Construction and shape optimization of simplicial meshes in $d$-dimensional space

TL;DR

This paper presents a constructive method for creating face-to-face simplicial partitions in any dimension, generalizing Sommerville's approach, and identifies optimal shape parameters for these partitions.

Contribution

It generalizes Sommerville's tetrahedral space-filling method to arbitrary dimensions and determines optimal shape parameters for the resulting simplicial meshes.

Findings

Constructive proof of simplicial partitions in any dimension.

Parametrization of partitions by d parameters.

Identification of shape optimal parameters.

Abstract

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.