A Semi-Analytic Diagonalization FEM for the Spectral Fractional Laplacian
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909326952628224 |
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| author | Salgado, Abner J. Sawyer, Shane E. |
| author_facet | Salgado, Abner J. Sawyer, Shane E. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_17388 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Semi-Analytic Diagonalization FEM for the Spectral Fractional Laplacian Salgado, Abner J. Sawyer, Shane E. Numerical Analysis 26A33, 65N12, 65N30, 33C10, 41A55 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. |
| title | A Semi-Analytic Diagonalization FEM for the Spectral Fractional Laplacian |
| topic | Numerical Analysis 26A33, 65N12, 65N30, 33C10, 41A55 |
| url | https://arxiv.org/abs/2409.17388 |