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Parallel Tetrahedral Mesh Refinement

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The Adaptive Mesh Refinement is one of the main techniques used for the solution of 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. We analyzed the Rivara's longest-edge bisection algorithm, studied parallelization techniques for the problem, and presented a parallel methodology for the refinement of non-uniform tetrahedral meshes. The proposed algorithm is practical for real-life applications and it is also scalable for large mesh structures. We describe a usable data structure for distributed environments and present a utility using the inter-process communication. The PTMR utility is capable of distributing the mesh data among processors and it can accomplish the refinement process within acceptable time limits.