Analysis of multigrid methods for non-shared memory systems by a simple performance model

Abstract

The system behaviour of parallel processors normally depends in a complex way on many parameters. We investigate the quality of a linear model for the transport in non-shared memory systems by the example of a multigrid method. To this purpose, this method was implemented on the processor kit DIRMU-25 for measuring the required computing time. On the other hand, we have developed a simple abstract process model describing the computational work by one parameter and the transport work by two parameters. The simulation of the abstract model is compared with the implementation at the measuring points. In this way, we obtain information about the quality of the model and the interpretation of the parameters used. The results of this comparison enable us to forecast system performance for large systems by simulation. Though not being optimal for the DIRMU-25 system, the used algorithm is sufficiently complex to illustrate, in particular, the transport characteristics of the system.