Multigrid Newton–Krylov method for radiation in diffusive semitransparent media

We present a fast multigrid solver for simplified PNPN (SPNSPN) 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 SPNSPN approximations capture the correct asymptotic behavior of the numerical solution with a computational cost lower than using the full radiative transfer equations.