The Solution of the Time–Dependent S_N Equations on Parallel Architectures

Abstract

The rapid growth of computing power, in the form of parallel architectures, over the last decade has provided the unprecedented capability for computational scientists and engineers to carry out large scale simulations of radiation transport and radiation-hydrodynamic phenomena. The development of massively parallel architectures on the scale of tens of thousands of processors provides, in principle, the rate of floating point operations needed to carry out multidimensional deterministic transport simulations involving multiple physical timescales. However, this new technological advance presents a tremendous challenge to the transport simulation developer in implementing a method for the parallel solution of the time-dependent discrete-ordinates Boltzmann equation on such platforms. Traditional iterative methods, such as source iteration, that have been developed in many research communities have undesirable features that present obstacles to efficient parallelization. In this paper we present an alternative approach, the full linear system solution via Krylov subspace algorithms, that is more readily amenable to implementation on massively parallel architectures.