An efficient solver for problems of scattering by bodies of revolution
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2003
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909853432152064 |
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| author | Han, YoungAe |
| author_facet | Han, YoungAe |
| contents | This proposal relates to the design, analysis and application of a novel numerical scheme for the solution of axisymmetric scattering problems. To this end, a procedure is introduced to iteratively evaluate the solution of the Lippmann-Schwinger integral equation in $O(N\log^2 N)$ operations, where $N$ is the number of the discretization points. The method achieves its efficiency through the use of the addition theorem and Fast Legendre Transforms (FLT).
For globally smooth sound velocities/refractive indexes the method is spectrally accurate. More generally the order of convergence is tied to and in fact, limited by, the smoothness of the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0311515 |
| institution | arXiv |
| publishDate | 2003 |
| record_format | arxiv |
| spellingShingle | An efficient solver for problems of scattering by bodies of revolution Han, YoungAe Numerical Analysis 65Rxx;78-xx This proposal relates to the design, analysis and application of a novel numerical scheme for the solution of axisymmetric scattering problems. To this end, a procedure is introduced to iteratively evaluate the solution of the Lippmann-Schwinger integral equation in $O(N\log^2 N)$ operations, where $N$ is the number of the discretization points. The method achieves its efficiency through the use of the addition theorem and Fast Legendre Transforms (FLT). For globally smooth sound velocities/refractive indexes the method is spectrally accurate. More generally the order of convergence is tied to and in fact, limited by, the smoothness of the solution. |
| title | An efficient solver for problems of scattering by bodies of revolution |
| topic | Numerical Analysis 65Rxx;78-xx |
| url | https://arxiv.org/abs/math/0311515 |