Monomial cubature rules since “Stroud”: a compilation — part 2

We describe a nonadaptive automatic cubature routine for integration over a wide variety of two-dimensional domains, including infinite regions. The underlying algorithm first maps the region onto the unit square, applies a periodizing sixth-order Sidi transformation and then generates a sequence of approximations based on embedded lattice rules. Numerical experiments suggest that the routine is reliable and efficient for a wide range of integrand types and that it is often more effective than other published routines for integrands with a singularity along the boundary and for integration over infinite domains.