Efficient Spectral Methods for PDEs with Spectral Fractional Laplacian

被引：3
作者：
Sheng C. [1 ]
Cao D. [2 ]
Shen J. [2 ]
机构：
[1] School of Mathematics, Shanghai University of Finance and Economics, Shanghai
[2] Department of Mathematics, Purdue University, West Lafayette, 47907-1957, IN
来源：
Journal of Scientific Computing | 2021年 / 88卷 / 01期
基金：
美国国家科学基金会;
关键词：
Error analysis; Fourier-like basis function; Spectral fractional Laplacian; Spectral method;
D O I：
10.1007/s10915-021-01491-2
中图分类号：
学科分类号：
摘要：
We develop efficient spectral methods for the spectral fractional Laplacian equation and parabolic PDEs with spectral fractional Laplacian on rectangular domains. The key idea is to construct eigenfunctions of discrete Laplacian (also referred to Fourier-like basis) by using the Fourierization method. Under this basis, the non-local fractional Laplacian operator can be trivially evaluated, leading to very efficient algorithms for PDEs involving spectral fractional Laplacian. We provide a rigorous error analysis of the proposed methods for the case with homogeneous boundary conditions, as well as ample numerical results to show their effectiveness. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
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