On numerical integration in isogeometric subdivision methods for PDEs on surfaces

摘要

Subdivision surfaces offer great flexibility in capturing irregular topologies combined with higher order smoothness. For instance, Loop and Catmull-Clark subdivision schemes provide C-2 smoothness everywhere except at extraordinary vertices, where the generated surfaces are C-1 smooth. The combination of flexibility and smoothness leads to their frequent use in geometric modeling and makes them an ideal candidate for performing isogeometric analysis of higher order problems with irregular topologies, e.g. thin shell problems. In the neighborhood of extraordinary vertices, however, the resulting surfaces (and the functions defined on them) are non-polynomial. Thus numerical integration based on quadrature has to be performed carefully to preserve the expected higher order consistency.