doi:10.1137/19M128377X
Project: MOE2018-T2-1-059
MOE2017-T2-2-144
Journal: SIAM Journal on Numerical Analysis
Abstract: In this paper, we propose a fast spectral-Galerkin method for solving PDEs involving an integral fractional Laplacian in Rd, which is built upon two essential components: (i) the Dunford- Taylor formulation of the fractional Laplacian; and (ii) Fourier-like biorthogonal mapped Chebyshev functions (MCFs) as basis functions. As a result, the fractional Laplacian can be fully diagonalized, and the complexity of solving an elliptic fractional PDE is quasi-optimal, i.e., O((N log2 N)d) with N being the number of modes in each spatial direction. Ample numerical tests for various decaying exact solutions show that the convergence of the fast solver perfectly matches the order of theoretical error estimates. With a suitable time discretization, the fast solver can be directly applied to a large class of nonlinear fractional PDEs. As an example, we solve the fractional nonlinear Schrödinger equation by using the fourth-order time-splitting method together with the proposed MCF-spectral-Galerkin method.
URI: https://hdl.handle.net/10356/146051
ISSN: 0036-1429
DOI: 10.1137/19M128377X
Rights: © 2020 Society for Industrial and Applied Mathematics. All rights reserved. This paper was published in SIAM Journal on Numerical Analysis and is made available with permission of Society for Industrial and Applied Mathematics.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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