Statistics – Methodology
Scientific paper
Sep 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999jqsrt..63...15k&link_type=abstract
Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 63, issue 1, pp. 15-29
Statistics
Methodology
11
Radiative Transfer: Numerical Methods
Scientific paper
A new nonlinear solution method is developed and applied to a non-equilibrium radiation diffusion problem. With this new method, Newton-like super-linear convergence is achieved in the nonlinear iteration, without the complexity of forming or inverting the Jacobian from a standard Newton method. The method is a unique combination of an outer Newton-based iteration and an inner conjugate gradient-like (Krylov) iteration. The effects of the Jacobian are probed only through approximate matrix-vector products required in the conjugate gradient-like iteration. The methodology behind the Jacobian-free Newton-Krylov method is given in detail. It is demonstrated that a simple, successive substitution, linearization produces an effective preconditioning matrix for the Krylov method. The efficiencies of different methods are compared and the benefits of converging the nonlinearities within a time step are demonstrated.
Knoll D. A.
Olsen G. L.
Rider W. J.
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