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

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