Computing Low-Distortion B-Spline Volumetric Domain Parameterizations For IGA

Spline basis is used to provide a consistent expression of the geometric model and the analysis model in isogeometric analysis(IGA).IGA offers a new solution to the problem of the inconsistency between the geometric model and the analysis model in traditional numerical analysis methods.A fundamental problem in IGA is the volumetric domain parameterizations of the computational domain,that is,how to obtain a volume spline representation of the input model.Many methods of computing volumetric domain parameterizations have been proposed.Some methods rely on manual specification,which is tedious and subject to trial and error.Other methods can automatically generate volumetric domain parameterizations,but these methods restrict the shape of the parameter domain to a cube.These methods produce high-distortion volumetric domain parameterizations when the geometry of the model differs significantly from a cube.To solve the problem,this dissertation proposes a novel low-distortion B-spline volumetric domain parameterization method for IGA.The core of the method is to introduce the geometric shape of the parameter domain as new variables into the optimization problem to further reduce the distortion of the volumetric domain parameterizations.For a given tetrahedral computational domain,the proposed algorithm alternately optimizes the geometric shape of the parameter domain and the mapping from the computational domain to the parameter domain such that the boundary correspondences are established.Then according to the boundary correspondences,the discrete volumetric domain parameterizations are constructed by alternately optimizing the geometric shape of the parameter domain and the discrete volumetric domain parameterization mapping in order to reduce the distortion of the discrete volumetric domain parameterizations.Finally,the B-spline basis is used to fit the discrete volumetric domain parameterization mapping to obtain B-spline volumetric domain parameterizations with low distortion for IGA.This method can generate B-spline volumetric domain parameterizations with low distortion for IGA.The algorithm is tested on a dataset of 215 complex models and the results demonstrate the robustness and effectiveness of the algorithm.Compared to state-of-the-art methods,this method achieves bijective B-spline volumetric domain parameterizations with lower distortion.