Parallel Implicit Solvers for Radiation Transport Systems: Highlights

Chromatic contour plot of photon energy in a Marshak wave passing from left to right through a slab of material in the diffusive transport regime, with triangular and circular inhomogeneities. Superimposed triangular elements show the adaptive refinement occuring in the vicinity of material property jumps in this Newton MG code (L. Stals, 1999). To see a movie of the Marshak wave passage, click here.

A full-approximation-scheme multigrid code and a Newton-Krylov-Schwarz code for solving fluid mechanics problems (with a mathematical structure identical to that of multicomponent diffusive radiation transport) have been ported to the ASCI platforms using MPI.

Two of the ASCI machines and one external machine of more than 1000 processors (a 600 MHz T3E) have been benchmarked on one or both these codes with the benchmarking process still on-going, subject to dedicated platform availability. Algorithmic and processor scalability are excellent; however, per processor performance is well below peak (5% to 25% of peak, depending upon machine and code, after careful attention). [ Fixed-size Speedup curve for FAS code on ASCI Red | Fixed-size Speedup curve for FAS code on ASCI Blue | Fixed-size Speedup curve for FAS code on Cray T3E | Comparison of various CPUs on FAS MG code | Fixed-size Performance metrics for NKS code on T3E (pdf slide) | Fixed-size Performance metrics for NKS code on ASCI Red (pdf slide) ]

Inefficiencies in per-processor performance have been quantitatively studied and the results widely publicized, memory bandwidth being the chief limiting factor. New orderings have been proposed and evaluated in a cache-trace simulator for flux-evaluation kernels on unstructured grids which maximize data locality. Peak performance bounds for implicit unstructured solvers

A hierarchy of models for radiation transport problems in the diffusive (optically thick) limit has been developed in conjunction with DOE scientists. Write-up defining graded RT problems (pdf)

Adaptations of our solvers to the particular difficulties of radiation transport problems (coarsening strategies, discretization approximations, time-stepping strategies) have begun to be explored, and results presented at key conferences and discussed with cognizant DOE scientists.