Subdivision Isogeometric Analysis: A Todo List

Subdivision techniques are natural when extending isogeometric analysis beyond regular grid control nets, i.e., to integrated design and analysis of irregular layouts in several variables. This report identifies and discusses several challenges that need to be addressed to place the use of subdivision techniques for isogeometric analysis on a solid foundation. The report highlights issues of regularity, approximation and numerical quadrature. The challenges are illustrated by an implementation solving elliptic partial differential equations in the space of trivariate Catmull-Clark subdivision.