针对单元尺寸值过渡剧烈会导致有限元网格包含低质量单元的问题，提出基于优化原理的单元尺寸场光滑化理论及对应的几何自适应四面体网格生成算法。首先输入 CAD 模型，生成一套覆盖模型内部的非结构背景网格；然后结合用户参数计算背景网格点上的曲率和邻近特征，以获得自适应CAD模型几何特征的初始单元尺寸场；再以最小化初始单元尺寸场的改变为目标，以单元尺寸值过渡受控为约束，通过求解一类凸优化问题光滑初始尺寸场；最后以光滑后的尺寸场为输入，先后在 CAD 模型表面与内部生成曲面网格和实体网格。实验结果表明，文中算法仅需5个用户参数，即可在给定CAD模型内部全自动生成高质量的四面体网格。%To avoid the generation of low-quality elements in regions where abrupt changes of element sizes are defined, a nonlinear programming problem (NLP) is formulated to help smooth the sizing function de-fined on an unstructured background mesh, and a geometry-based adaptive tetrahedral mesh generation al-gorithm is thus set up with this novel element-sizing smoothing algorithm as one of the key ingredients. The proposed algorithm inputs a valid and closed CAD model and creates an unstructured background mesh to cover the problem domain defined by this CAD model. Then, an initial sizing function can be set up by cal-culating a sizing value at each background mesh node. Note that this size value is adapted to the curvature and proximity features of the CAD model. After that, a convex NLP is solved to smooth this sizing function such that the changes of element scales are under control. By using the smoothed sizing function to control the distributions of element scales, high-quality surface and volume meshes can finally be produced on the surface and interior of the CAD model, respectively. Numerical experiments show that, the proposed algo-rithm can be executed in a fully automatic fashion, and the user could manipulate the results of this algo- rithm through five global user parameters.
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