Numerical Methods in Multidimensional Radiative Transfer (eBook)

Guido Kanschat, Erik Meinköhn, Rolf Rannacher, Rainer Wehrse (Herausgeber)

eBook Download: PDF

2008 | 2009
VIII, 309 Seiten
Springer Berlin (Verlag)
978-3-540-85369-5 (ISBN)

Infos

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.

Inhalt

Preface 5
Contents 7
Introduction: The Radiation Field and its Transfer Equation 9
Stochastic Properties of the Radiative Transfer Equation 27
An Approach to Neutrino Radiative Transfer in Supernova Simulations 35
A Finite Element Method for the Even-Parity Radiative Transfer Equation Using the PN Approximation 47
Solution of Radiative Transfer Problems with Finite Elements 57
A General-Purpose Finite Element Method for 3D Radiative Transfer Problems 107
Radiative Transfer in 4D: The Inclusion of Kinematical Information 183
A Problem-Orientable Numerical Algorithm for Modeling Multi- Dimensional Radiative MHD Flows in Astrophysics – the Hierarchical Solution Scenario 193
Rapidly-Converging Methods for Solving Multilevel Transfer Problems 225
Radiative Transfer in NLTE Model Atmospheres 235
The Solution of the Radiative Transfer Equation in Axial Symmetry 245
Multidimensional Radiation Hydrodynamics 255
Probing the Initial Conditions for Star Formation with Monte Carlo Radiative Transfer Simulations 267
Radiative Transfer Through the Intergalactic Medium 279
Radiative Transfer with Finite Elements: Application to the Lya Emission of High-Redshift Galaxies 287
Radiative Transfer Problem in Dusty Galaxies: Ray- Tracing Approach 297
Shape Reconstruction for an Inverse Radiative Transfer Problem Arising in Medical Imaging 307

Produkt-Details

• Erscheint lt. Verlag: 24.12.2008
• Zusatzinfo: VIII, 309 p. 86 illus.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik
• Themenwelt: Technik
• Schlagworte: climatology • Finite Element Method • Model • Modeling • Numerical analysis • Physics • radiation fields • radiative transfer equation • Simulation
• ISBN-10: 3-540-85369-3 / 3540853693
• ISBN-13: 978-3-540-85369-5 / 9783540853695