Parallel iterative difference schemes based on prediction techniques for transport method

Abstract

Particle transport calculations are inherently expensive because of the large variable space that must be discretized, and usually the fully implicit schemes in time discretization are used. There exist some bottleneck problems in implementing the Sn transport method on massively parallel computers, such as strong correlation of data and algorithmic consecutiveness. In this paper the spatial domain decomposition procedures are studied for numerically solving the discrete ordinates Sn transport equations. We introduce a parallel solution strategy for transport calculations,which combines the source iterative methods with a technique based on the prediction-correction on the interface of sub-domains. Moreover the two choices of initial values of the source iterative methods are proposed and compared. Numerical experiments show the parallel iterative schemes with interface prediction-correction are unconditionally stable, and have the same accuracy as the original implicit schemes. Moreover, they have fairly high parallelism, and high efficiency due to the construction of our parallel scheme and the good choice of the initial guess of source iteration.