Radiation transport plays an important role in numerous fields of study, including astrophysics, laser fusion, and combustion applications such as modeling of coal-fired power generation systems and wildfire spread. A diffusion approximation provides a reasonably accurate description of penetration of radiation from a hot source to a cold medium in materials with short mean free paths. This approximation features a nonlinear conduction coefficient that leads to formation of a sharply defined thermal front, or Marshak wave, in which the solution can vary several orders of magnitude over a very short distance. Resolving these localized features with adaptive mesh refinement (AMR) concentrates computational effort by increasing spatial resolution only locally. Previously we have demonstrated the effectiveness of combining AMR with implicit time integration to solve these highly nonlinear time-dependent problems. The key to this approach has been the use of effective multilevel preconditioners that exploit the hierarchical structure of AMR grids.

Our previous work used the Fast Adaptive Grid (FAC) method which is multiplicative in nature. While extremely robust FAC does impose sequential processing of levels in an AMR hierarchy. The additive variants of FAC, namely AFAC and AFACx, provide the opportunity to overlap communication and computation. However, little is known about their performance as preconditioners for difficult problems. We report on efforts to solve multimaterial equilibrium radiation diffusion problems using structured AMR and the Newton-Krylov method preconditioned by FAC, AFAC,or AFACx. We describe our FAC, AFAC, and AFACx solvers and report on their performance.

This work was performed under the auspices of the U.S. Department of Energy by Los Alamos National Laboratory under contract W-7405-ENG-36. Los Alamos National Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness. LAUR 05-0750.