A Monte Carlo synthetic-acceleration method for solving the thermal radiation diffusion equation

作者：Evans Thomas M^*; Mosher Scott W; Slattery Stuart R; Hamilton Steven P

来源：Journal of Computational Physics, 2014, 258: 338-358.

DOI：10.1016/j.jcp.2013.10.043

• Radiation diffusion
• Synthetic acceleration
• Monte Carlo
• Sparse matrix systems

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.

• 出版日期2014-2-1