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Generalized numerical integration of moments
Author(s) -
Griffiths D. V.
Publication year - 1991
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.1620320108
Subject(s) - numerical integration , mathematics , legendre polynomials , sampling (signal processing) , gaussian , limit (mathematics) , generalization , mathematical analysis , symmetry (geometry) , weighting , range (aeronautics) , rotational symmetry , gauss , geometry , physics , materials science , quantum mechanics , detector , acoustics , optics , composite material
Sampling points and weighting coefficients of the Gaussian type are presented for integrands typically encountered in axisymmetric finite elements. The proposed method is a generalization of Gaussian Integration of Moments for non‐zero limits of integration. The method achieves one extra order of accuracy in the integration of polynomials as compared with the Gauss‐Legendre method with the same number of sampling points. Although the locations of sampling points require the solution of non‐linear equations, analytical solutions are presented for the cases of one and two sampling points. Special cases of these general expressions are shown to include both Gauss‐Legendre integration corresponding to an integration range at a considerable distance from the axis of symmetry, and Fishman integration corresponding to an integration range whose lower limit lies on the axis of symmetry.