Planar domain parameterization for isogeometric analysis based on Teichmüller mapping

Given the boundary curve of a planar domain, finding a parametric spline representation for the domain is called domain parameterization. A good parameterization of the computational domain plays a key role in isogeometric analysis since it influences the accuracy of the subsequent analysis. In this paper, we propose a new approach for planar domain parameterization based on Teichmüller map-a special map in the class of quasi-conformal map. Under given correspondence of four boundary curves, a unique Teichmüller map between a unit square and a computational domain can be obtained, which guarantees a bijection map and minimizes the maximal conformality distortion. We propose an efficient iterative algorithm to compute the Teichmüller map based on alternating direction method of multipliers (ADMM). Experimental results show that our method can produce more uniform parameterization and increase the accuracy as well as decrease the condition numbers of the stiffness matrices in isogeometric analysis than other state of the art approaches.