Partial Newton-Krylov Iterative Methods for a System of Energy Equations with Three-Temperatures

Abstract

Computer codes containing both hydrodynamic and radiation play a central role in simulating both astrophysical and inertial confinement fusion (ICF) phenomena. A crucial aspect of these codes is that they require an implicit solution of the radiative diffusion equations. In this article we propose a frame of partial Newton-Krylov iterative methods for nonlinear systems derived from implicit solution of 2-D energy equations with three-temperature. First, a partial Newton method is developed to solve the nonlinear system obtained from a nine-point difference scheme. Second, preconditioned Krylov subspace methods are applied to solve the partial Newton correction equation. For comparison, we choose three preconditioners—partial scaling, ILUT, and full scaling plus ILUT—and four Krylov subspace methods—GMRES, FOM, BiCGSTAB, and TFQMR. Numerical results show the efficiency of our method and also show that the scaling preconditioned BiCGSTAB and ILUT preconditioned GMRES are better choices.

This project is supported partly by the Nature Science Foundation of China (10571017), the National Basic Research Program of China (2005CB221300), and the Foundation of National Key Laboratory of Computational Physics.