Boundary integration over linear polyhedra
Exact formulas are given for evaluating double and triple integrals of monomials over linear regular polyhedra in \({\mathbb{R}}^ 3\). The integration method presented here enables practical formulas to be obtained for the exact evaluation of the integrals \(\iint_{S}f(p)dS\quad and\quad \iiint_{P}f(p)dV,\) where S and P are linear and regular 2- or 3-polyhedra in \({\mathbb{R}}^ 3\), dS and dV are the differential surface and the differential volume, respectively. An implementation of the proposed integration methodology and a program written in Pascal are presented.
scientific article; zbMATH DE number 4143320