A Sylvester equation approach for the computation of zero-group-velocity points in waveguides
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908483068100608 |
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| author | Plestenjak, Bor Kiefer, Daniel A. Gravenkamp, Hauke |
| author_facet | Plestenjak, Bor Kiefer, Daniel A. Gravenkamp, Hauke |
| contents | Eigenvalues of parameter-dependent quadratic eigenvalue problems form eigencurves. The critical points on these curves, where the derivative vanishes, are of practical interest.
A particular example is found in the dispersion curves of elastic waveguides, where such points are called zero-group-velocity (ZGV) points. Recently, it was revealed that the problem of computing ZGV points can be modeled as a multiparameter eigenvalue problem (MEP), and several numerical methods were devised. Due to their complexity, these methods are feasible only for problems involving small matrices. In this paper, we improve the efficiency of these methods by exploiting the link to the Sylvester equation. This approach enables the computation of ZGV points for problems with much larger matrices, such as multi-layered plates and three-dimensional structures of complex cross-sections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09584 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Sylvester equation approach for the computation of zero-group-velocity points in waveguides Plestenjak, Bor Kiefer, Daniel A. Gravenkamp, Hauke Numerical Analysis Computational Physics 65F15, 15A18, 15A22, 74J05, 74S05, 35B38 Eigenvalues of parameter-dependent quadratic eigenvalue problems form eigencurves. The critical points on these curves, where the derivative vanishes, are of practical interest. A particular example is found in the dispersion curves of elastic waveguides, where such points are called zero-group-velocity (ZGV) points. Recently, it was revealed that the problem of computing ZGV points can be modeled as a multiparameter eigenvalue problem (MEP), and several numerical methods were devised. Due to their complexity, these methods are feasible only for problems involving small matrices. In this paper, we improve the efficiency of these methods by exploiting the link to the Sylvester equation. This approach enables the computation of ZGV points for problems with much larger matrices, such as multi-layered plates and three-dimensional structures of complex cross-sections. |
| title | A Sylvester equation approach for the computation of zero-group-velocity points in waveguides |
| topic | Numerical Analysis Computational Physics 65F15, 15A18, 15A22, 74J05, 74S05, 35B38 |
| url | https://arxiv.org/abs/2411.09584 |