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:我们建议一种方法,使高orger meshes 变形,使其边界和界面与隐含定义的几何相重叠/对称。我们的重点特别放在目标表面被指定为平滑离散函数的零等相向状态的情况。这种假设情景的常见例子包括使用水平设定函数代表多材料配置中的物质界面,以及形状和地形优化的变化中的地貌变化。拟议方法将网目优化问题表述成一个网目质量衡量标准的总和的变式最小化,使用目标Matrix 优化参数(TMOP)和一个惩罚术语,该术语弱化地迫使选定网格的面部与目标表面保持一致。该方法的不同特征是使用源网目来以足够准确的方式代表设定的星位功能,以及用于设定惩罚权重和选择与目标相适应的网格面的适应战略是水平设定字段的相近度。我们证明,拟议的方法对于使用2和3种不同元素类型Curvial-D域生成边界和界面的网格和界面的网格来说是稳健的。