Performance Comparison of Linear System Solvers for CMFD Acceleration on GPU Architectures

nTRACER uses the method of characteristics (MOC) coupled with the coarse mesh finite difference (CMFD) acceleration for solving the transport equation. So far the focus of optimization was on the MOC calculation since the majority of the calculation time is spent on the ray tracing calculation. As the result, we have recently observed a promising result on the feasibility of GPU acceleration of the MOC calculation. Afterwards the optimization of the CMFD acceleration became critical. Therefore, performance of several linear system solvers on GPU under the CMFD framework are studied in this work. ILU preconditioned BiCGSTAB could not solve the small linear systems occurring from the group condensation effectively, resulting in even worse performance than the unpreconditioned version. Nonetheless, preconditioned Krylov methods are still preferred in that it can solve various linear systems with a wide range of numerical properties. The utilization of unpreconditioned BiCGSTAB is discouraged because of its poor convergence behavior. Also, the convergence of stationary methods is only assured when the system is diagonally dominant. However, the diagonal dominance may be broken in the CMFD linear system due to the existence of the correction factors. Therefore, use of highly parallelizable preconditioners, such as the Sparse Approximate Inverse (SPAI) preconditioner, should be investigated.