This method greatly reduces the number of message sent and will reduce message start-up overhead. Use of this topology would simplify programming and may be used as advice by the runtime system to effectively map the communication requirements of the application to the interconnection network of the computer. The motivation for seeking a parallel solution for FDL3DI centered on increased performance and examination of larger grids. Therefore, it is important to consider the maximum number of processors which can be used for a grid of a certain size and to consider the maximum possible problem size for a given machine configuration, i.e., the number of processors and the amount of RAM per processor. Scaling the Number of Processors When scaling a fixed-size problem to large numbers of processors, the two major considerations are parallel speedup and parallel efficiency.
Good performance is characterized by high efficiency.
The implications of the above equation are significant for parallel code. Therefore, regardless of the number of processors devoted to this mythical application, the maximum attainable speedup is four. Ultimately, the scalability of FDL3DI will be determined by the relative size of T P with respect to T A . The results are reported in Table 1. Note that for very large grids, the maximum attainable speedup is near twenty.