The Parallel Solution of Radiation Transport Equations

Linda Stals

Department of Computer Science, Old Dominion University, Norfolk, VA 23529-01, U.S.A. and ICASE, NASA Langley Res. Ctr, Hampton, VA 23681-2199. U.S.A.


Radiation transport equations arise in the study of many different fields, such as combustion, astrophysics and hypersonic flow. The solution of these equations presents interesting challenges due to large jumps in the coefficients and strong non-linearities. In this talk we plan to compare the parallel efficiency of several techniques that may be used to solve these non-linear equations.

Under certain physical assumptions, such as isotropic radiation, optically thick material and temperature equilibrium, radiation transport may be modeled by a system of three non-linear equations. As a first approach we consider the case where all energies are in equilibrium and the system is reduced to a single highly non-linear equation. The radiation may travel through inhomogeneous material, which translates into large jumps in the coefficients. Furthermore, a flux limiter is often included and it changes the equations from being locally parabolic to hyperbolic. As a consequence of all of these features, the equations are very difficult and time consuming to solve.

To be able to solve the types of problems we are interested in we need to look at algorithms that show both parallel scalability and algorithmic scalability, ignoring one of these aspects means that we can not fully exploit available resources and will fall short of our goals. Techniques such as the multigrid method and adaptive finite elements have good algorithmic scalability, we want to measure their parallel scalability in relation to the radiation transport equations. Specifically, we shall focus on the performance of an inexact Newton multigrid scheme and compare it with the Full Approximation Scheme (FAS). Furthermore, we will also look at how the use of adaptive refinement affect the solution time.