Reduced Precision Diffusion Synthetic Acceleration for S$_N$ Neutron Transport in LLNL's ARDRA using Hypre

Abstract

Fast solution times in production discrete ordinates transport codes often require the use of diffusion synthetic acceleration (DSA). A good implementation of DSA will substantially reduce the number of iterations to converge the transport solution at the cost of solving a diffusion-like linear system at each iteration. Often fewer transport iterations will lead to smaller times to solution. Recent work has shown the promise of reduced precision preconditioning. Time and memory cost can be decreased as long as the reduced precision does not substantially degrade the convergence behavior of the higher precision linear system being solved. In this paper, we discuss the algorithmic implications of accelerating transport iterations in double precision (64 bit) while using a reduced precision (32 bit) DSA solve. We initially implement a stand alone code to investigate any theoretical limitations of reduced precision DSA in slabs. Then we implement reduced precision DSA in ARDRA, Lawrence Livermore National Laboratory's (LLNL) discrete ordinance neutral particle transport code, coupled with {\it hypre}, LLNL's scalable linear solver and multigrid methods library capable of mixed precision linear solves Then we solve various neutron transport problems of interest. We find that in most circumstances, DSA acceleration in reduced precision has little to no impact on the acceleration properties of DSA when used with source iteration in most circumstances. However, as tighter tolerances are required, reduced precision DSA may fail to successfully accelerate the transport solve and increase time to solution.