A methodology for performance modeling and simulation validation of parallel 3-D finite element mesh refinement with tetrahedra

The design and implementation of parallel finite element methods (FEMs) is a complex and error-prone task that can benefit significantly by simulating models of them first. However, such simulations are useful only if they accurately predict the performance of the parallel system being modeled. The purpose of this contribution is to present a new, practical methodology for validation of a promising modeling and simulation approach for parallel 3-D FEMs. To meet this goal, a parallel 3-D unstructured mesh refinement model is developed and implemented based on a detailed software prototype and parallel system architecture parameters in order to simulate the functionality and runtime behavior of the algorithm. Estimates for key performance measures are derived from these simulations and are validated with benchmark problem computations obtained using the actual parallel system. The results illustrate the potential benefits of the new methodology for designing high performance parallel FEM algorithms. Index Terms--Finite element methods, mesh generation, parallel processing, petri nets.