Smooth Analysis-Suitable Parameterization Based on a Weighted and Modified Liao Functional. (November 2021) - Wang, Xu; Ma, Weiyin
Abstract: Analysis-suitable parameterization is a fundamental problem in IGA (IsoGeometric Analysis) implementation which significantly influences computational accuracy and efficiency. This paper proposes a variational framework to address the problem of producing a smooth parameterization of a computational domain represented in B-spline form. In order to control both angle and area distortions, a weighted and modified Liao functional is constructed. The weighting function is a modification of the Gaussian function used to penalize area distortion while a modified Liao functional is used to minimize the angle distortion. A Jacobian regularization scheme is adopted so that invalid initial solutions are acceptable and untangling of folding parameterization is made possible. An L-BFGS algorithm is applied to solve this unconstrained optimization problem. Experimental results show that the proposed objective functional could effectively untangle folding parameterization and further produce better results with lower area and angle distortions compared with other functionals and state-of-the-art parameterization techniques. Graphical abstract: Highlights: Present an unconstrained optimization for smooth analysis-suitable parameterization. The weighted and modified Liao functional minimizes angle and area distortions. An L-BFGS algorithm is applied to solve this unconstrained optimization problem. A Jacobian regularization is used to avoid the need of a non-folding initial solution. The optimization produces smooth parameterization suitable for isogeometric analysis.