Cost Function for Dynamic Load Balancing of Explicit Parallel CFD Solvers with Variable Time-stepping Strategies

Abstract

Parallel computing has been the main approach for solving large-size computational problems as in computational fluid dynamics, electromagnetics, structural mechanics, computational chemistry, etc. Due to the rapid advance of networking technology and wide availability of workstations in many institutions, networked heterogeneous workstations become attractive for parallel computations. One inherent problem for parallel computing on networked heterogeneous workstations is load balancing. Since parallel processes exchange information periodically, fast processes frequently wait for needed information from slow processes. Therefore, the slowest process among all parallel computation processes dictates the computation time of the whole program execution. The main task of load balancing is to reduce the processing time for the slowest process and to reduce the communication time among processes. It is not very difficult to find a reasonably good optimization algorithm for load balancing. However, the main difficulty for load balancing is how to find an accurate optimization cost function that can predict the program execution time for any given load distribution in a multi-user heterogeneous network environment. In this paper, we describe a practical approach for the derivation of a cost function for load balancing of an explicit parallel CFD solver using variable time-stepping algorithms. In this approach, the relative CPU speeds of computers and networks are measured since they are usually unknown to typical computer users. Then the elapsed program execution time on each processor is derived. Experimental results demonstrate that the proposed cost function is reasonably accurate. This cost function can be used for other parallel computation applications that are based on the domain decomposition approach.