We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero isocontour of a smooth discrete function. Common examples of this scenario include using level set functions to represent material interfaces in multimaterial configurations, and evolving geometries in shape and topology optimization. The proposed method formulates the mesh optimization problem as a variational minimization of the sum of a chosen mesh-quality metric using the Target-Matrix Optimization Paradigm (TMOP) and a penalty term that weakly forces the selected faces of the mesh to align with the target surface. The distinct features of the method are use of a source mesh to represent the level set function with sufficient accuracy, and adaptive strategies for setting the penalization weight and selecting the faces of the mesh to be fit to the target isocontour of the level set field. We demonstrate that the proposed method is robust for generating boundary- and interface-fitted meshes for curvilinear domains using different element types in 2D and 3D.

翻译：我们提出一种方法，使高阶网格的边界和界面与隐式定义的几何形状重合/对齐。特别关注目标曲面被定义为光滑离散函数的零等值线的情况。常见应用包括：使用水平集函数表示多材料配置中的材料界面，以及形状与拓扑优化中几何体的演化。该方法将网格优化问题表述为变分最小化，其目标函数由目标矩阵优化范式(Target-Matrix Optimization Paradigm, TMOP)选取的网格质量度量与惩罚项之和构成，该惩罚项弱约束网格选定面与目标曲面对齐。该方法的核心特征在于：使用源网格确保水平集函数的足够精度，并采用自适应策略设置惩罚权重以及选择需拟合至水平集场目标等值线的网格面。实验证明，该方法在二维和三维空间中针对不同单元类型的曲线域，能够稳健生成边界与界面拟合网格。