Parallel Performance of Multilevel Preconditioners for Multi-Material Equilibrium Radiation Diffusion on Adaptively Refined Grids

Bobby Philip

Email: bphilip@lanl.gov
Postal address: MS B256, CCS-3, PO B0x 1663, Los Alamos National Laboratory, Los Alamos, NM 87545

Radiation transport plays an important role in numerous fields of study, including astrophysics, laser fusion, fission reactor core simulations, combustion applications, 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 in serial. The key to this approach has been the use of effective multilevel preconditioners that exploit the hierarchical structure of AMR grids.
 
 A comparison of the performance of two multiplicative and two additive multilevel preconditioners for Jacobian-free Newton-Krylov (JFNK) methods is presented. The preconditioned JFNK method is used to simulate multi-material radiation diffusion on cell-centered dynamic structured adaptive mesh refinement (SAMR) grids. Multiplicative methods visit each level in the AMR hierarchy in a prescribed order, and require communication after treating each refinement level.  On the other hand, additive methods only require communication after all levels have been visited.  The multiplicative preconditioners considered are the Fast Adaptive Composite grid (FAC) method and an algebraic multigrid (AMG) method implemented in the LAMG package. The additive preconditioners in the study are AFACx and multilevel diagonal scaling (MDS). We will compare parallel performance, scalability, robustness, and ease of implementation. Time permitting, a brief overview of the object oriented package SA-MRSolvers, used within our applications will also be presented.