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Numerical Methods in Multidimensional Radiative Transfer

Editat de Guido Kanschat, Erik Meinköhn, Rolf Rannacher, Rainer Wehrse
en Limba Engleză Paperback – 3 dec 2008
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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Specificații

ISBN-13: 9783540853688
ISBN-10: 3540853685
Pagini: 320
Ilustrații: VIII, 309 p. 86 illus.
Dimensiuni: 155 x 235 x 17 mm
Greutate: 0.48 kg
Ediția:2009
Editura: Springer Berlin, Heidelberg
Colecția Springer
Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Descriere

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.

Cuprins

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.

Textul de pe ultima copertă

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.


Caracteristici

Includes supplementary material: sn.pub/extras