The processor allocation problem is addressed in the context of the parallelization of a finite element modeling program on a processor mesh. A heuristic two-step, graph-based mapping scheme with polynomial-time complexity is developed: 1) initial generation of a graph partition for nearest-neighbor mapping of the finite element graph onto the processor graph, and, 2) a heuristic boundary refinement procedure to incrementally alter the initial partition for improved load balancing among the processors. The effectiveness of the approach is gaged both by estimation using a model with empirically determined parameters, as well as implementation and experimental measurement on a 16 node hypercube parallel computer.