The solution of the time-dependent discrete-ordinates form of the
Boltzmann
equation arises in wide variety of transport and radiation-hydrodynamic
problems. In this talk I will describe one approach to the numerical
solution of this equation on massively parallel architectures. Instead
of using a more traditional source-iteration method, we employ Krylov
subspace algorithms to solve the full linear system arising
from the implicitly-discretized Boltzmann equation. This approach
offers
numerous advantages and a few drawbacks. The approach is also easily
extensible, via Newton-Krylov methods, to non-linear cases where
radiation-heating or radiation-hydrodynamic effects are included in the
problem. The success of this full linear system method lies in the
development of preconditioners which aid the convergence of the
iterative
Krylov-subspace algorithms. I will discuss some preconditioning
strategies
that are useful for broad classes of problems.
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