Parallel tetrahedral mesh refinement

Abstract

The Adaptive Mesh Refinement is one of the main techniques used for the solutionof Partial Differential Equations. Since 3-dimensional structures are more complex,there are few refinement methods especially for parallel environments. On the other hand, many algorithms have been proposed for 2-dimensional structures. Weanalyzed the Rivara̕s longest-edge bisection algorithm, studied parallelization techniquesfor the problem, and presented a parallel methodology for the refinement ofnon-uniform tetrahedral meshes. The proposed algorithm is practical for real-life applicationsand it is also scalable for large mesh structures. We describe a usable datastructure for distributed environments and present a utility using the inter-process communication. The PTMR utility is capable of distributing the mesh data amongprocessors and it can accomplish the refinement process within acceptable time limits.