Energy-Minimized High-Order Surface Meshes
The construction of suitable curvilinear meshes for high-order methods in computational fluid dynamics still remains a challenge. This paper investigates a strictly local construction and optimization method for high-order surface meshes. The optimization procedure combines fitting and minimization of energy functionals related to bending and stretching. The weight of the energy functionals in this combination is gradually reduced during the process by application of blending functions. We apply the method to analytically defined smooth surfaces as well as triangulated scanning data. For both classes of test cases the method improves the mesh quality notably and preserves the accuracy of least-squares fitting. Three different blending functions for the energy weighting have been investigated. Furthermore, we incorporated and tested methods to reduce the additional computational costs of performing the optimization.
The authors gratefully acknowledge the funding of this project by the German Research Foundation (DFG, STI 157/4-1). We thank the Center for Information Services and High Performance Computing (ZIH) at TU Dresden for generous allocations of computer time.
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