High-order cubature rules for tetrahedra
Authors:
- Jan Jaśkowiec,
- N. Sukumar
Abstract
In this paper, we construct new high-order numerical integration schemes fortetrahedra, with positive weights and integration points that are in the interiorof the domain. The construction of cubature rules is a challenging problem,which requires the solution of strongly nonlinear algebraic (moment) equationswith side conditions given by affine inequality constraints. We present a robustalgorithm based on a sequence of three modified Newton procedures to solvethe constrained minimization problem. In the literature, numerical integrationrules for the tetrahedron are available up to orderp=15. We obtain inte-gration rules for the tetrahedron fromp=2top=20, which are computedusing multiprecision arithmetic. Forp≤15, our approach provides integrationrules that have the same or fewer number of integration points than existingrules; forp=16 top=20, our rules are new. Numerical tests are presentedthat verify the polynomial-precision of the cubature rules. Convergence stud-ies are performed for the integration of exponential, rational, weakly singularand trigonometric test functions over tetrahedra with flat and curved faces. Inall tests, improvements in accuracy is realized aspis increased, though in somecases nonmonotonic convergence is observed.
- Record ID
- CUT75ab5281b095464a951234629731a550
- Publication categories
- ;
- Author
- Journal series
- International Journal for Numerical Methods in Engineering, ISSN 0029-5981, e-ISSN 1097-0207
- Issue year
- 2020
- Vol
- 121
- No
- 11
- Pages
- 2418-2436
- Other elements of collation
- rys.; schem.; tab.; wykr.; Bibliografia (na s.) - 2435-2436; Bibliografia (liczba pozycji) - 38; Oznaczenie streszczenia - Summ.; Data udostępnienia on-line - 2020-01-10; Numeracja w czasopiśmie - Vol. 121, Iss. 11
- Keywords in English
- least squares, numerical integration, polynomial basis, positive weights, strictly interior integration points, tetrahedral domain
- DOI
- DOI:10.1002/nme.6313 Opening in a new tab
- URL
- https://onlinelibrary.wiley.com/doi/10.1002/nme.6313 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/CUT75ab5281b095464a951234629731a550/
- URN
urn:pkr-prod:CUT75ab5281b095464a951234629731a550
* 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.