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Line Formation in Multi-Dimensional Media

Published online by Cambridge University Press:  08 February 2017

H. P. Jones  and
A. Skumanich
H. P. Jones
Affiliation:
High Altitude Observatory and University of Colorado, Boulder, Colorado
A. Skumanich
Affiliation:
High Altitude Observatory and University of Colorado, Boulder, Colorado

Abstract

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The flux divergence technique of Athay and Skumanich (1967) is generalized for application to media whose properties vary in more than one spatial dimension. In this method, the flux divergence is viewed as an integro-differential functional of the source function. The source function is then expanded in terms of basis functions along characteristic paths, and, with the help of various interpolations, the flux divergence is converted to an approximate linear algebraic operator on a discrete spatial grid. A large but finite set of linear, inhomogeneous, simultaneous algebraic equations with known matrix coefficients is thus generated and is solved by direct matrix inversion for the source function at each point of the spatial grid.

Some aspects of the accuracy, stability, and computational convenience of the technique are discussed. Sample solutions for depth dependent, axially symmetric variations of temperature are shown.

Keywords

radiative transfer in inhomogeneous mediline formation in multi-dimensional medinumerical methods in transfematrix methods for integro-differential operators
Type
Part B. Theoretical Methods for Handling Non-LTE Problems
Information
International Astronomical Union Colloquium , Volume 2: Spectrum Formation in Stars With Steady-State Extended Atmospheres , August 1970 , pp. 138 - 170
Copyright
Copyright © 1970

References

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