A general method is introduced for constructing two-dimensional (2D) surface meshes embedded in three-dimensional (3D) space time, and 3D hypersurface meshes embedded in four-dimensional (4D) space time. In particular, we begin by dividing the space-time domain into time slabs. Each time slab is equipped with an initial plane (hyperplane), in conjunction with an unstructured simplicial surface (hypersurface) mesh that covers the initial plane. We then obtain the vertices of the terminating plane (hyperplane) of the time slab from the vertices of the initial plane using a space-time trajectory-tracking approach. Next, these vertices are used to create an unstructured simplicial mesh on the terminating plane (hyperplane). Thereafter, the initial and terminating boundary vertices are stitched together to form simplicial meshes on the intermediate surfaces or sides of the time slab. After describing this new mesh-generation method in rigorous detail, we provide the results of multiple numerical experiments which demonstrate its validity and flexibility.

翻译：本文提出了一种通用方法，用于构建嵌入三维（3D）时空中的二维（2D）曲面网格，以及嵌入四维（4D）时空中的三维（3D）超曲面网格。具体而言，我们首先将时空域划分为时间切片。每个时间切片配备一个初始平面（超平面），并附有覆盖该初始平面的非结构化单纯形曲面（超曲面）网格。然后，利用时空轨迹追踪方法，从初始平面的顶点获取时间切片终止平面（超平面）的顶点。接下来，这些顶点被用于在终止平面（超平面）上生成非结构化单纯形网格。此后，将初始与终止边界顶点进行拼接，以在时间切片的中介面或侧面形成单纯形网格。在严格详尽地描述这一新型网格生成方法后，我们提供了多项数值实验的结果，验证了该方法的有效性与灵活性。