Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 338-358 |
| Number of pages | 21 |
| Journal | Journal of Computational Physics |
| Volume | 258 |
| DOIs | |
| State | Published - Feb 1 2014 |
Funding
Work for this paper was supported by Oak Ridge National Laboratory , which is managed and operated by UT-Battelle, LLC, for the U.S. Department of Energy under Contract No. DEAC05-00OR22725 . The early part of this work was performed at Los Alamos National Laboratory under U.S. Government contract W-7405-ENG-36 .
| Funders | Funder number |
|---|---|
| U.S. Department of Energy | |
| Oak Ridge National Laboratory |
Keywords
- Monte Carlo
- Radiation diffusion
- Sparse matrix systems
- Synthetic acceleration