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Efficient symmetrical cubature rules for complete polynomials of high degree over the unit cube
Author(s) -
Dunavant D. A.
Publication year - 1986
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620230306
Subject(s) - unit cube , cube (algebra) , degree (music) , numerical integration , mathematics , polynomial , gaussian , unit (ring theory) , product (mathematics) , algorithm , combinatorics , mathematical analysis , geometry , physics , mathematics education , quantum mechanics , acoustics
The fully symmetrical cubature rules developed and presented are at present the most economically available for numerical integration over the unit cube of complete polynomial functions up to and including nineteenth order. Conventional Gaussian triple product integration formulae, by comparison, require more than twice as many integration points and weights.