EQP - A 2D/3D library for integration of polynomials times step function

Abstract

The EQuivalent Polynomials library, EQP, herein provided is a powerful tool for the numerical integration, with classical quadrature rules (e.g. Gauss–Legendre), of a function given by the product of an arbitrary polynomial times a Heaviside step function. The library can handle a multiplicity of shapes for the integration domain in one, two and three dimensions. Originally developed by Ventura (Ventura, 2006) to overcome the long-standing problem of integrating discontinuous functions in the context of the eXtended Finite Element Method, EQP library has been recently generalized to meet the needs of very different fields, spanning from computational mechanics, to computer graphics, evaluation of geometric region (mass) properties and computer simulation in general.

Keywords

• Numerical integration
• Heaviside step function
• Polynomial functions
• Computer graphics
• Library
• Fortran