The equations of thermal radiation transport consist of a transport equation for the angular radiation intensity coupled with a material temperature equation. The temperature can be eliminated from the transport equation by linearizing the Planck function. This elimination process results in a re-emission source that that is mathematically identical to a fission source
with the absorption cross section playing the role of the fission cross section and the normalized Rosseland function playing the role of the fission spectrum. The resultant transport equation can be iteratively solved in the traditional manner by lagging this source. However, when the radiation-material coupling is strong, the spectral radius for this process can be arbitrarily close to unity. A technique known as the linear multifrequency-grey (LMFG) method is
unconditionally effective for accelerating these source iterations in one-dimensional geometries,but can seriously degrade in multidimensional geometries with severe material inhomogeneities. Because this degradation is due to a relatively small number of eigenvalues, recasting the LMFG method as a preconditioned Krylov technique can be expected to significantly improve performance. We will show that there are two very distinct ways to formulate a LMFGpreconditioned system, discuss the potential advantages and disadvantages of each one, and present preliminary computational results.
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