Symmetric quadrature rules for tetrahedra based on a cubic close-packed lattice arrangement

Autor:	Lee Shunn, Frank Ham
Rok vydání:	2012
Předmět:	Applied Mathematics Mathematical analysis Gauss–Kronrod quadrature formula Quadrature (mathematics) Cubatures for tetrahedra Combinatorics symbols.namesake Computational Mathematics Cubic close-packed Numerical integration symbols Tetrahedron Gaussian quadrature Rapid convergence Mathematics
Zdroj:	Journal of Computational and Applied Mathematics. 236(17):4348-4364
ISSN:	0377-0427
DOI:	10.1016/j.cam.2012.03.032
Popis:	A family of quadrature rules for integration over tetrahedral volumes is developed. The underlying structure of the rules is based on the cubic close-packed (CCP) lattice arrangement using 1, 4, 10, 20, 35, and 56 quadrature points. The rules are characterized by rapid convergence, positive weights, and symmetry. Each rule is an optimal approximation in the sense that lower-order terms have zero contribution to the truncation error and the leading-order error term is minimized. Quadrature formulas up to order 9 are presented with relevant numerical examples.
Databáze:	OpenAIRE
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