Surface And Hypersurface Meshing Techniques for Space-Time Finite Element Methods

A novel 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 trajectorytracking 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.& COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

A novel method is introduced for constructing 2D surface meshes in 3D space time and 3D hypersurface meshes in 4D space time. The time-space domain is divided into time slabs, each equipped with an initial plane or hyperplane and an unstructured simplicial surface or hypersurface mesh. The vertices of the terminating plane or hyperplane are obtained from the vertices of the initial plane using a space-time trajectory tracking approach. The validity and flexibility of this method are demonstrated through multiple numerical experiments.