Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 266, Issue -, Pages 18-38Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2014.01.007
Keywords
Quadrature; Integration; Symmetric; Triangle; Tetrahedron; Simplex
Categories
Funding
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1114816] Funding Source: National Science Foundation
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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.
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