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A General-Purpose Finite Element Method for 3D Radiative Transfer Problems

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Numerical Methods in Multidimensional Radiative Transfer

Summary

This paper presents a continuous finite-element method for solving the resonance-line transfer problem in moving media. The algorithm is capable of dealing with three spatial dimensions, using unstructured grids which are adaptively refined by means of an a-posteriori error indicator. Application of the method to coherent isotropic scattering and complete redistribution gives a result of matrix structure which is discussed in the paper. The solution is obtained by way of an iterative procedure, which solves a succession of quasi-monochromatic radiative transfer problems. It is therefore immediately evident that any simulation of the extended frequency-dependent model requires a solution strategy for the elementary monochromatic transfer problem, which is fast as well as accurate. The present implementation is applicable to arbitrary model configurations with optical depths up to 103–104. Additionally, a combination of a discontinuous finite-element method with a superior preconditioning method is presented, which is designed to overcome the extremely poor convergence properties of the linear solver for optically thick and highly scattering media.

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  1. Institute f. Theoret. Astrophysics, University of Heidelberg, Tiergartenstr. 15, D–69121, Heidelberg, Germany

    Erik Meinköhn

  2. Institute of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294/293, D–69120, Heidelberg, Germany

    Erik Meinköhn

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  1. Erik Meinköhn
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Guido Kanschat Erik Meinköhn Rolf Rannacher Rainer Wehrse

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Meinköhn, E. (2009). A General-Purpose Finite Element Method for 3D Radiative Transfer Problems. In: Kanschat, G., Meinköhn, E., Rannacher, R., Wehrse, R. (eds) Numerical Methods in Multidimensional Radiative Transfer. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85369-5_6

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