Symmetric quadrature rules for simplexes based on sphere close packed lattice arrangements

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:266

Article

Williams, D. M.¹  Shunn, L.²  Jameson, A.¹ 

[1] Stanford Univ, Dept Aeronaut & Astronaut, Stanford, CA 94305 USA

[2] Cascade Technol, Palo Alto, CA 94303 USA

关键词: Quadrature;    Integration;    Symmetric;    Triangle;    Tetrahedron;    Simplex;   

DOI  :  10.1016/j.cam.2014.01.007

来源: Elsevier

【 摘 要 】

Sphere close packed (SCP) lattice arrangements of points are well-suited for formulating symmetric quadrature rules on simplexes, as they are symmetric under affine transformations of the simplex unto itself in 2D and 3D. As a result, SCP lattice arrangements have been utilized to formulate symmetric quadrature rules with N-p = 1, 4, 10, 20, 35, and 56 points on the 3-simplex (Shunn and Ham, 2012). In what follows, the work on the 3-simplex is extended, and SCP lattices are employed to identify symmetric quadrature rules with N-p = 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, and 66 points on the 2-simplex and N-p = 84 points on the 3-simplex. These rules are found to be capable of exactly integrating polynomials of up to degree 17 in 20 and up to degree 9 in 3D. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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