Modelling the runtime of scientific programs on parallel computers

Message passing programs for parallel machines with a distributed address space using communication operations of portable communication libraries such as PVM and MPI guarantee portability for most of the parallel machines available. But due to specific implementations of the runtime libraries on each specific platforms, the same program may have different runtimes on different machines, i.e., the efficiency is often not portable. Quantitative results about the runtimes of collective communication operations on specific parallel machines can therefore be helpful. We show that the execution time of collective communication operations can be modelled by runtime functions in closed form. As example, we consider the Cray T3D and T3E machines. We demonstrate that the runtime functions can be used to model the computation and communication behavior of complete programs by investigating the parallel implementation of a solution method for ordinary differential equations. As application, we consider the use of this method for solving a time-dependent reaction-diffusion equation.