SIMC – Symbolic Implicit Monte Carlo

Time-dependent transport of radiation from resonance lines involving spontaneous emission is used in the study of stellar atmospheres and in laser produced plasmas. The transport equation for photons is coupled to a time-dependent level population equation. This system of equations can prove difficult to solve due to stiffness and the wide range of opacity inherent in an atomic line profile.

Advances have been made in the area of Monte Carlo methods for this problem. Encouraged by the success and robustness of implicit Monte Carlo techniques in local thermodynamic equilibrium, an implicit method was developed for line transport. While Implicit Monte Carlo (IMC) works very well for most cases, it contains an effective scattering term that is inefficient when dealing with optically thick problems and which becomes negative for an atomic line in the gain regime. The Symbolic Implicit Monte Carlo (SIMC) method was born in the notion that you can track and score spontaneously emitted particles with an unknown symbolic weight that is determined at the end of a time step. This removes the source of the ineffiency, the effective scattering term, from the IMC method.

Current work on the difference formulation is showing even greater gains in accuracy in highly opaque media where the temperature does not change greatly. This work is focused on frequency independent, 1-D line transport and frequency dependent, 1-D LTE transport.


Eugene Brooks (lead)
M. Scott McKinley
Abe Szoke
Frank Daffin


Overview of SIMC

F. Daffin, M. S. McKinley, E. D. Brooks, and A. Szoke, “An Evaluation of the Difference Formulation for the Transport of Atomic Lines”, (to be submitted).

E. D. Brooks, M. S. McKinley, F. Daffin, A. Szoke, “Symbolic Implicit Monte Carlo Radiation Transport in the Difference Formulation: A Piecewise Constant Discretization”, Journal of Computational Physics, Volume 189, Issue 1, 20 July 2003, Pages 330-349. (PDF Version)

Szoke A., Brooks E., "The Transport Equation in Optically Thick Media," Submitted to JQRST, UCRL-JC-152828 (June 2003). (PDF version)

McKinley M.S., Brooks E., and Szoke A., “Comparison of Implicit and Symbolic Implicit Monte Carlo Line Transport with Frequency Weight Vector Extension,” J. Comp Phys., Vol 189, No. 1, p. 330-349, UCRL-ID-147898 (July 2003). (HTML, PDF version)

Brooks E., “Symbolic Implicit Monte Carlo,” J. Comp. Phys.,Vol. 83, No. 2, p.433-446, UCRL-97630 (August 1989).  (PDF version)

Brooks E., Fleck J., “Implicit Monte Carlo Scheme For Calculating Time Dependent Line Transport,” J. Comp. Phys., Vol 67, No. 1, UCRL-93349 (November 1986). (PDF version)

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Updated:  August 6, 2004