A Comparison of Algorithms for the Efficient Solution of the Linear Systems Arising from Multigroup Flux-limited Diffusion Problems
Flux-limited diffusion has become a popular method for treating radiation transport in multidimensional astrophysical simulation codes with multi-group flux-limited diffusion (MGFLD) undergoing increasing use in a number of applications. The most computationally demanding aspect of this technique is the solution of the large linear systems that arise from the implicit finite-difference scheme that is used to solve the underlying integro-PDEs that describe MGFLD. The solution of these linear systems often dominates the computational cost of carrying out astrophysical simulations. Hence, efficient methods for solving these systems are highly desirable. In this paper we examine the numerical efficiency of a number of iterative Krylov subspace methods for the solution of the MGFLD linear systems arising from a series of challenging test problems. The problems we employ were designed to test the capabilities of the linear-system solvers under difficult conditions. The algorithms and preconditioners we examine in this study were selected on the basis that they are relatively easy to parallelize. We find that certain algorithm/preconditioner combinations consistently outperform others for a series of test problems. Additionally, we find that the method of preparing the linear system for solution by scaling the system has a dramatic effect on the convergence behavior of the iterative methods.
Swesty, F. D., Dennis C. Smolarski, S. J., & Saylor, P. E. (2004). A Comparison of Algorithms for the Efficient Solution of the Linear Systems Arising from Multigroup Flux-limited Diffusion Problems. The Astrophysical Journal Supplement Series, 153(1), 369. https://doi.org/10.1086/420785