Cubature rules with positive weights on union of disks

In this work we present a new algorithm that computes cubature formulas with positive weights, interior nodes and fixed algebraic degree of precision, over domains Ω that are arbitrary union of disks. This novel approach first determines the boundary ∂ Ω and then defines a decomposition of Ω by means of nonoverlapping circular segments and polygons, where algebraic positive interior rules can be locally constructed. The resulting global Positive Interior (PI) formula is finally compressed by Caratheodory- Tchakaloff subsampling implemented via NonNegative Least-Squares.