Numerical Methods in Multidimensional Radiative Transfer

The book provides an overview of the numerical modelling of radiation fields in multidimensional geometries. It covers advances and problems in the mathematical treatment of the radiative transfer equation, a partial integro-differential equation of high dimension that describes the propagation of the radiation in various fields. Highly accurate and fast methods with sound analytical foundations are particularly emphasized. The volume should not only serve as a basis for the selection of suitable methods for actual radiative transfer problems in disciplines from astronomy and climatology to radiological diagnostics but also be a starting point for additional mathematical investigations on many still unknown aspects of the transfer equation. Front Matter....Pages i-viii Introduction: The Radiation Field and its Transfer Equation....Pages 1-18 Stochastic Properties of the Radiative Transfer Equation....Pages 19-25 An Approach to Neutrino Radiative Transfer in Supernova Simulations....Pages 27-37 A Finite Element Method for the Even-Parity Radiative Transfer Equation Using the P N Approximation....Pages 39-48 Solution of Radiative Transfer Problems with Finite Elements....Pages 49-98 A General-Purpose Finite Element Method for 3D Radiative Transfer Problems....Pages 99-173 Radiative Transfer in 4D: The Inclusion of Kinematical Information....Pages 175-184 A Problem-Orientable Numerical Algorithm for Modeling Multi-Dimensional Radiative MHD Flows in Astrophysics – the Hierarchical Solution Scenario....Pages 185-215 Rapidly-Converging Methods for Solving Multilevel Transfer Problems....Pages 217-226 Radiative Transfer in NLTE Model Atmospheres....Pages 227-236 The Solution of the Radiative Transfer Equation in Axial Symmetry....Pages 237-246 Multidimensional Radiation Hydrodynamics....Pages 247-257 Probing the Initial Conditions for Star Formation with Monte Carlo Radiative Transfer Simulations....Pages 259-270 Radiative Transfer Through the Intergalactic Medium....Pages 271-277 Radiative Transfer with Finite Elements: Application to the Ly α Emission of High-Redshift Galaxies....Pages 279-287 Radiative Transfer Problem in Dusty Galaxies: Ray-Tracing Approach....Pages 289-298 Shape Reconstruction for an Inverse Radiative Transfer Problem Arising in Medical Imaging....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. This book provides an overview of the numerical modelling of radiation fields in multidimensional geometries. It covers advances and problems in the mathematical treatment of the radiative transfer equation, a partial integro-differential equation of high dimension that describes the propagation of the radiation in various fields. Highly accurate and fast methods with sound analytical foundations are particularly emphasized. The volume should not only serve as a basis for the selection of suitable methods for actual radiative transfer problems in disciplines from astronomy and climatology to radiological diagnostics but also be a starting point for additional mathematical investigations on many still unknown aspects of the transfer equation