Numerical Methods in Multidimensional Radiative Transfer

By: Guido Kanschat (Editor), Erik MeinkÃ¶hn (Editor), Rolf Rannacher (Editor)

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Paperback | 3 December 2008

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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.

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Non-Fiction Science Physics Thermodynamics & Heat Earth Sciences, Geography, Environment, Planning Earth Sciences Meteorology & Climatology Mathematics Calculus & Mathematical Analysis Numerical Analysis Astronomy, Space & Time Engineering & Technology

Technology in General Engineering in General Computing & I.T.Computer Science Artificial Intelligence

Introduction: The Radiation Field and its Transfer Equation	p. 1
Stochastic Properties of the Radiative Transfer Equation	p. 19
An Approach to Neutrino Radiative Transfer in Supernova Simulations	p. 27
A Finite Element Method for the Even-Parity Radiative Transfer Equation Using the PN Approximation	p. 39
Solution of Radiative Transfer Problems with Finite Elements	p. 49
A General-Purpose Finite Element Method for 3D Radiative Transfer Problems	p. 99
Radiative Transfer in 4D: The Inclusion of Kinematical Information	p. 175
A Problem-Orientable Numerical Algorithm for Modeling Multi-Dimensional Radiative MHD Flows in Astrophysics - the Hierarchical Solution Scenario	p. 185
Rapidly-Converging Methods for Solving Multilevel Transfer Problems	p. 217
Radiative Transfer in NLTE Model Atmospheres	p. 227
The Solution of the Radiative Transfer Equation in Axial Symmetry	p. 237
Multidimensional Radiation Hydrodynamics	p. 247
Probing the Initial Conditions for Star Formation with Monte Carlo Radiative Transfer Simulations	p. 259
Radiative Transfer Through the Intergalactic Medium	p. 271
Radiative Transfer with Finite Elements: Application to the Ly Emission of High-Redshift Galaxies	p. 279
Radiative Transfer Problem in Dusty Galaxies: Ray-Tracing Approach	p. 289
Shape Reconstruction for an Inverse Radiative Transfer Problem Arising in Medical Imaging	p. 299
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Numerical Methods in Multidimensional Radiative Transfer

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