Waveform relaxation method for reactor dynamics

Abstract

We investigate the concurrent solution of differential equations by the wave-form relaxation (WR) method, an iterative method for analyzing linear and nonlinear dynamical systems in the time domain. The method, at each iteration, decomposes the system into several dynamical subsystems, each of which is analyzed for the entire given time interval. Such a method, when efficiently implemented, results in algorithms with a highly parallelizable concurrent fraction. It treats the time-dependent problem as a whole and solves for all unknowns simultaneously. In this thesis, the waveform relaxation method is introduced and applied to two types of reactor dynamics problems: one is the point kinetics with six groups of delayed neutron precursors equations, the other is the Korea Multipurpose Research Reactor (KMRR) plant model, which consists of 39 first-order nonlinear dynamics equations. From the results, it is observed that significant speedup can be achieved in reactor dynamics problems, if parallel characteristics of the WR method are used appropriately. It is concluded that the WR method can be applied to reactor dynamics equations and is a good algorithm for implementation on parallel machines.