论文标题
边界和接口拟合的高阶网状变形与隐式几何形状
High-Order Mesh Morphing for Boundary and Interface Fitting to Implicit Geometries
论文作者
论文摘要
我们提出了一种将高孔子网格的变形的方法，使它们的边界和接口与隐式定义的几何形状重合/对齐。我们的重点尤其是当规定目标表面为平滑离散函数的零异内膜时。这种情况的常见示例包括使用级别集合功能来表示多材料配置中的材料界面，并以形状和拓扑优化的形状和拓扑形状发展。所提出的方法使用目标矩阵优化范式（TMOP）（TMOP）和一个罚款，将所选网格质量度量的总和的变异最小化和罚款效果弱迫使所选面孔与目标表面保持一致。该方法的独特特征是使用源网格以足够的精度来表示级别集合功能，以及设置惩罚权重的自适应策略，并选择网格的脸部，以适合级别设置字段的目标Isocontour。我们证明了所提出的方法对于使用2D和3D中的不同元素类型生成曲线域的边界和接口拟合网格。
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.
