A Semi-Analytic Diagonalization FEM for the Spectral Fractional Laplacian
Numerical Analysis
2024-09-27 v1 Numerical Analysis
Abstract
We present a technique for approximating solutions to the spectral fractional Laplacian, which is based on the Caffarelli-Silvestre extension and diagonalization. Our scheme uses the analytic solution to the associated eigenvalue problem in the extended dimension. We show its relation to a quadrature scheme. Numerical examples demonstrate the performance of the method.
Keywords
Cite
@article{arxiv.2409.17388,
title = {A Semi-Analytic Diagonalization FEM for the Spectral Fractional Laplacian},
author = {Abner J. Salgado and Shane E. Sawyer},
journal= {arXiv preprint arXiv:2409.17388},
year = {2024}
}