You can find in the following publications a detailed explanation of the technique of the Equivalent Polynomials, including cases not covered by the Library:
Ventura G., On the elimination of quadrature subcells for discontinuous functions in the extended finite-element method. International Journal for Numerical Methods in Engineering 66 (2006) 761–795.
Ventura G., Benvenuti E., Equivalent polynomials for quadrature in heaviside function enriched elements, International Journal for Numerical Methods in Engineering 102 (2015) 688–710.
Mariggiò G., Fichera S., Corrado M., Ventura G., EQP - A 2D/3D library for integration of polynomials times step function. SoftwareX, 12 (2020) 100636.
The above papers, except SoftwareX publication, cannot be available for direct download due to copyright limitations. However, you can download below my internal report on the technique.
You can download below my internal report on the technique that originated the Equivalent Polynomial Library. It is limited to the Heaviside function enrichment, although the technique is much more general. When citing my work please cite always the Journal papers. This is the best way to support my efforts.
Internal Report on Heaviside Enriched Elements
The basic reference document about the Library is already enclosed in the Library package, but is here available as well.
EQP Library Reference Document and Application Note
The reference documentation for the version of the Library including the ability to handle two discontinuities can be found in the following paper submitted for publication:
Fichera S., Mariggiò G., Corrado M., Ventura G., Enhanced EQP - A library for integration of polynomials times double step function in quadrilateral domains. Paper submitted to SoftwareX, 2023.