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SIAM J. Sci. Comput. 19, pp. 266-279 (14 pages)
A Fast Multilevel Algorithm for the Solution of Nonlinear Systems of Conductive-Radiative Heat Transfer Equations
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Add to FacebookIn this paper we describe and analyze a fast multilevel algorithm for the solution of a system of nonlinear integro-differential equations that model steady-state combined conductive-radiative heat transfer. This system of equations for radiative intensity and temperature can be formulated as a compact fixed point problem in temperature alone with a fixed point map that requires both a solution of the linear transport equation and the linear heat equation for its evaluation. We obtain an efficient evaluation of the fixed point map by coupling a finite element diffusion solver with a fast transport solver developed by the second author. As a solver we apply a modification of the Atkinson--Brakhage method, with Newton--GMRES as the coarse mesh solver, to the full nonlinear system. We compare our discretization/solver pair with Newton--GMRES and the classical Atkinson--Brakhage algorithm.
© 1998 Society for Industrial and Applied Mathematics
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