Analytical Integration within Polyhedra

Abstract

Arbitrary shapes of engineering objects demand spatial discretization in design analysis. Therein, an accurate estimation of energy-like integrals, within each volume subset, becomes essential to formulate a variety of approximate solution procedures. Higher numerical accuracy in finite element methods, especially in evaluations of system matrices, is incessantly sought to make commercial computer programs more dependable. Three-dimensional thermo-viscoplastic stress analyses motivated this research. In addition, applications in optimization can be cited. The divergence theorem of vector calculus provided the algorithm that leads to better accuracy as compared with conventional numerical quadratures.