Authors: J. M. Banoczi and C. T. Kelley

A Multilevel Method for Conductive-Radiative Heat Transfer

We present a fast multilevel algorithm for the solution of a system of
nonlinear integro-differential equations that model
steady-state combined radiative-conductive heat transfer. The equations
can be formulated as a compact fixed point problem
with a fixed point map that requires both
a solution of the linear transport equation and the linear heat equation
for its evaluation.  We use fast transport solvers developed by the
second author to construct an efficient evaluation of the fixed point
map and then apply a recent modification of the Atkinson-Brakhage 
method, with Newton-GMRES as the coarse mesh solver,
to the full nonlinear system.