Abstract
High-order methods are increasingly popular in computational fluid dynamics, but the construction of suitable curvilinear meshes still remains a challenge. This paper presents a strictly local optimization method to construct high-order triangular surface patches of high quality and accuracy. It combines fitting and energy-minimization, in which approximate bending and stretching functionals are minimized by means of an incremental procedure. The method was applied to analytically defined smooth surfaces as well as scattered surface data derived from scanning data. In both cases the optimization yielded considerable improvements in patch quality, while preserving the accuracy of pure least-squares fitting. As intended, the method achieves the greatest benefit with coarse meshes and high polynomial order.
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