Construction of Smooth Isogeometric Function Spaces on Singularly Parameterized Domains
We aim at constructing a smooth basis for isogeometric function spaces on domains of reduced geometric regularity. In this context an isogeometric function is the composition of a piecewise rational function with the inverse of a piecewise rational geometry parameterization. We consider two types of singular parameterizations, domains where a part of the boundary is mapped onto one point and domains where the two parameter lines at a corner of the parameter domain are collinear in the physical domain. We locally map a singular tensor-product patch of arbitrary degree onto a triangular patch, thus splitting the parameterization into a singular bilinear mapping and a regular mapping on a triangular domain. This construction yields an isogeometric function space of prescribed smoothness. Generalizations to higher dimensions are also possible and are briefly discussed in the final section.
The work presented here is partially supported by the Italian MIUR through the FIRB “Futuro in Ricerca” Grant RBFR08CZ0S and by the European Research Council through the FP7 Ideas Consolidator Grant HIgeoM. This support is gratefully acknowledged.