Q000002: Xiao–Gimbutas

Integral\(\displaystyle \int f(x)\,\mathrm{d}x\)
NotesIf \(f(x)\) is a degree \(n\) polynomial, then an order \(n\) Xiao–Gimbutas rule will integrate it exactly.
References
Xiao, Hong and Gimbutas, Zydrunas. A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers & Mathematics with Applications 59(2), 663–676, 2010. [DOI: 10.1016/j.camwa.2009.10.027]

Triangle

Order 1

↓ show points and weights ↓

Order 2

↓ show points and weights ↓

Order 3

↓ show points and weights ↓

Order 4

↓ show points and weights ↓

Order 5

↓ show points and weights ↓
View higher order rules

Tetrahedron

Order 1

↓ show points and weights ↓

Order 2

↓ show points and weights ↓

Order 3

↓ show points and weights ↓

Order 4

↓ show points and weights ↓

Order 5

↓ show points and weights ↓
View higher order rules