Theoretical and numerical analysis of a minimal residual solver for 2D Boltzmann transport equation
Journal of Computational and Applied Mathematics
Efficient numerical methods for radiation in gas turbines
Journal of Computational and Applied Mathematics
Partial moment entropy approximation to radiative heat transfer
Journal of Computational Physics
Optimal control in radiative transfer
Optimization Methods & Software
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In this paper we describe a fast multilevel algorithm for the solution of a system of nonlinear integro-differential equations that model steady-state combined conductive-radiative heat transfer in two space dimensions. This extends our previous work in one space dimension. We formulate the equations as a compact fixed point problem with the temperature as the unknown. The fixed point map requires both a Poisson solve and a transport solve for its evaluation. As a solver for both the transport problem and the full system we apply the Atkinson--Brakhage algorithm, using Newton-GMRES as the solver on the coarse mesh. We compare our solver choices with Newton-GMRES. Under modest stability and convergence assumptions on the transport solver, we prove convergence of the multilevel method for the complete system.