Naval Postgraduate School
Convergence of inner/outer source iterations with finite termination of the inner iterations
Neta_Convergence.pdf (1.662Mb)Abstract
A two-stage (nested) iteration strategy, in
which the outer iteration is analogous to a block Gauss-Seidel
method and the inner iteration to a Jacobi method for each
of these blocks, often are used in the numerical solution of
discretized approximations to the neutron transport equation.
This paper is concerned with the effect, within a continuous
space model, of errors from finite termination of the inner
iterations upon the overall convergence. The main result
is that convergence occurs, to the solution of the original
problem, in the limit that both the outer iteration index and
the minimum over all outer indices and all groups ("blocks")
jointly become large. Positivity properties (in the sense of
cone preserving) are used extensively.
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