Mapping finite element graphs on hypercubes

Two-way stripe partition mapping and greedy assignment mapping are proposed for mapping finite-element graphs (FEGs) onto hypercubes. They can be used to map both 2-D and 3-D FEGs on hypercubes. Two-way stripe partition mapping is a two-phase mapping approach. In the first phase, two-way stripe partition is used to achieve low communication cost. In the second phase, the load transfer heuristic is used to balance the computational load among processors. Greedy assignment mapping tries to minimize the communication cost and balance the computational load of processors simultaneously. The estimated lower bound speed up and the estimated upper bound speedup are derived for both bidirectional and unidirectional communication, to measure the mapping results. Simulation results show that the speedups for two-way stripe partition mapping are better than those for greedy assignment mapping when the load balance criterion is achieved in both approaches. The greedy approach, however, gives good performance at a much lower cost