On the numerical solution of the elastodynamic problem by a boundary integral equation method
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2017
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| _version_ | 1866911781388025856 |
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| author | Chapko, Roman Mindrinos, Leonidas |
| author_facet | Chapko, Roman Mindrinos, Leonidas |
| contents | A numerical method for the Dirichlet initial boundary value problem for the elastic equation in the exterior and unbounded region of a smooth closed simply connected 2-dimensional domain, is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and a boundary integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the time-depended problem to a sequence of stationary boundary value problems, which are solved by a boundary layer approach resulting to a sequence of boundary integral equations of the first kind. The numerical discretization and solution are obtained by a trigonometrical quadrature method. Numerical results are included. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1705_07611 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | On the numerical solution of the elastodynamic problem by a boundary integral equation method Chapko, Roman Mindrinos, Leonidas Numerical Analysis Analysis of PDEs A numerical method for the Dirichlet initial boundary value problem for the elastic equation in the exterior and unbounded region of a smooth closed simply connected 2-dimensional domain, is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and a boundary integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the time-depended problem to a sequence of stationary boundary value problems, which are solved by a boundary layer approach resulting to a sequence of boundary integral equations of the first kind. The numerical discretization and solution are obtained by a trigonometrical quadrature method. Numerical results are included. |
| title | On the numerical solution of the elastodynamic problem by a boundary integral equation method |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/1705.07611 |