Cheap and stable quadrature on polyhedral elements
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915140105928704 |
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| author | Sommariva, Alvise Vianello, Marco |
| author_facet | Sommariva, Alvise Vianello, Marco |
| contents | We discuss a cheap tetrahedra-free approach to the numerical integration of polynomials on polyhedral elements, based on hyperinterpolation in a bounding box and Chebyshev moment computation via the divergence theorem. No conditioning issues arise, since no matrix factorization or inversion is needed. The resulting quadrature formula is theoretically stable even in the presence of some negative weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cheap and stable quadrature on polyhedral elements Sommariva, Alvise Vianello, Marco Numerical Analysis 65D32 We discuss a cheap tetrahedra-free approach to the numerical integration of polynomials on polyhedral elements, based on hyperinterpolation in a bounding box and Chebyshev moment computation via the divergence theorem. No conditioning issues arise, since no matrix factorization or inversion is needed. The resulting quadrature formula is theoretically stable even in the presence of some negative weights. |
| title | Cheap and stable quadrature on polyhedral elements |
| topic | Numerical Analysis 65D32 |
| url | https://arxiv.org/abs/2502.03446 |