A Two-Grid Method for Nonlinear Radiation Diffusion

Carol S. Woodward

Lawrence Livermore National Laboratory
P.O. Box 808, L-561
Livermore, CA 94551

Todd S. Coffey
North Carolina State University
Box 8205
Raleigh, NC 27695-8205


Abstract

We present a two-grid method for nonlinear radiation diffusion. This method, which is an extension of the two-grid scheme developed by J. Xu, solves a coupled nonlinear diffusion system on a coarse grid, then projects the solution to the original fine grid where a linearized version of the problem is solved. The main idea is to capture the nonlinearities of the problem on the coarse grid leaving only a linear correction on the fine grid. The algorithm has been incorporated into a three-dimensional fully implicit radiation diffusion simulation code. We employ BDF time integration methods, Newton-Krylov nonlinear solvers, and multigrid preconditioners. Numerical results will be given demonstrating the scheme on some sample three-dimensional test problems.