Tree Partition of Unity Method

Even though all presented components of our multilevel PUM, the PU construction, the numerical quadrature scheme, and the multilevel solver, are designed for general point sets P and general covers C _Ω we applied our meshfree discretization method to uniform node arrangements only; up to now. So far we did not have to deal with the challenging task of the cover construction for irregular point sets. In this chapter we now focus on this very critical issue of constructing a suitable cover C _Ω for a general given point set efficiently.