Boundary integration of polynomials over an arbitrary linear hexahedron in Euclidean three-dimensional space (Q1808052)

The authors derive complicated formulas for the exact evaluation of integrals of polynomials over a hexahedron. They consider several methods based on different subdivisions of the hexahedron combined with the reduction of the volume integrals to surface integrals, and for one of the methods, a final reduction to line integrals. The resulting formulas should be suitable for implementation with symbolic algebra systems. A detailed example is used to illustrate the methods. There is a brief discussion of relative efficiencies of the methods, but no comparison is made with simpler methods which could use a standard subdivision of the hexahedron into tetrahedra combined with simple integration formulas that are exact for low-order polynomials.