Implicit Solution of Radiation-Diffusion Problems Using Newton-Krylov-Multigrid Methods

Carol S. Woodward, Peter Brown, Britton Chang, Frank Graziani and Craig Kapfer

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


Modeling of radiation-diffusion processes has traditionally been accomplished through simulations based on decoupling and linearizing the basic physics equations. By applying these techniques, physicists have simplified their model enough that problems of moderate sizes could be solved. However, new applications demand the simulation of larger problems for which the inaccuracies and nonscalability of current algorithms prevent solution. Recent work in iterative methods has provided computational scientists with new tools for solving these problems.

In this talk, we present an algorithm for the implicit solution of the diffusion approximation coupled to a material temperature equation. This algorithm uses a stiff ODE solver coupled with Newton's method for solving the implicit equations arising at each time step. The Jacobian systems are solved by applying GMRES preconditioned with a semicoarsening multigrid algorithm. By combining the nonlinear Newton iteration with a multigrid preconditioner, we hope to take advantage of the fast, robust nonlinear convergence of Newton's method and the scalability of the linear multigrid method. Numerical results will be shown indicating that the method is accurate. Furthermore, both algorithmic and parallel scalabilities will be explored.

This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract W-7405-Eng-48. UCRL-JC-135152 abs