Can a space-time mesh be generated to efficiently solve numerical problems using the discontinuous Galerkin (DG) method? This paper addresses the problem of generating simplicial space-time meshes for solving DG systems. The DG methods are valuable for a wide array of numerical problems. The research focuses on satisfying a cone constraint, where the dihedral angle of each interior mesh face must be less than or equal to a specified angle function. When this constraint is violated, elements must be coupled, increasing computational complexity. An algorithm is presented for generating meshes where the size of element groups needing to be coupled is limited by a constant number k, valid for any nD×TIME domain. The value of 'k' in this algorithm is based on a node degree in an n-dimensional space domain mesh. By developing this mesh generation technique, the study contributes to improved efficiency and applicability of DG methods for solving complex numerical problems in various fields.
Fitting for the International Journal of Foundations of Computer Science, this paper addresses a foundational problem in numerical methods with direct relevance to computer science. The development of an algorithm for mesh generation aligns with the journal's focus on theoretical and practical advancements in computer science foundations.