Numerical Methods in Multidimensional Radiative Transfer [electronic resource] / edited by Guido Kanschat, Erik Meinköhn, Rolf Rannacher, Rainer Wehrse.

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

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.