| Abstract: | To efficiently execute a finite element program on a 2D torus, we need to map nodes of the corresponding finite element graph to processors of a 2D torus such that each processor has approximately the same amount of computational load and the communication among processors is minimized. If nodes of a finite element graph do not increase during the execution of a program, the mapping only needs to be performed once. However, if a finite element graph is solution-adaptive, that is, nodes of a finite element graph increase discretely due to the refinement of some finite elements during the execution of a program, a dynamic load-balancing algorithm has to be performed many times in order to balance the computational load of processors while keeping the communication cost as low as possible. In the paper we propose a parallel dynamic load-balancing algorithm (LB) to deal with the load-imbalancing problem of a solution-adaptive finite element program on a 2D torus. The algorithm uses an iterative approach to achieve load-balancing. We have implemented the proposed algorithm along with two parallel mapping algorithms, parallel orthogonal recursive bisection (ORB) and parallel recursive mincut bipartitioning (MC), on a simulated 2D torus. Three criteria, the execution time of load-balancing algorithms, the computation time of an application program under different load balancing algorithms, and the total execution time of an application program (under several refinement phases) are used for performance evaluation. Simulation results show that (1) the execution of LB is faster than those of MC and ORB; (2) the mappings of LB are better than those of ORB and MC; and (3) the speedups of LB are better than those of ORB and MC. |
