Graph Equilibrium Radiative Transfer
Analytic Solutions and Computational Methods
Contents
This book is currently being written and expanded. New chapters are added regularly as the content is developed and refined. The complete version will be available at radiative-transfer.org upon completion.
The Breakthrough
This book presents an analytical method for solving multiple scattering and absorption-reemission in radiative transfer systems. Given exchange factor data (computed numerically for complex geometries, or analytically for convex transparent enclosures), the method provides exact solutions to the energy redistribution problem through linear system approaches rather than iterative Monte Carlo sampling.
Key advantages include: - Computational efficiency: Orders of magnitude faster than traditional ray tracing, especially for high extinction media - Enhanced accuracy: Eliminates Monte Carlo noise while providing mathematical guarantees - Broad applicability: Works for spectral problems and anisotropic scattering - Validation capability: Serves as a reference standard for verifying other computational methods
This represents a significant advance in computational radiative transfer, moving from purely stochastic methods to hybrid analytical-numerical approaches with proven mathematical properties.
Resources
Book Source Code: Complete source for this book is available at github.com/NikoBiele/graph-equilibrium-radiative-transfer
Julia Package: All methods are implemented in the registered package RayTraceHeatTransfer.jl
Contents
Navigate through the book using the sidebars, or jump directly to any part:
Part I: Introduction and Overview
Part II: Domain and Geometry Setup
Part III: Exchange Factor Transformation
Part IV: Exchange Factor Smoothing
Part VII: Beyond Radiative Transfer
Your journey into analytical radiative transfer starts here.