High-order numerical integration on regular embedded surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916159645810688 |
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| author | Zavalani, Gentian Hecht, Michael |
| author_facet | Zavalani, Gentian Hecht, Michael |
| contents | We present a high-order surface quadrature (HOSQ) for accurately approximating regular surface integrals on closed surfaces. The initial step of our approach rests on exploiting square-squeezing--a homeomorphic bilinear square-simplex transformation, re-parametrizing any surface triangulation to a quadrilateral mesh. For each resulting quadrilateral domain we interpolate the geometry by tensor polynomials in Chebyshev--Lobatto grids. Posterior the tensor-product Clenshaw-Curtis quadrature is applied to compute the resulting integral. We demonstrate efficiency, fast runtime performance, high-order accuracy, and robustness for complex geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09178 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-order numerical integration on regular embedded surfaces Zavalani, Gentian Hecht, Michael Numerical Analysis 65D15, 65D30, 65D32 We present a high-order surface quadrature (HOSQ) for accurately approximating regular surface integrals on closed surfaces. The initial step of our approach rests on exploiting square-squeezing--a homeomorphic bilinear square-simplex transformation, re-parametrizing any surface triangulation to a quadrilateral mesh. For each resulting quadrilateral domain we interpolate the geometry by tensor polynomials in Chebyshev--Lobatto grids. Posterior the tensor-product Clenshaw-Curtis quadrature is applied to compute the resulting integral. We demonstrate efficiency, fast runtime performance, high-order accuracy, and robustness for complex geometries. |
| title | High-order numerical integration on regular embedded surfaces |
| topic | Numerical Analysis 65D15, 65D30, 65D32 |
| url | https://arxiv.org/abs/2403.09178 |