High‐order symmetric cubature rules for tetrahedra and pyramids
Authors:
- Jan Jaśkowiec,
- N. Sukumar
Abstract
In this article, we present an algorithm to construct high‐order fully symmetric cubature rules for tetrahedral and pyramidal elements, with positive weights and integration points that are in the interior of the domain. Cubature rules are fully symmetric if they are invariant to affine transformations of the domain. We divide the integration points into symmetry orbits where each orbit contains all the points generated by the permutation stars. These relations are represented by equality constraints. The construction of symmetric cubature rules require the solution of nonlinear polynomial equations with both inequality and equality constraints. For higher orders, we use an algorithm that consists of five sequential phases to produce the cubature rules. In the literature, symmetric numerical integration rules are available for the tetrahedron for orders p = 1–10, 14, and for the pyramid up to p = 10. We have obtained fully symmetric cubature rules for both of these elements up to order p = 20. Numerical tests are presented that verify the polynomial‐precision of the cubature rules. Convergence studies are performed for the integration of exponential, weakly singular, and trigonometric test functions over both elements with flat and curved faces. With increase in p, improvements in accuracy is realized, though nonmonotonic convergence is observed.
- Record ID
- CUTe232c7be175a467d99e65ca3278fed1b
- Publication categories
- ;
- Author
- Journal series
- International Journal for Numerical Methods in Engineering, ISSN 0029-5981, e-ISSN 1097-0207
- Issue year
- 2021
- Vol
- 122
- No
- 1
- Pages
- 148-171
- Other elements of collation
- rys.; schem.; tab.; wykr.; Bibliografia (na s.) - 171; Bibliografia (liczba pozycji) - 29; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 122, Iss. 1
- Keywords in English
- numerical integration, positive weights, pyramidal element, strictly interior integration points, symmetric cubature rules, tetrahedral element
- DOI
- DOI:10.1002/nme.6528 Opening in a new tab
- URL
- https://onlinelibrary.wiley.com/doi/full/10.1002/nme.6528 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 200
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTe232c7be175a467d99e65ca3278fed1b/
- URN
urn:pkr-prod:CUTe232c7be175a467d99e65ca3278fed1b
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.