Parallel Hierarchical Tetrahedral-Octahedral Subdivision Mesh Refinement: Performance Modeling, Simulation and Validation

Designing parallel finite element methods is a complex task that can benefit by simulating models of them first. However, such simulations are useful only if they can accurately predict the performance of the parallel system being modeled. We have developed an approach utilizing Petri nets (PN) for modeling and simulating hierarchical tetrahedral-octahedral (HTO) subdivision in parallel 3-D unstructured mesh refinement. A model is implemented based on a detailed software prototype and parallel system architecture parameters, and simulates the behavior of the algorithm. Subsequently, estimates for performance measures are derived from the simulations. The potential benefits of this approach for developing high performance parallel mesh refinement algorithms are validated with MPI benchmark results obtained using McGill University's CLUMEQ Supercomputer Centre facilities