Numerical Methods in Multidimensional Radiative Transfer

1. Front Matter

   Pages i-viii

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2. Introduction: The Radiation Field and its Transfer Equation

   • Guido Kanschat, Erik Meinköhn, Rolf Rannacher, Rainer Wehrse

   Pages 1-18

3. Stochastic Properties of the Radiative Transfer Equation

   • Wilhelm von Waldenfels

   Pages 19-25

4. An Approach to Neutrino Radiative Transfer in Supernova Simulations

   • Christian Y. Cardall

   Pages 27-37

5. A Finite Element Method for the Even-Parity Radiative Transfer Equation Using the P _N Approximation

   • Stephen Wright, Simon Arridge, Martin Schweiger

   Pages 39-48

6. Solution of Radiative Transfer Problems with Finite Elements

   • Guido Kanschat

   Pages 49-98

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

   • Erik Meinköhn

   Pages 99-173

8. Radiative Transfer in 4D: The Inclusion of Kinematical Information

   • Maarten Baes

   Pages 175-184

9. A Problem-Orientable Numerical Algorithm for Modeling Multi-Dimensional Radiative MHD Flows in Astrophysics – the Hierarchical Solution Scenario

   • A. Hujeirat

   Pages 185-215

10. Rapidly-Converging Methods for Solving Multilevel Transfer Problems

    • Eugene H. Avrett

    Pages 217-226

11. Radiative Transfer in NLTE Model Atmospheres

    • Jiří Kubát

    Pages 227-236

12. The Solution of the Radiative Transfer Equation in Axial Symmetry

    • Daniela Korčáková, Jiří Kubát

    Pages 237-246

13. Multidimensional Radiation Hydrodynamics

    • Wolfgang Kalkofen

    Pages 247-257

14. Probing the Initial Conditions for Star Formation with Monte Carlo Radiative Transfer Simulations

    • Dimitris Stamatellos, Anthony P. Whitworth

    Pages 259-270

15. Radiative Transfer Through the Intergalactic Medium

    • Avery Meiksin

    Pages 271-277

16. Radiative Transfer with Finite Elements: Application to the Lyα Emission of High-Redshift Galaxies

    • Sabine Richling

    Pages 279-287

17. Radiative Transfer Problem in Dusty Galaxies: Ray-Tracing Approach

    • Dmitrij Semionov, Vladas Vansevičius

    Pages 289-298

18. Shape Reconstruction for an Inverse Radiative Transfer Problem Arising in Medical Imaging

    • Oliver Dorn

    Pages 299-309

Traditionally, radiative transfer has been the domain of astrophysicists and climatologists. In nuclear technology one has been dealing with the ana- gous equations of neutron transport. In recent years, applications of radiative transferincombustionmachinedesignandinmedicinebecamemoreandmore important. In all these disciplines one uses the radiative transfer equation to model the formation of the radiation ?eld and its propagation. For slabs and spheres e?ective algorithms for the solution of the transfer equation have been ava- able for quite some time. In addition, the analysis of the equation is quite well developed. Unfortunately, in many modern applications the approximation of a 1D geometry is no longer adequate and one has to consider the full 3D dependencies. This makes the modeling immensely more intricate. The main reasons for the di?culties result from the fact that not only the dimension of the geometric space has to be increased but one also has to employ two angle variables (instead of one) and very often one has to consider frequency coupling (due to motion or redistribution in spectral lines). In actual cal- lations this leads to extremely large matrices which, in addition, are usually badly conditioned and therefore require special care. Analytical solutions are not available except for very special cases. Although radiative transfer problems are interesting also from a ma- ematical point of view, mathematicians have largely neglected the transfer equation for a long time.

• Climatology
• Simulation
• finite element method
• model
• modeling
• numerical analysis
• physics
• radiation fields
• radiative transfer equation

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