Simultaneous interior and boundary optimization of volumetric domain parameterizations for IGA

Abstract

We present a novel method to compute bijective volumetric domain parameterizations with low distortion for isogeometric analysis. Central to this approach is a simultaneous optimization of the interior and the boundary mappings. The simultaneous optimization is formulated as a constrained optimization problem. The objective is a combination of a distortion metric of the volumetric domain parameterization and a similarity error between the mapped parametric domain and the computational domain. Bijection is ensured as the constraint. The success of our method to solve this very challenging problem relies on two key components: (1) a tet-to-spline optimization strategy that mitigates the difficulty to handle the similarity error and (2) a three-step initialization procedure that enables effective distortion reduction. We demonstrate the efficacy of our method on various complex models. Compared to state-of-the-art methods, our method achieves bijective volumetric domain parameterizations with much lower distortion.