Article
| Title: | Stable computation of Laplacian eigenfunctions corresponding to clustered eigenvalues (English) |
| Author: | Endo, Ryoki |
| Author: | Liu, Xuefeng |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 70 |
| Issue: | 5 |
| Year: | 2025 |
| Pages: | 595-609 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The accurate computation of eigenfunctions corresponding to tightly clustered Laplacian eigenvalues remains an extremely difficult problem. Using the shape difference quotient of eigenvalues, we propose a stable computation method for the eigenfunctions of clustered eigenvalues caused by domain perturbation. (English) |
| Keyword: | stable eigenfunction computation |
| Keyword: | clustered eigenvalues |
| Keyword: | finite element method |
| Keyword: | shape derivative |
| Keyword: | difference quotient of eigenvalues |
| MSC: | 65N25 |
| MSC: | 65N30 |
| DOI: | 10.21136/AM.2025.0132-25 |
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| Date available: | 2025-11-07T16:05:33Z |
| Last updated: | 2025-11-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153150 |
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| Reference: | [2] Endo, R., Liu, X.: The second Dirichlet eigenvalue is simple on every non-equilateral triangle, Part II: Nearly equilateral triangles.Available at https://arxiv.org/abs/2305.14063v6 (2025), 24 pages. 10.48550/arXiv.2305.14063 |
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| Reference: | [4] Liu, X.: Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems.SpringerBriefs in Mathematics. Springer, Singapore (2024). Zbl 1562.65007, MR 4807655, 10.1007/978-981-97-3577-8 |
| Reference: | [5] Liu, X., Vejchodský, T.: Fully computable a posteriori error bounds for eigenfunctions.Numer. Math. 152 (2022), 183-221. Zbl 1496.65204, MR 4474059, 10.1007/s00211-022-01304-0 |
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| Reference: | [7] Ogita, T., Aishima, K.: Iterative refinement for symmetric eigenvalue decomposition. II. Clustered eigenvalues.Japan J. Ind. Appl. Math. 36 (2019), 435-459. Zbl 1418.65049, MR 3975924, 10.1007/s13160-019-00348-4 |
| Reference: | [8] Parlett, B. N.: The Symmetric Eigenvalue Problem.Classics in Applied Mathematics 20. SIAM, Philadelphia (1998). Zbl 0885.65039, MR 1490034, 10.1137/1.9781611971163 |
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