A $p$-version of convolution quadrature in wave propagation
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916451269476352 |
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| author | Rieder, Alexander |
| author_facet | Rieder, Alexander |
| contents | We consider a novel way of discretizing wave scattering problems using the general formalism of convolution quadrature, but instead of reducing the timestep size ($h$-method), we achieve accuracy by increasing the order of the method ($p$-method). We base this method on discontinuous Galerkin timestepping and use the Z-transform. We show that for a certain class of incident waves, the resulting schemes observes(root)-exponential convergence rate with respect to the number of boundary integral operators that need to be applied. Numerical experiments confirm the findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A $p$-version of convolution quadrature in wave propagation Rieder, Alexander Numerical Analysis We consider a novel way of discretizing wave scattering problems using the general formalism of convolution quadrature, but instead of reducing the timestep size ($h$-method), we achieve accuracy by increasing the order of the method ($p$-method). We base this method on discontinuous Galerkin timestepping and use the Z-transform. We show that for a certain class of incident waves, the resulting schemes observes(root)-exponential convergence rate with respect to the number of boundary integral operators that need to be applied. Numerical experiments confirm the findings. |
| title | A $p$-version of convolution quadrature in wave propagation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2402.17712 |