Evaluation of Gauss Rules with a Centralised Dynamic Load Balancing Technique in Parallel Computing Systems

Abstract

Evaluation of Gauss rules with a centralised dynamic load balancing technique under PVM-based environment in approximating one-dimensional definite integrals on parallel computing systems is described. Gauss rules are normally applied in pairs, so that both an approximation to the integral and an estimate of the error in the approximation can be evaluated together. It is usual to subdivide the range of integration into n subintervals, and these rules are applied separately to each of these subintervals. The aim is to satisfy the accuracy requirement (this is assured if the sum of the estimated absolute errors across the n subintervals is less than absolute accuracy, ∈) whilst keeping the number of evaluations of the integrand to a minimum. The load balancing operation is realised by initialising a centralised pool of task from which a workload (subintervals) to be performed is distributed to the various contending slave processors. Besides, the centralised pool of task technique involved master-slave relationship, where a master processor engaged in interval decomposition into n subintervals. Subsequently, these subintervals are distributed to the slave processors to ensure a workload balanced state is attained. Whenever a slave processor completes its subinterval computation, the partially approximated results are returned to the master. By way of reducing the communication overhead, that would have been associated with the integral evaluation process. The effectiveness of the approach used in connection with the novel workload management scheme is demonstrated in the result obtained and the global workload optimisation for the tested application problems.