Graph Equilibrium Radiative Transfer

Analytic Solutions and Computational Methods

Author

Nikolaj Maack Bielefeld

Published

September 3, 2025

Contents

🚧 Book Under Development

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 V: Anisotropic Extension

Part VI: Spectral Extension

Part VII: Beyond Radiative Transfer


Your journey into analytical radiative transfer starts here.