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Tensor‐based Gauss–Jacobi numerical integration for high‐order mass and stiffness matrices
Author(s) -
Bittencourt M. L.,
Vazquez T. G.
Publication year - 2009
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.2580
Subject(s) - mathematics , hexahedron , stiffness , stiffness matrix , gaussian quadrature , tetrahedron , finite element method , mathematical analysis , gauss , tangent stiffness matrix , geometry , physics , structural engineering , nyström method , engineering , quantum mechanics , integral equation
Abstract In this work, we choose the points and weights of the Gauss–Jacobi, Gauss–Radau–Jacobi and Gauss–Lobatto–Jacobi quadrature rules that optimize the number of operations for the mass and stiffness matrices of the high‐order finite element method. The procedure is particularly applied to the mass and stiffness matrices using the tensor‐based nodal and modal shape functions given in ( Int. J. Numer. Meth. Engng 2007; 71 (5):529–563). For square and hexahedron elements, we show that it is possible to use tensor product of the 1D mass and stiffness matrices for the Poisson and elasticity problem. For the triangular and tetrahedron elements, an analogous analysis given in ( Int. J. Numer. Meth. Engng 2005; 63 (2):1530–1558) was considered for the selection of the optimal points and weights for the stiffness matrix coefficients for triangles and mass and stiffness matrices for tetrahedra. Copyright © 2009 John Wiley & Sons, Ltd.