Efficient simultaneous solution of multi-physics multi-scale nonlinear coupled system in HTR reactor based on nonlinear elimination method

•The comparison between nonlinear and linear preconditioning is performed.•It is demonstrated that equivalent convergence rate is achieved in nonlinear and linear preconditioning.•The computational efficiency of linear preconditioning is always higher than that of nonlinear preconditioning.•When JFNK is applied to the engineering code, linear preconditioning has an absolute advantage over nonlinear preconditioning.