Multigrid Newton–Krylov method for radiation in diffusive semitransparent media

Abstract

We present a fast multigrid solver for simplified P N ( SP N ) approximations to the diffusive radiation in non-grey semitransparent media. The method consists on reformulating the equations as a nonlinear fixed point problem in the temperature only. Given a mesh hierarchy, time and space discretizations are performed using second-order implicit and finite differencing methods, respectively. At each mesh level, a Newton–Krylov algorithm is applied to the discrete equations. As a smoother on the coarse meshes we propose the Atkinson–Brakhage operator. Numerical results are shown for glass cooling process using different geometry enclosures. The SP N approximations capture the correct asymptotic behavior of the numerical solution with a computational cost lower than using the full radiative transfer equations.