An efficient parallel iteration algorithm for radiation diffusion equation

Yanzhong Yao

Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics,

P. O. Box 8009, Beijing 100088, China

The radiation hydrodynamic problem is a classic multi-physical and multi-scale problem, which occurs in many applications such as inertial confinement fusion (ICF), strong explosion and astrophysical systems. When we numerically simulate this problem, we usually need to solve the radiation diffusion equations with discontinues or multi-scale coefficients. Owing to the numerical stability, we use the fully implicit computation scheme to discretize these equations, which lead to a large nonlinear algebraic system at each time step. The computational cost of solving this system is very expensive, and so we have to use massive parallel computer in order to get the numerical solution within an acceptable time. However the implicit scheme cannot be implemented directly on parallel computer since there is strong data coupling among the computation meshes, it is very difficult to design the parallel computation method. In this talk, we discuss an efficient parallelization algorithm for the radiation diffusion equation. This algorithm is based on the domain decomposition method, and it integrates the extrapolation technique and the Jacobi style semi-implicit scheme, which present a novel prediction approach for the inner bound values of the sub-domains. This algorithm makes the prediction value of the inner bound more reasonable and gives relatively accurate iterative initial value, which can decrease the number of iterations and improve the parallel computation efficiency remarkably.