A discrete Perfectly Matched Layer for peridynamic scalar waves in two-dimensional viscous media
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929700421500928 |
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| author | Du, Yu Li, Yonglin Zhang, Jiwei |
| author_facet | Du, Yu Li, Yonglin Zhang, Jiwei |
| contents | In this paper, we propose a discrete perfectly matched layer (PML) for the peridynamic scalar wave-type problems in viscous media. Constructing PMLs for nonlocal models is often challenging, mainly due to the fact that nonlocal operators are usually associated with various kernels. We first convert the continua model to a spatial semi-discretized version by adopting quadrature-based finite difference scheme, and then derive the PML equations from the semi-discretized equations using discrete analytic continuation. The harmonic exponential fundamental solutions (plane wave modes) of the semi-discretized equations are absorbed by the PML layer without reflection and are exponentially damped. The excellent efficiency and stability of discrete PML are demonstrated in numerical tests by comparison with exact absorbing boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03713 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A discrete Perfectly Matched Layer for peridynamic scalar waves in two-dimensional viscous media Du, Yu Li, Yonglin Zhang, Jiwei Numerical Analysis 65N30, 65R20, 46N20, 45A05, 78A40 G.1.0; G.1.8 In this paper, we propose a discrete perfectly matched layer (PML) for the peridynamic scalar wave-type problems in viscous media. Constructing PMLs for nonlocal models is often challenging, mainly due to the fact that nonlocal operators are usually associated with various kernels. We first convert the continua model to a spatial semi-discretized version by adopting quadrature-based finite difference scheme, and then derive the PML equations from the semi-discretized equations using discrete analytic continuation. The harmonic exponential fundamental solutions (plane wave modes) of the semi-discretized equations are absorbed by the PML layer without reflection and are exponentially damped. The excellent efficiency and stability of discrete PML are demonstrated in numerical tests by comparison with exact absorbing boundary conditions. |
| title | A discrete Perfectly Matched Layer for peridynamic scalar waves in two-dimensional viscous media |
| topic | Numerical Analysis 65N30, 65R20, 46N20, 45A05, 78A40 G.1.0; G.1.8 |
| url | https://arxiv.org/abs/2502.03713 |