A High-Order Quadrature Method for Implicitly Defined Hypersurfaces and Regions
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908408643321856 |
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| author | Zhao, Zibo |
| author_facet | Zhao, Zibo |
| contents | This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided into small tetrahedrons, and by employing the change of variables formula, the approach yields an algorithm requiring only one-dimensional root finding and standard Gaussian quadrature. The resulting quadrature scheme guarantees strictly positive weights and inherits the high-order accuracy of Gaussian quadrature. Numerical convergence tests confirm the method's high-order accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A High-Order Quadrature Method for Implicitly Defined Hypersurfaces and Regions Zhao, Zibo Numerical Analysis This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided into small tetrahedrons, and by employing the change of variables formula, the approach yields an algorithm requiring only one-dimensional root finding and standard Gaussian quadrature. The resulting quadrature scheme guarantees strictly positive weights and inherits the high-order accuracy of Gaussian quadrature. Numerical convergence tests confirm the method's high-order accuracy. |
| title | A High-Order Quadrature Method for Implicitly Defined Hypersurfaces and Regions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2506.13078 |