论文标题
框架框架设计的拓扑
Topology of Frame Field Design for Hex Meshing
论文作者
论文摘要
在过去的十年中，框架字段已成为为CFD和CAE应用生成六面体网格的有希望的方法。一个重要的问题要求在与有效的六面体网格相对应的体积上构建与边界对准的框架场的构建。当固定边界框架场和奇点图时，我们就可以在二进制八面体组中具有变量的单程方程系统的解决方案提供了必要且充分的条件。关于一般$ CW $ - 销售量的一般组成，这可以简化这些系统的灵活性。一路上，我们从代数拓扑的角度来看框架场设计，证明了各种结果，有些已知，有些是新的。
In the past decade frame fields have emerged as a promising approach for generating hexahedral meshes for CFD and CAE applications. One important problem asks for construction of a boundary-aligned frame field with prescribed singularity constraints over a volume that corresponds to a valid hexahedral mesh. We give a necessary and sufficient condition in terms of solutions to a system of monomial equations with variables in the binary octahedral group when a boundary frame field and singularity graph have been fixed. This is phrased with respect to general $CW$-decompositions of the volume, which allows some flexibility in simplifying these systems. Along the way we look at frame field design from an algebraic topological perspective, proving various results, some known, some new.
