$d$维空间中单纯形网格的构造与形状optimization
Construction and shape optimization of simplicial meshes in $d$-dimensional space
摘要：
我们提供了一个建设性的证明，一个面对面的简单的分区的d维空间的任意d推广的想法Sommerville，用于创建空间填充四面体的三角形基地，任何尺寸。增加维数的每一步构造都被确定为一个正参数，因此d维单纯划分由d个参数参数化。给出了这些参数的形状最优值。
英文摘要：
We provide a constructive proof of a face-to-face simplical partition of a d-dimensional space for arbitrary d by generalizing the idea of Sommerville, used to create space-filling tetrahedra out of triangular base, to any dimension. Each step of construction that increases the dimension is determined up to a positive parameter, d-dimensional simplical partition is therefore parametrized by d parameters. We show the shape optimal value of those parameters.
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