Sequential Monte Carlo techniques for the solution of linear systems
Journal of Scientific Computing
A linear-discontinuous spatial differencing scheme for Sn radiative transfer calculations
Journal of Computational Physics
A residual Monte Carlo method for discrete thermal radiative diffusion
Journal of Computational Physics
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Hi-index | 31.45 |
We present a novel synthetic-acceleration-based Monte Carlo method for solving the equilibrium thermal radiation diffusion equation in three spatial dimensions. The algorithm performance is compared against traditional solution techniques using a Marshak benchmark problem and a more complex multiple material problem. Our results show that our Monte Carlo method is an effective solver for sparse matrix systems. For solutions converged to the same tolerance, it performs competitively with deterministic methods including preconditioned conjugate gradient and GMRES. We also discuss various aspects of preconditioning the method and its general applicability to broader classes of problems.