A Binomial Tree Based Parallel Load-balancing Method for Solution-adaptive Finite Element Graphs on Distributed Memory Multicomputers

In this paper, we propose a binomial tree based parallel load-balancing method (BINOTPLB) to deal with the load imbalance of solution-adaptive finite element application programs on distributed memory multicomputers. The main idea of the BINOTPLB method is first to construct a binomial tree based condensed processor graph. Based on the condensed processor graph, a prefix code tree is built. From the prefix code tree, a schedule for performing load transfer among processors can be determined by concurrently and recursively dividing the prefix code tree into two subtrees and finding a maximum matching for processors in the two subtrees until the leaves are reached. Since each leaf is a binomial tree and a binomial tree can also be divided into two equal halves of binomial trees, the approach used to determine the schedule of a prefix code tree could also be applied to the binomial trees. We have implemented the BINOTPLB method on an SP2 parallel machine and compared its performance with two load-balancing methods, the directed diffusion method and the multilevel diffusion method, and three mapping methods, the JOSTLE-MS method, the MLkP method, and the PARTY library method. Three criteria, the execution time of mapping/load-balancing methods, the execution time of an application program under different mapping/load-balancing methods, and the speedups achieved by mapping/load-balancing methods for an application program, are used for the performance evaluation. The experimental results show that the BINOTPLB method outperforms other methods for most of test samples. *Correspondence addressee † The author is currently with the department of infomation management, The Overseas Chinese Institute of Technology. 188 Journal of the Chinese Institute of Engineers, Vol. 24, No. 2 (2001)