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Tree-Based Parallel Load-Balancing Methods for Solution-Adaptive Finite Element Graphs on Distributed Memory Multicomputers

To solve the load imbalance problem of a solution-adaptive finite element application program on a distributed memory multicomputer, nodes of a refined finite element graph can be remapped to processors or load of a refined finite element graph can be redistributed based on the current load of each processor. For the former case, remapping can be performed by some fast mapping algorithms. For the latter case, a load-balancing algorithm can be applied to balance the computational load of each processor. In this paper, three tree-based parallel load-balancing methods, the MCSTLB method, the BTLB method, and the CBTLB method, were proposed to deal with the load imbalance problems of solution-adaptive finite element application programs. To evaluate the performance of the proposed methods, we have implemented those methods along with three mapping methods, the AE/ORB method, the AE/MC method, and the MLkP method, on an SP2 parallel machine. Three criteria, the execution time of mapping/load-balancing methods, the execution time of a solution-adaptive finite element application program under different mapping/load-balancing methods, and the speedups achieved by mapping/load-balancing methods for a solution-adaptive finite element application program, are used for the performance evaluation. The experimental results show that 1) if the initial mapping is performed by a mapping method and the same mapping method and load-balancing methods were used in each refinement to balance the load of processors, the execution time of an application program under a load-balancing method is always shorter than that of the mapping method, and 2) the execution time of an application program under the CBTLB method is shorter than that of the BTLB method and the MCSTLB method.