Efficient Spectral Methods for PDEs with Spectral Fractional Laplacian

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 metho...

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Bibliographic Details
Published in:Journal of scientific computing 2021-07, Vol.88 (1), p.4, Article 4
Main Authors: Sheng, Changtao, Cao, Duo, Shen, Jie
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Boundary conditions
Computational Mathematics and Numerical Analysis
Eigenvalues
Eigenvectors
Error analysis
Finite element analysis
Laplace equation
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Parabolic differential equations
Partial differential equations
Spacetime
Spectral methods
Theoretical
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Summary: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-021-01491-2