The preconditioned Jacobian-free Newton-Krylov methods for nonequilibrium radiation diffusion equations

In general, it is difficult to use the Newton-Krylov methods to solve the large-scale multi-variable nonequilibrium reaction-diffusion systems. In this paper, by employing two new semi-implicit discretization schemes to construct the preconditioners, the preconditioned Newton-Krylov methods are presented to solve the multidimensional problems. These methods cannot only improve the number of iterations, but also speed up the convergence of solutions. Numerical results are given to illustrate the effectiveness.