Isogeometric analysis based on extended CatmullClark subdivision
In this paper, we propose a subdivision-based finite element method as an integration of the isogeometric analysis (IGA) framework which adopts the uniform representation for geometric modeling and finite element simulation. The finite element function space is induced from the limit form of CatmullClark surface subdivision containing boundary subdivision schemes which has C1 C 1 continuity everywhere. It is capable of exactly representing complex geometries with any shaped boundaries which are represented as piecewise cubic B-spline curves. It is compatible with modern Computer Aided Design (CAD) software systems. The advantage of this strategy admits quadrilateral meshes of arbitrary topology. In this work, the computational domains with planar geometries are considered. We establish the approximation properties of CatmullClark surface subdivision function based on the BrambleHilbert lemma. Numerical tests are performed through three Poissons equations with the Dirichlet boundary condition to corroborate the theoretical proof.
isogeometric analysis catmullclark subdivision computer aided design finite element analysis