Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis

The numerical integration of discontinuous functions is an abiding problem addressed by various authors. This subject gained even more attention in the context extended finite element method (XFEM), which exact crucial to obtaining reliable results. In this scope, equivalent polynomials represent effective circumvent while exploiting standard Gauss quadrature rule exactly integrate times step function. Certain scenarios, however, might require two (i.e., problems branching cracks, kinking cracks or crack junctions within a single occur). context, use has been investigated authors, and algorithm arbitrary Heaviside quadrilateral domains developed presented paper. Moreover, also implemented into software library (DD_EQP) prove its precision effectiveness proposed method’s ease implementation any existing computational framework. first towards number discontinuities domains. Both have wide application range, addition fracture mechanics, from mathematical computing complex geometric regions, computer graphics mechanics.