Analysis and design of parallel 3-D mesh refinement dynamic load balancing algorithms for finite element electromagnetics with tetrahedra

We develop a simulation-based approach for the computational analysis and design of dynamic load balancing algorithms in parallel three-dimensional unstructured mesh refinement with tetrahedra. A Petri Nets model is implemented based on a random polling algorithm and the target multiprocessor architecture, which simulates the behavior of the parallel mesh refinement. Subsequently, estimates for performance measures are derived from discrete event simulations. The benefits of this new approach for developing high-performance parallel mesh refinement algorithms are demonstrated with results for an example geometric mesh refinement model. Index Terms--Adaptive systems, electromagnetic analysis, finite element method (FEM), parallel processing, software methodology.