Numerical integration over implicitly defined domains with topological guarantee
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910753032765440 |
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| author | Yang, Tianhui Qarariyah, Ammar Kang, Hongmei Deng, Jiansong |
| author_facet | Yang, Tianhui Qarariyah, Ammar Kang, Hongmei Deng, Jiansong |
| contents | Numerical integration over the implicitly defined domains is challenging due to topological variances of implicit functions. In this paper, we use interval arithmetic to identify the boundary of the integration domain exactly, thus getting the correct topology of the domain. Furthermore, a geometry-based local error estimate is explored to guide the hierarchical subdivision and save the computation cost. Numerical experiments are presented to demonstrate the accuracy and the potential of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_03498 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Numerical integration over implicitly defined domains with topological guarantee Yang, Tianhui Qarariyah, Ammar Kang, Hongmei Deng, Jiansong Numerical Analysis 65G30, 65D30 Numerical integration over the implicitly defined domains is challenging due to topological variances of implicit functions. In this paper, we use interval arithmetic to identify the boundary of the integration domain exactly, thus getting the correct topology of the domain. Furthermore, a geometry-based local error estimate is explored to guide the hierarchical subdivision and save the computation cost. Numerical experiments are presented to demonstrate the accuracy and the potential of the proposed method. |
| title | Numerical integration over implicitly defined domains with topological guarantee |
| topic | Numerical Analysis 65G30, 65D30 |
| url | https://arxiv.org/abs/1901.03498 |