Spectral Method for the Fractional Laplacian in 2D and 3D

Understand

A spectral method is considered for approximating the fractional Laplacian and solving the fractional Poisson problem in 2D and 3D unit balls.

• The method is based on the explicit formulation of the eigenfunctions and eigenvalues of the fractional Laplacian in the unit balls under the weighted $L^2$ space.
• The resulting method enjoys spectral accuracy for all fractional index $\alpha\in (0,2)$ and is computationally efficient due to the orthogonality of the basis functions.
• We also proposed a numerical integration strategy for computing the coefficients.